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Case Solutions Corporate Finance Ross, Westerfield, Jaffe, and Jordan 11th edition 10/20/2015 Prepared by: Brad Jordan University of Kentucky Joe Smolira Belmont University

C­2  CASE SOLUTIONS

CHAPTER 31 CASE  C­3  

CHAPTER 2 CASH FLOWS AT WARF COMPUTERS The operating cash flow for the company is: (NOTE: All numbers are in thousands of dollars) OCF = EBIT + Depreciation – Current taxes OCF = $2,080 + 248 – 605 OCF = $1,723 To calculate the cash flow from assets, we need to find the capital spending and change in net working capital. The capital spending for the year was: Capital spending Ending net fixed assets – Beginning net fixed assets + Depreciation Net capital spending

$3,601 2,796 248 $1,053

And the change in net working capital was: Change in net working capital Ending NWC – Beginning NWC Change in NWC

$1,135 914 $221

So, the cash flow from assets was: Cash flow from assets Operating cash flow – Net capital spending – Change in NWC Cash flow from assets

$1,723 1,053 221 $449

The cash flow to creditors was: Cash flow to creditors Interest paid – Net New Borrowing Cash flow to Creditors

$137 31 $106

The cash flow to stockholders was: Cash flow to stockholders Dividends paid – Net new equity raised Cash flow to Stockholders

$292 – (–51) $343

The accounting cash flow statement of cash flows for the year was: Statement of Cash Flows Operations Net income Depreciation Deferred taxes Changes in assets and liabilities Accounts receivable Inventories Accounts payable Accrued expenses Other Total cash flow from operations

$1,167 248 171 (48) 22 34 (154) (14) $1,426

Investing activities Acquisition of fixed assets Sale of fixed assets Total cash flow from investing activities

$(1,482) 429 $(1,053)

Financing activities Retirement of debt Proceeds of long-term debt Dividends Repurchase of stock Proceeds from new stock issues Total cash flow from financing activities

$(197) 228 (292) (66) 15 $(312)

Change in cash (on balance sheet)

$61

CHAPTER 31 CASE  C­5   Answers to questions 1. The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow from operations and a positive cash flow from assets. The firm invested $221 in new net working capital and $1,053 in new fixed assets. The firm was able to return $343 to its stockholders and $106 to creditors. 2. The financial cash flows present a more accurate picture of the company since it accurately reflects interest cash flows as a financing decision rather than an operating decision. 3. The expansion plans look like they are probably a good idea. The company was able to return a significant amount of cash to its shareholders during the year, but a better use of these cash flows may have been to retain them for the expansion. This decision will be discussed in more detail later in the book.

CHAPTER 3 RATIOS AND FINANCIAL PLANNING AT EAST COAST YACHTS 1.

The calculations for the ratios listed are: Current ratio = $15,823,700 / $21,320,300 Current ratio = .74 times Quick ratio = ($15,823,700 – 6,627,300) / $21,320,300 Quick ratio = .43 times Total asset turnover = $210,900,000 / $117,304,900 Total asset turnover = 1.80 times Inventory turnover = $148,600,000 / $6,627,300 Inventory turnover = 22.42 times Receivables turnover = $210,900,000 / $5,910,800 Receivables turnover = 35.68 times Total debt ratio = ($117,304,900 – 59,584,600) / $117,304,900 Total debt ratio = .49 times Debt–equity ratio = ($21,320,300 + 36,400,000) / $59,584,600 Debt–equity ratio = .97 times Equity multiplier = $117,304,900 / $59,584,600

Equity multiplier = 1.97 times Interest coverage = $30,229,000 / $3,791,000 Interest coverage = 7.97 times Profit margin = $15,862,800 / $210,900,000 Profit margin = .0752, or 7.52% Return on assets = $15,862,800 / $117,304,900 Return on assets = .1352, or 13.52% Return on equity = $15,862,800 / $59,584,600 Return on equity = .2662, or 26.62%

CHAPTER 31 CASE  C­7   2.

Regarding the liquidity ratios, East Coast Yachts current ratio is below the median industry ratio. This implies the company has less liquidity than the industry in general. However, the current ratio is above the lower quartile, so there are companies in the industry with lower liquidity than East Coast Yachts. The company may have more predictable cash flows, or more access to short-term borrowing. The turnover ratios are all higher than the industry median; in fact, all three turnover ratios are above the upper quartile. This may mean that East Coast Yachts is more efficient than the industry in using its assets to generate sales. The financial leverage ratios are all below the industry median, but above the lower quartile. East Coast Yachts generally has less debt than comparable companies, but is still within the normal range. The profit margin for the company is about the same as the industry median, the ROA is slightly higher than the industry median, and the ROE is well above the industry median. East Coast Yachts seems to be performing well in the profitability area. Overall, East Coast Yachts’ performance seems good, although the liquidity ratios indicate that a closer look may be needed in this area.

Below is a list of possible reasons it may be good or bad that each ratio is higher or lower than the industry. Note that the list is not exhaustive, but merely one possible explanation for each ratio. Ratio Current ratio Quick ratio Total asset turnover Inventory turnover Receivables turnover

Good Better at managing current accounts. Better at managing current accounts. Better at utilizing assets. Better at inventory management, possibly due to better procedures. Better at collecting receivables.

Total debt ratio

Less debt than industry median means the company is less likely to experience credit problems.

Debt-equity ratio

Less debt than industry median means the company is less likely to experience credit problems.

Equity multiplier

Less debt than industry median means the company is less likely to experience credit problems.

Interest coverage

Less debt than industry median means the company is less likely to experience credit problems.

Profit margin

The PM is slightly above the industry median, so it is performing better than many peers. Company is performing above many of its peers. Company is performing above many of its peers.

ROA ROE

Bad May be having liquidity problems. May be having liquidity problems. Assets may be older and depreciated, requiring extensive investment soon. Could be experiencing inventory shortages. May have credit terms that are too strict. Decreasing receivables turnover may increase sales. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE. Increasing the amount of debt can increase shareholder returns. Especially notice that it will increase ROE. May be able to better control costs. Assets may be old and depreciated relative to industry. Profit margin and EM could still be increased, which would further increase ROE.

If you created an Inventory / Current liabilities ratio, East Coast Yachts would have a ratio that is lower than the industry median. The current ratio is below the industry median, while the quick ratio is above the industry median. This implies that East Coast Yachts has less inventory to current liabilities than the industry median. Because the cash ratio is lower than the industry median, East Coast Yachts has less inventory than the industry median, but more accounts receivable.

CHAPTER 31 CASE  C­9   3.

To calculate the internal growth rate, we first need to find the ROE and the retention ratio, so: ROE = Net income / Total equity ROE = $15,862,800 / $59,584,600 ROE = .2662, or 26.62% b = Addition to RE / Net income b = $11,103,499 / $15,862,800 b = .70, or 70% So, the sustainable growth rate is: Sustainable growth rate = (ROE × b) / [1 – (ROE × b)] Sustainable growth rate = [.2662(.70)] / [1 – .2662(.70)] Sustainable growth rate = .2290, or 22.90% The sustainable growth rate is the growth rate the company can achieve with no external financing while maintaining a constant debt–equity ratio. At the sustainable growth rate, the pro forma statements next year will be: Income statement Sales COGS Other expenses Depreciation EBIT Interest Taxable income Taxes (40%) Net income Dividends Add to RE

$259,201,872 182,633,467 30,961,657 6,879,000 $38,727,748 3,791,000 $34,936,748 13,974,699 $20,962,049 $6,289,224 14,672,825

Balance sheet Assets Current Assets Cash Accounts rec. Inventory Total CA

$4,038,092 7,264,535 8,145,133 $19,447,760

Liabilities & Equity Current Liabilities Accounts Payable $8,575,784 Notes Payable 17,627,448 Total CL $26,203,232 Long-term debt

$36,400,000

$5,580,000 68,677,425 $74,257,425

Fixed assets Net PP&E

$124,723,172

Shareholder Equity Common stock Retained earnings Total Equity

Total Assets

$144,170,933

Total L&E

So, the EFN is: EFN = Total assets – Total liabilities and equity EFN = $144,170,933 – 136,860,657 EFN = $7,310,276 The ratios with these pro forma statements are: Current ratio = $19,447,760 / $26,203,232 Current ratio = .74 times Quick ratio = ($19,447,760 – 8,145,133) / $26,203,232 Quick ratio = .43 times Total asset turnover = $259,201,872 / $144,170,933 Total asset turnover = 1.80 times Inventory turnover = $182,633,467 / $8,145,133 Inventory turnover = 22.42 times Receivables turnover = $259,201,872 / $7,264,535 Receivables turnover = 35.68 times Total debt ratio = ($144,170,933 – 74,257,425) / $144,170,933 Total debt ratio = .48 times Debt–equity ratio = ($26,203,232 + 36,400,000) / $74,257,425 Debt–equity ratio = .84 times

$136,860,657

CHAPTER 31 CASE  C­11   Equity multiplier = $144,170,933 / $74,257,425 Equity multiplier = 1.94 times Interest coverage = $38,727,748 / $3,791,000 Interest coverage = 10.22 times Profit margin = $20,962,049 / $259,201,872 Profit margin = .0809, or 8.09% Return on assets = $20,962,049 / $144,170,933 Return on assets = .1454, or 14.54% Return on equity = $20,962,049 / $74,257,425 Return on equity = .2823, or 28.23% The only ratios that changed are the debt ratio, the interest coverage ratio, profit margin, return on assets, and return on equity. The debt ratio changes because long-term debt is assumed to remain fixed in the pro forma statements. The other ratios change slightly because interest and depreciation are also assumed to remain constant as well. 4.

Pro forma financial statements for next year at a 20 percent growth rate are: Income statement Sales COGS Other expenses Depreciation EBIT Interest Taxable income Taxes (40%) Net income Dividends Add to RE

$253,080,000 178,320,000 30,230,400 6,879,000 $37,650,600 3,791,000 $33,859,600 13,543,840 $20,315,760 $6,095,318 14,220,442

Balance sheet Assets Current Assets Cash Accounts rec. Inventory Total CA

$3,942,720 7,092,960 7,952,760 $18,988,440

Liabilities & Equity Current Liabilities Accounts Payable $8,373,240 Notes Payable 17,211,120 Total CL $25,584,360 Long-term debt

$36,400,000

$5,580,000 68,225,042 $73,805,042

Fixed assets Net PP&E

$121,777,440

Shareholder Equity Common stock Retained earnings Total Equity

Total Assets

$140,765,880

Total L&E

$135,789,402

So, the EFN is: EFN = Total assets – Total liabilities and equity EFN = $140,765,880 – 135,789,402 EFN = $4,976,478 5.

Now we are assuming the company can only build in amounts of $25 million. We will assume that the company will go ahead with the fixed asset acquisition. In this case, the pro forma financial statement calculation will change slightly. To estimate the new depreciation charge, we will find the current depreciation as a percentage of fixed assets, then apply this percentage to the new fixed assets. The depreciation as a percentage of assets this year was: Depreciation percentage = $6,879,000 / $101,481,200 Depreciation percentage = .0678, or 6.78% The new level of fixed assets with the $25 million purchase will be: New fixed assets = $101,481,200 + 25,000,000 = $126,481,200 So, the pro forma depreciation as a percentage of sales will be: Pro forma depreciation = .0678($126,481,200) Pro forma depreciation = $8,573,649

CHAPTER 31 CASE  C­13   We will use this amount in the pro forma income statement. So, the pro forma income statement will be: Income statement Sales COGS Other expenses Depreciation EBIT Interest Taxable income Taxes (40%) Net income

$253,080,000 178,320,000 30,230,400 8,573,649 $35,955,951 3,791,000 $32,164,951 12,865,980 $19,298,971

Dividends Add to RE

$5,790,252 13,508,719

The pro forma balance sheet will remain the same except for the fixed asset and equity accounts. The fixed asset account will increase by $25 million, rather than the growth rate of sales. Balance sheet Assets Current Assets Cash Accounts rec. Inventory Total CA

$3,942,720 7,092,960 7,952,760 $18,988,440

Liabilities & Equity Current Liabilities Accounts Payable $8,373,240 Notes Payable 17,211,120 Total CL $25,584,360 Long-term debt

$36,400,000

$5,580,000 67,513,319 $73,093,319

Fixed assets Net PP&E

$126,481,200

Shareholder Equity Common stock Retained earnings Total Equity

Total Assets

$145,469,640

Total L&E

$135,077,679

So, the EFN is: EFN = Total assets – Total liabilities and equity EFN = $145,469,640 – 135,077,679 EFN = $10,391,961 Since the fixed assets have increased at a faster percentage than sales, the capacity utilization for next year will decrease.

CHAPTER 4 THE MBA DECISION 1.

Age is obviously an important factor. The younger an individual is, the more time there is for the (hopefully) increased salary to offset the cost of the decision to return to school for an MBA. The cost includes both the explicit costs such as tuition, as well as the opportunity cost of the lost salary.

2.

Perhaps the most important nonquantifiable factors would be whether or not he is married and if he has any children. With a spouse and/or children, he may be less inclined to return for an MBA since his family may be less amenable to the time and money constraints imposed by classes. Other factors would include his willingness and desire to pursue an MBA, job satisfaction, and how important the prestige of a job is to him, regardless of the salary.

3.

He has three choices: remain at his current job, pursue a Wilton MBA, or pursue a Mt. Perry MBA. In this analysis, room and board costs are irrelevant since presumably they will be the same whether he attends college or keeps his current job. We need to find the aftertax value of each, so: Remain at current job: Aftertax salary = $65,000(1 – .26) Aftertax salary = $48,100 His salary will grow at 3 percent per year, so the present value of his aftertax salary is: PV = C {[1 / (r – g)] – [1 / (r – g)] × [(1 + g) / (1 + r)]t} PV = $48,100{[1 / (.063 – .03)] – [1 / (.063 – .03)] × [(1 + .03) / (1 + .063)] 40} PV = $1,044,728.37 Wilton MBA: Costs: The direct costs will occur today and in one year, and include tuition, books and supplies, health insurance, and the room and board increase. So the total direct costs are: PV of direct expenses = ($70,000 + 3,000 + 3,000 + 2,000) + ($70,000 + 3,000 + 3,000 + 2,000) / 1.063 PV of direct expenses = $151,377.23

CHAPTER 31 CASE  C­15   The financial benefits are the bonus to be paid in 2 years and the future salary. PV of aftertax bonus paid in 2 years = $20,000(1 – .31) / 1.0632 PV of aftertax bonus paid in 2 years = $12,212.72 Aftertax salary = $110,000(1 – .31) Aftertax salary = $75,900 His salary will grow at 4 percent per year. We must also remember that he will now only work for 38 years, so the present value of his aftertax salary is: PV = C {[1 / (r – g)] – [1 / (r – g)] × [(1 + g) / (1 + r)]t} PV = $75,900{[1 / (.063 – .04)] – [1 / (.063 – .04)] × [(1 + .04) / (1 + .063)] 38} PV = $1,862,801.41 Since the first salary payment will be received three years from today, so we need to discount this for two years to find the value today, which will be: PV = $1,862,801.41 / 1.0632 PV = $1,648,542.05 So, the total value of a Wilton MBA is: Value = –$151,377.23 + 12,212.72 + 1,648,542.05 Value = $1,509,377.54 Mount Perry MBA: The direct costs will occur today and include tuition, books and supplies, health insurance, and the room and board increase. So the total direct costs are: Total direct costs = $85,000 + 4,500 + 3,000 + 2,000 Total direct costs = $94,500 Note, this is also the PV of the direct costs since they are all paid today. The financial benefits are the bonus to be paid in 1 year and the future salary. PV of aftertax bonus paid in 1 year = $18,000(1 – .29) / 1.063 PV of aftertax bonus paid in 1 year = $12,022.58 His aftertax salary at his new job will be: Aftertax salary = $92,000(1 – .29) Aftertax salary = $65,320

His salary will grow at 3.5 percent per year. We must also remember that he will now only work for 39 years, so the present value of his aftertax salary is: PV = C {[1 / (r – g)] – [1 / (r – g)] × [(1 + g) / (1 + r)]t} PV = $65,320{[1 / (.063 – .035)] – [1 / (.063 – .035)] × [(1 + .035) / (1 + .063)] 39} PV = $1,509,165.86 Since the first salary payment will be received two years from today, we need to discount this for one year to find the value today, which will be: PV = $1,509,165.86 / 1.063 PV = $1,419,723.29 So, the total value of a Mount Perry MBA is: Value = –$94,500 + 12,022.58 + 1,419,723.29 Value = $1,337,245.87 4.

He is somewhat correct. Calculating the future value of each decision will result in the option with the highest present value having the highest future value. Thus, a future value analysis will result in the same decision. However, his statement that a future value analysis is the correct method is wrong since a present value analysis will give the correct answer as well.

5.

To find the salary offer he would need to make the Wilton MBA as financially attractive as the as the current job, we need to take the PV of his current job, add the costs of attending Wilton, and the PV of the bonus on an aftertax basis. Note, this assumes that the singing bonus is constant. So, the necessary PV to make the Wilton MBA the same as his current job will be: PV = $1,044,728.37 + 151,377.23 – 12,212.72 PV = $1,183,892.88 This PV will make his current job exactly equal to the Wilton MBA on a financial basis. Since the salary will not start for 3 years, we need to find the value in 2 years so that it is the present value of growing annuity. So: Value in 2 years = $1,183,892.88(1.0652) Value in 2 years = $1,337,762.25 Since his salary will still be a growing annuity, the aftertax salary needed is: PV = C {[1 / (r – g)] – [1 / (r – g)] × [(1 + g) / (1 + r)]t} $1,337,762.25 = C {[1 / (.063 – .04)] – [1 / (.063 – .04)] × [(1 + .04) / (1 + .063)] 38} C = $54,507.24 This is the aftertax salary. So, the pretax salary must be: Pretax salary = $54,507.24 / (1 – .31) Pretax salary = $78,995.99

CHAPTER 31 CASE  C­17   6.

The cost (interest rate) of the decision depends on the riskiness of the use of the funds, not the source of the funds. Therefore, whether he can pay cash or must borrow is irrelevant. This is an important concept which will be discussed further in capital budgeting and the cost of capital in later chapters.

CHAPTER 5 BULLOCK GOLD MINING 1.

An example spreadsheet is:

CHAPTER 31 CASE  C­19   2.

Since the NPV of the mine is positive, the company should open the mine. We should note, it may be advantageous to delay the mine opening because of real options, a topic covered in more detail in a later chapter.

3.

There are many possible variations on the VBA code to calculate the payback period. Below is a VBA program from http://www.vbaexpress.com/kb/getarticle.php?kb_id=252. Function PAYBACK(invest, finflow) Dim x As Double, v As Double Dim c As Integer, i As Integer x = Abs(invest) i=1 c = finflow.Count Do x=x-v v = finflow.Cells(i).Value If x = v Then PAYBACK = i Exit Function ElseIf x < v Then P=i-1 Z=x/v PAYBACK = P + Z Exit Function End If i=i+1 Loop Until i > c PAYBACK = "no payback" End Function

CHAPTER 6, Case #1 BETHESDA MINING To analyze this project, we must calculate the incremental cash flows generated by the project. Since net working capital is built up ahead of sales, the initial cash flow depends in part on this cash outflow. So, we will begin by calculating sales. Each year, the company will sell 500,000 tons under contract, and the rest on the spot market. The total sales revenue is the price per ton under contract times 500,000 tons, plus the spot market sales times the spot market price. The sales per year will be:

Contract Spot Total

Year 1 $43,000,000 9,240,000 $52,240,000

Year 2 $43,000,000 13,860,000 $56,860,000

Year 3 $43,000,000 17,710,000 $60,710,000

Year 4 $43,000,000 6,930,000 $49,930,000

The current aftertax value of the land is an opportunity cost. The initial outlay for net working capital is the required net working capital percentage times Year 1 sales, or: Initial net working capital = .05($52,240,000) = $2,612,000 So, the cash flow today is: Equipment Land NWC Total

–$95,000,000 –6,500,000 –2,612,000 –$104,112,000

Now we can calculate the OCF each year. The OCF is:

Sales VC FC Dep. EBT Tax NI + Dep. OCF

Year 1 $52,240,00 0 19,220,000 4,100,000 13,575,500 $15,344,50 0 5,830,910 $9,513,590 13,575,500 $23,089,09 0

Year 2 Year 3 $56,860,00 0 $60,710,000 21,080,000 22,630,000 4,100,000 4,100,000 23,265,500 16,615,500 $8,414,500 $17,364,500 3,197,510 6,598,510 $5,216,990 $10,765,990 23,265,500 16,615,500 $28,482,49 0 $27,381,490

Year 4 $49,930,00 0 18,290,000 4,100,000 11,865,500 $15,674,50 0 5,956,310 $9,718,190 11,865,500 $21,583,69 0

Year 5

Year 6

$2,700,000

–$2,700,000 –1,026,000 –$1,674,000 0

–2,280,000 $2,280,000 0

–$1,674,000

$2,280,000

CHAPTER 31 CASE  C­21   Years 5 and 6 are of particular interest. Year 5 has an expense of $2.7 million to reclaim the land, and it is the only expense for the year. Taxes that year are a credit, an assumption given in the case. In Year 6, the charitable donation is irrelevant in itself since it is required for the company to donate the land in order to receive the necessary permits. However, the donation of the land does mean that the company will receive a tax credit on the donation of the land, so this tax credit is relevant. Next, we need to calculate the net working capital cash flow each year. NWC is 5 percent of next year’s sales, so the NWC requirement each year is:

Beg. NWC End NWC NWC CF

Year 1 $2,612,000 2,843,000 –$231,000

Year 2 $2,843,000 3,035,500 –$192,500

Year 3 $3,035,500 2,496,500 $539,000

Year 4 $2,496,500 $2,496,500

The last cash flow we need to account for is the salvage value. The fact that the company is keeping the equipment for another project is irrelevant. The aftertax salvage value of the equipment should be used as the cost of equipment for the new project. In other words, the equipment could be sold after this project. Keeping the equipment is an opportunity cost associated with that project. The book value of the equipment is the original cost, minus the accumulated depreciation, or: Book value of equipment = $95,000,000 – 13,575,500 – 23,265,500 – 16,615,500 – 11,865,500 Book value of equipment = $29,678,000 Since the market value of the equipment is $57 million, the equipment is sold at a gain to book value, so the sale will incur the taxes of: Taxes on sale of equipment = ($29,678,000 – 57,000,000)(.38) Taxes on sale of equipment = –$10,382,360 And the aftertax salvage value of the equipment is: Aftertax salvage value = $57,000,000 – 10,382,360 Aftertax salvage value = $46,671,640

So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax salvage value, are: Time 0 1 2 3 4 5 6

Cash flow –$104,112,000 22,858,090 28,289,990 27,920,490 70,697,830 –1,674,000 2,280,000

So, the capital budgeting analysis for the project is: Payback period = 3 + $25,043,430 / $70,697,830 Payback period = 3.35 years PI = ($22,858,090 / 1.12 + $28,289,990 / 1.122 + $27,920,490 / 1.123 + $70,697,830 / 1.124 – $1,674,000 / 1.125 + $2,280,000 / 1.126) / $104,112,000 Profitability index = 1.0371 The NPV is: NPV = –$104,112,000 + $22,858,090 / 1.12 + $28,289,990 / 1.122 + $27,920,490 / 1.123 + $70,697,830 / 1.124 – $1,674,000 / 1.125 + $2,280,000 / 1.126 NPV = $3,857,864.51 The equation for IRR is: 0 = –$104,112,000 + $22,858,090 / (1 + IRR) + $28,289,990 / (1 + IRR)2 + $27,920,490 / (1 + IRR)3 + $70,697,830 / (1 + IRR)4 – $1,674,000 / (1 + IRR)5 + $2,280,000 / (1 + IRR)6 Using a spreadsheet or financial calculator, the IRR for the project is: IRR = 13.45% Note, although the sign changes if the cash flows indicate up to 3 IRRs, a glance at the NPV profile shows only one real IRR. In the final analysis, the company should accept the project since the NPV is positive.

CHAPTER 6, Case #2 GOODWEEK TIRES, INC.

CHAPTER 31 CASE  C­23  

The cash flow to start the project is the $160 million equipment cost and the $9 million required for net working capital, yielding a total cash outflow today of $169 million. The research and development costs and the marketing test are sunk costs. We can calculate the future cash flows on a nominal basis or a real basis. Since the depreciation is given in nominal values, we will calculate the cash flows in nominal terms. The same solution can be found using real cash flows. Since the price and variable costs increase by 1 percent, and the inflation rate is 3.25 percent, the nominal growth in both variables is: (1 + R) = (1 + r)(1 + h) R = [(1.01)(1.0325)] – 1 R = .0428, or 4.28% To analyze this project, we must calculate the incremental cash flows generated by the project. We will calculate the real cash flows, although using nominal cash flows will result in the same NPV. The sales of new automobiles will grow by 2.5 percent per year, and there are four tires per car. Since the company expects to capture 11 percent of the market, the number of tires sold in the OEM market will be:

Automobiles sold Tires for automobiles sold SuperTread tires sold

Year 1 6,200,000 24,800,000 2,728,000

Year 2 6,355,000 25,420,000 2,796,200

Year 3 6,513,875 26,055,500 2,866,105

Year 4 6,676,722 26,706,888 2,937,758

The number of tires sold in the replacement market will grow at 2 percent per year, and Goodweek will capture 8 percent of the market. So, the number of tires sold in the replacement market will be:

Total tires sold in market SuperTread tires sold

Year 1 32,000,000 2,560,000

Year 2 32,640,000 2,611,200

Year 3 33,292,800 2,663,424

Year 4 33,958,656 2,716,692

The tires will be sold in each market at a different price. The price will increase each year at the rate calculated earlier, so the price each year will be:

OEM Replacement

Year 1 $41.00 $62.00

Year 2 $42.76 $64.66

Year 3 $44.59 $67.42

Year 4 $46.50 $70.31

Multiplying the number of tires sold in each market by the respective price in that market, the revenue each year will be:

OEM market Replacement market Total

Year 1 $111,848,000 158,720,000 $270,568,000

Year 2 $119,553,838 168,827,528 $288,381,366

Year 3 $127,790,574 179,578,718 $307,369,292

Year 4 $136,594,786 191,014,560 $327,609,346

Now we can calculate the incremental cash flows each year. We will calculate the nominal cash flows. Doing so, we find:

Revenue Variable costs Mkt. and general costs Depreciation EBT Tax Net income OCF

Year 1 $270,568,000 153,352,000 43,000,000 22,864,000 $51,352,000 20,540,800 $30,811,200 $53,675,200

Year 2 $288,381,366 163,530,185 44,397,500 39,184,000 $41,269,680 16,507,872 $24,761,808 $63,945,808

Year 3 $307,369,292 163,915,828 45,840,419 27,984,000 $69,629,045 27,851,618 $41,777,427 $69,761,427

Year 4 $327,609,346 167,627,528 47,330,232 19,984,000 $92,667,586 37,067,034 $55,600,551 $75,584,551

Net working capital is a percentage of sales, so the net working capital requirements will change every year. The net working capital cash flows will be:

Beginning Ending NWC cash flow

Year 1 $9,000,000 40,585,200 –$31,585,200

Year 2 $40,585,200 43,257,205 –$2,672,005

Year 3 $43,257,205 46,105,394 –$2,848,189

Year 4 $46,105,394 $46,105,394

The book value of the equipment is the original cost minus the accumulated depreciation. The book value of equipment each year will be:

Book value of equipment

Year 1 $137,136,000

Year 2 $97,952,000

Year 3 $69,968,000

Year 4 $49,984,000

Since the market value of the equipment is $54 million, the equipment is sold at a gain to book value, so the sale will incur the taxes of: Taxes on sale of equipment = ($49,984,000 – 65,000,000)(.40) = –$6,006,400 And the aftertax salvage value of the equipment is: Aftertax salvage value = $65,000,000 – 6,006,400 Aftertax salvage value = $58,993,600

CHAPTER 31 CASE  C­25   So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax salvage value, are: Time 0 1 2 3 4

Cash flow –$169,000,000 22,090,000 61,273,803 66,913,238 180,683,545

So, the payback period for the project is: Payback period = 3 + $18,722,959 / $180,683,545 Payback period = 3.10 years The discounted cash flows are: Time 0 1 2 3 4

Discounted cash flow –$169,000,000 19,479,718 47,648,445 45,885,227 109,261,305

Discounted payback period = 3 + $55,986,611 / $109,261,305 Discounted payback period = 3.51 years The required return for the project is in nominal terms, so the profitability index is: Profitability index = ($22,090,000/1.134 + $61,273,803/1.1342 + $66,913,238/1.1343 + $180,683,545/1.1344) / $169,000,000 Profitability index = 1.3152 The equation for IRR is: 0 = –$169,000,000 + $22,090,000/(1 + IRR) + $61,273,803/(1 + IRR)2 + $66,913,238/(1 + IRR)3 + $180,683,545/(1 + IRR)4 Using a spreadsheet or financial calculator, the IRR for the project is: IRR = 24.04% NPV = –$169,000,000 + $22,090,000/1.134 + $61,273,803/1.1342 + $66,913,238/1.1343 + $180,683,545/1.1344 NPV = $53,274,694.74 In the final analysis, the company should accept the project since the NPV is positive.

CHAPTER 7  BUNYAN LUMBER, LLC The company is faced with the option of when to harvest the lumber. Whatever harvest cycle the company chooses, it will follow that cycle in perpetuity. Since the forest was planted 20 years ago, the options available in the case are 40-, 45-, 50, and 55-year harvest cycles. No matter what harvest cycle the company chooses, it will always thin the timber 20 years after harvests and replants. The cash flows will grow at the inflation rate, so we can use the real or nominal cash flows. In this case, it is simpler to use real cash flows, although nominal cash flows would yield the same result. So, the real required return on the project is: (1 + R) = (1 + r)(1 + h) 1.10 = (1 + r)(1.037) r = .0608, or 6.08% The conservation funds are expected to grow at a slower rate than inflation, so the real return for the conservation fund will be: (1 + R) = (1 + r)(1 + h) 1.10 = (1 + r)(1.032) r = .0659, or 6.59% The company will thin the forest today regardless of the harvest schedule, so this first thinning is not an incremental cash flow, but future thinning is part of the analysis since the thinning schedule is determined by the harvest schedule. The cash flow from the thinning process is: Cash flow from thinning = Acres thinned × Cash flow per acre Cash flow from thinning = 5,000($1,000) Cash flow from thinning = $5,000,000 The real cost of the conservation fund is constant, but the expense will be tax deductible, so the aftertax cost of the conservation fund will be: Aftertax conservation fund cost = (1 – .35)($250,000) Aftertax conservation fund cost = $162,500 For each analysis, the revenue and costs are: Revenue = [∑ (% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 – defect rate) Tractor cost = (Cost MBF)(MBF per acre)(acres) Road cost = (Cost MBF)(MBF per acre)(acres) Sale preparation and administration = (Cost MBF)(MBF acre)(acres)

CHAPTER 31 CASE  C­27   Excavator piling, broadcast burning, site preparation, and planting costs are the cost of each per acre times the number of acres. These costs are the same no matter what the harvest schedule since they are based on acres, not MBF.

Now we can calculate the cash flow for each harvest schedule. One important note is that no depreciation is given in the case. Since the harvest time is likely to be short, the assumption is that no depreciation is attributable to the harvest. This implies that operating cash flow is equal to net income. Now we can calculate the NPV of each harvest schedule. The NPV of each harvest schedule is the NPV of the first harvest, the NPV of the thinning, the NPV of all future harvests, minus the present value of the conservation fund costs. 40-year harvest schedule: Revenue Tractor cost Road Sale preparation & admin Excavator piling Broadcast burning Site preparation Planting costs EBIT Taxes Net income (OCF)

$40,359,135 9,870,000 3,525,000 1,269,000 750,000 1,500,000 725,000 1,125,000 $21,595,135 7,558,297 $14,036,838

The PV of the first harvest in 20 years is: PVFirst = $14,036,838/(1 + .0608)20 PVFirst = $4,315,098 Thinning will also occur on a 40-year schedule, with the next thinning 40 years from today. The effective 40-year interest rate for the project is: 40-year project interest rate = [(1 + .0608) 40] – 1 40-year project interest rate = 958.17% We also need the 40-year interest rate for the conservation fund, which will be: 40-year conservation interest rate = [(1 + .0659) 40] – 1 40-year conservation interest rate = 1,183.87% Since we have the cash flows from each thinning, and the next thinning will occur in 40 years, we can find the present value of future thinnings on this schedule, which will be: PVThinning = $5,000,000/9.5817 PVThinning = $521,825.80

CHAPTER 31 CASE  C­29   The operating cash flow from each harvest on the 40-year schedule is $14,036,838, so the present value of the cash flows from the harvests are: PVHarvest = [($14,036,838/9.5817)] / (1 + .0608)20 PVHarvest = $450,345.94 Now we can find the present value of the conservation fund deposits. The present value of these deposits is at Year 20 is: PVConservation = –$162,500 – $162,500/11.8387 PVConservation = –$176,226.22 And the value today is: PVConservation = –$176,226.22/(1 + .0659)20 PVConservation = –$49,182.52 So, the NPV of a 40-year harvest schedule is: NPV = $4,315,098 + 521,825.80 + 450,345.94 – 49,182.52 NPV = $5,238,087.63 45-year harvest schedule: Revenue Tractor cost Road Sale preparation & admin Excavator piling Broadcast burning Site preparation Planting costs EBIT Taxes Net income (OCF)

$47,051,600 11,480,000 4,100,000 1,476,000 750,000 1,500,000 725,000 1,125,000 $25,895,600 9,063,460 $16,832,140

The PV of the first harvest in 25 years is: PVFirst = $16,832,140 / (1 + .0608)25 PVFirst = $3,852,930 Thinning will also occur on a 45-year schedule, with the next thinning 45 years from today. The effective 45-year interest rate for the project is: 45-year project interest rate = [(1 + .0608) 45] – 1 45-year project interest rate = 1,321.11%

We also need the 45-year interest rate for the conservation fund, which will be: 45-year conservation interest rate = [(1 + .0659) 45] – 1 45-year conservation interest rate = 1,666.38% Since we have the cash flows from each thinning, and the next thinning will occur in 45 years, we can find the present value of future thinnings on this schedule, which will be: PVThinning = $5,000,000/13.2111 PVThinning = $378,470.46 The operating cash flow from each harvest on the 45-year schedule is $16,832,140, so the present value of the cash flows from the harvests are: PVHarvest = [($16,832,140/13.21111)] / (1 + .0608)25 PVHarvest = $291,644.04 Now we can find the present value of the conservation fund deposits. The present value of these deposits at Year 25 is: PVConservation = –$162,500 – $162,500/16.6638 PVConservation = –$172,251.67 And the value today is: PVConservation = –$172,251.67/(1 + .0659)25 PVConservation = –$34,941.27 So, the NPV of a 45-year harvest schedule is: NPV = $3,852,930 + 378,470.46 + 291,644.04 – 34,941.27 NPV = $4,488,103.20 50-year harvest schedule: Revenue Tractor cost Road Sale preparation & admin Excavator piling Broadcast burning Site preparation Planting costs EBIT Taxes Net income (OCF)

$49,699,440 12,110,000 4,325,000 1,557,000 750,000 1,500,000 725,000 1,125,000 $27,607,440 9,662,604 $17,944,836

CHAPTER 31 CASE  C­31   The PV of the first harvest in 30 years is: PVFirst = $17,944,836/(1 + .0608)30 PVFirst = $3,058,593 Thinning will also occur on a 50-year schedule, with the next thinning 50 years from today. The effective 50-year interest rate for the project is: 50-year project interest rate = [(1 + .0608) 50] – 1 50-year project interest rate = 1,808.52% We also need the 50-year interest rate for the conservation fund, which will be: 50-year conservation interest rate = [(1 + .0659) 50] – 1 50-year conservation interest rate = 2,330.24% Since we have the cash flows from each thinning, and the next thinning will occur in 50 years, we can find the present value of future thinnings on this schedule, which will be: PVThinning = $5,000,000/18.0852 PVThinning = $276,469.34 The operating cash flow from each harvest on the 50-year schedule is $17,944,836, so the present value of the cash flows from the harvests are: PVHarvest = [($17,944,836/18.0852] / (1 + .0608)30 PVHarvest = $169,121.42 Now we can find the present value of the conservation fund deposits. The present value of these deposits is at Year 30 is: PVConservation = –$162,500 – $162,500/23.3024 PVConservation = –$169,473.53 And the value today is: PVConservation = –$169,473.53/(1 + .0659)30 PVConservation = –$24,986.89 So, the NPV of a 50-year harvest schedule is: NPV = $3,058,593 + 276,469.34 + 169,121.42 – 24,986.89 NPV = $3,479,196.45

55-year harvest schedule: Revenue Tractor cost Road Sale preparation & admin Excavator piling Broadcast burning Site preparation Planting costs EBIT Taxes Net income (OCF)

$52,057,863 12,670,000 4,525,000 1,629,000 750,000 1,500,000 725,000 1,125,000 $29,133,863 10,196,852 $18,937,011

The PV of the first harvest in 35 years is: PVFirst = $18,937,011/(1 + .0608)35 PVFirst = $2,403,388 Thinning will also occur on a 55-year schedule, with the next thinning 55 years from today. The effective 55-year interest rate for the project is: 55-year project interest rate = [(1 + .0608) 55] – 1 55-year project interest rate = 2,463.10% We also need the 55-year interest rate for the conservation fund, which will be: 55-year conservation interest rate = [(1 + .0659) 55] – 1 55-year conservation interest rate = 3,243.60% Since we have the cash flows from each thinning, and the next thinning will occur in 55 years, we can find the present value of future thinnings on this schedule, which will be: PVThinning = $5,000,000/24.6310 PVThinning = $202,995.97 The operating cash flow from each harvest on the 55-year schedule is $18,937,011, so the present value of the cash flows from the harvests are: PVHarvest = [($18,937,011/24.6310] / (1 + .0608)35 PVHarvest = $97,575.62 Now we can find the present value of the conservation fund deposits. The present value of these deposits is at Year 35 is: PVConservation = –$162,500 – $162,500/32.4360 PVConservation = –$167,509.87

CHAPTER 31 CASE  C­33  

And the value today is: PVConservation = –$169,509.87/(1 + .0659)35 PVConservation = –$17,950.88 So, the NPV of a 55-year harvest schedule is: NPV = $2,403,388 + 202,995.97 + 97,575.62 – 17,950.88 NPV = $2,686,008.85 The company should use a 40-year harvest schedule since it has the highest NPV. Notice that when the NPV began to decline, it continued declining. This is expected since the growth in the trees increases at a decreasing rate. So, once we reach a point where the increased growth cannot overcome the increased effects of compounding, harvesting should take place. There is no point further in the future which will provide a higher NPV.

CHAPTER 8 FINANCING EAST COAST YACHT’S EXPANSION PLANS WITH A BOND ISSUE 1.

A rule of thumb with bond provisions is to determine who the provisions benefit. If the company benefits, the bond will have a higher coupon rate. If the bondholders benefit, the bond will have a lower coupon rate. a.

A bond with collateral will have a lower coupon rate. Bondholders have the claim on the collateral, even in bankruptcy. Collateral provides an asset that bondholders can claim, which lowers their risk in default. The downside of collateral is that the company generally cannot sell the asset used as collateral, and they will generally have to keep the asset in good working order.

b.

The more senior the bond is, the lower the coupon rate. Senior bonds get full payment in bankruptcy proceedings before subordinated bonds receive any payment. A potential problem may arise in that the bond covenant may restrict the company from issuing any future bonds senior to the current bonds.

c.

A sinking fund will reduce the coupon rate because it is a partial guarantee to bondholders. The problem with a sinking fund is that the company must make the interim payments into a sinking fund or face default. This means the company must be able to generate these cash flows.

2.

d.

A provision with a specific call date and prices would increase the coupon rate. The call provision would only be used when it is to the company’s advantage, thus the bondholder’s disadvantage. The downside is the higher coupon rate. The company benefits by being able to refinance at a lower rate if interest rates fall significantly, that is, enough to offset the call provision cost.

e.

A deferred call would reduce the coupon rate relative to a call provision without a deferred call. The bond will still have a higher rate relative to a plain vanilla bond. The deferred call means that the company cannot call the bond for a specified period. This offers the bondholders protection for this period. The disadvantage of a deferred call is that the company cannot call the bond during the call protection period. Interest rates could potentially fall to the point where it would be beneficial for the company to call the bond, yet the company is unable to do so.

f.

A make-whole call provision should lower the coupon rate in comparison to a call provision with specific dates since the make-whole call repays the bondholder the present value of the future cash flows. However, a make-whole call provision should not affect the coupon rate in comparison to a plain vanilla bond. Since the bondholders are made whole, they should be indifferent between a plain vanilla bond and a make-whole bond. If a bond with a make-whole provision is called, bondholders receive the market value of the bond, which they can reinvest in another bond with similar characteristics. If we compare this to a bond with a specific call price, investors rarely receive the full market value of the future cash flows.

g.

A positive covenant would reduce the coupon rate. The presence of positive covenants protects bondholders by forcing the company to undertake actions that benefit bondholders. Examples of positive covenants would be: the company must maintain audited financial statements; the company must maintain a minimum specified level of working capital or a minimum specified current ratio; the company must maintain any collateral in good working order. The negative side of positive covenants is that the company is restricted in its actions. The positive covenant may force the company into actions in the future that it would rather not undertake.

h.

A negative covenant would reduce the coupon rate. The presence of negative covenants protects bondholders from actions by the company that would harm the bondholders. Remember, the goal of a corporation is to maximize shareholder wealth. This says nothing about bondholders. Examples of negative covenants would be: the company cannot increase dividends, or at least increase beyond a specified level; the company cannot issue new bonds senior to the current bond issue; the company cannot sell any collateral. The downside of negative covenants is the restriction of the company’s actions.

i.

Even though the company is not public, a conversion feature would likely lower the coupon rate. The conversion feature would permit bondholders to benefit if the company does well and also goes public. The downside is that the company may be selling equity at a discounted price.

j.

The downside of a floating rate coupon is that if interest rates rise, the company has to pay a higher interest rate. However, if interest rates fall, the company pays a lower interest rate.

Since the coupon bonds will have a coupon rate equal to the YTM, they will sell at par. So, the number of coupon bonds to sell will be: (NOTE: The text has a typo. The coupon rate on the coupon bonds should be 7.5 percent.) Coupon bonds to sell = $50,000,000 / $1,000 = 50,000

CHAPTER 31 CASE  C­35  

The price of the 20-year, zero coupon bond when it is issued will be: Zero coupon price = $1,000 / 1.037540 = $229.34 So, the number of zero coupon bonds the company will need to sell is: Zero coupon bonds to sell = $50,000,000 / $229.34 = 218,016 3.

At maturity, the principal payment for the coupon bonds will be: Coupon bond principal payment at maturity = 50,000($1,000) = $50,000,000 The principal payment for the zero coupon bonds at maturity will be: Zero coupon bond payment at maturity = 218,016($1,000) = $218,016,000

4.

One of the main considerations is timing of the cash flows. The annual coupon payment on the coupon bonds will be: Annual coupon bond payments = 50,000($1,000)(.065) = $3,250,000 Since the interest payments are tax deductible, the aftertax cash flow from the interest payments will be: Aftertax coupon payments = $3,250,000(1 – .35) = $2,112,500 Even though interest payments are not actually made each year, the implied interest on the zero coupon bonds is tax deductible. The value of the zero coupon bonds next year will be: Value of zero in one year = $1,000/1.037538 = $246.86 So, the growth on the zero coupon bond was: Zero coupon growth = $246.86 – 229.34 = $17.52 This increase in value is tax deductible, so it reduces taxes even though there is no cash flow for interest payments. So, there is a positive cash flow created next year in the amount of: Zero cash flow = 218,016($17.52)(.35) = $1,336,929.23 This cash flow will increase each year since the value of the zero coupon bond will increase by a greater dollar amount each year.

5.

If the Treasury rate is 4.80 percent, the make-whole call price in 7 years is: P = $37.50({1 – [1/(1 + .026)]26 } / .026) + $1,000[1 / (1 + .026)26] P = $1,215.38 And, if the Treasury rate is 8.20 percent, the make-whole call price in 7 years is: P = $37.50({1 – [1/(1 + .043)]26 } / .043) + $1,000[1 / (1 + .043)26] P = $914.90

6.

The investor is not necessarily made whole with the make-whole call provision, but is made close to whole. Assume a company issues a bond with a make-whole call of the Treasury rate plus .5 percent. Further assume this is the correct average spread for the company’s bond over the life of the bond. Although the spread is correct on average, it is not correct at every specific time. The spread over the Treasury rate varies over the life of the bond, and is higher when the bond has a longer time to maturity. To see this, consider, at the extreme, the spread for any bond above the Treasury yield at maturity is zero. So, if the bond is called early in its life, the spread above the Treasury is likely to be too low. This means the investor is more than made whole. If the bond is called late in its life, the spread is too high. This means the interest rate used to calculate the present value of the cash flows is too high, which results in a lower present value. Thus, the bondholder is made less than whole. In practical terms, this difference is likely to be small, and it will almost always result in a higher price paid to the bondholder when compared to a traditional call feature.

CHAPTER 31 CASE  C­37   7.

There is no definitive answer to which type of bond the company should issue. If the intermediate cash flows for the coupon payments will be difficult, a zero coupon bond is likely to be the best solution. However, the zero coupon bond will require a larger payment at maturity. As for the type of call provision, a make-whole call provision is generally better for bondholders, therefore the coupon rate of the bond will likely be lower to sell the bond at par value. Again, there is a tradeoff.

CHAPTER 9 STOCK VALUATION AT RAGAN THERMAL SYSTEMS 1.

The total dividends paid by the company were $640,000. Since there are 300,000 shares outstanding, the total earnings for the company were: Total earnings = 300,000($5.35) = $1,605,000 This means the payout ratio was: Payout ratio = $640,000/$1,605,000 = .3988, or 39.88% So, the retention ratio was: Retention ratio = 1 – .3988 = .6012, or 60.12% Using the retention ratio, the company’s growth rate is: g = ROE × b = .21(.6012) = .1263, or 12.63% Now we can value the company using the entire dividend payment. The total value of the company’s equity under these assumptions is: Total equity value = D1 / (R – g) Total equity value = $640,000(1.1263) / (.18 – .1263) Total equity value = $13,413,286.96 So, the value per share is: Value per share = $13,413,286.96 / 300,000 Value per share = $44.71

2.

Since Nautilus Marine Engines had a write off which affected its earnings per share, we need to recalculate the industry EPS. So, the industry EPS is:

Industry EPS = ($1.19 + 1.26 + 2.07) / 3 = $1.51 Using this industry EPS, the industry payout ratio is: Industry payout ratio = $.44/$1.51 = .2898, or 28.98%

CHAPTER 31 CASE  C­39   So, the industry retention ratio is Industry retention ratio = 1 – .2898 = .7102, or 71.02% This means the industry growth rate is: Industry g = .11(.7102) = .0781, or 7.81% The company will continue to grow at its current pace for five years before slowing to the industry growth rate. So, the total dividends for each of the next six years will be: D1 = $640,000.00(1.1263) = $720,807.48 D2 = $720,807.48(1.1263) = $811,817.84 D3 = $811,817.84(1.1263) = $914,319.33 D4 = $914,319.33(1.1263) = $1,029,762.82 D5 = $1,029,762.82(1.1263) = $1,159,782.41 D6 = $1,159,782.41(1.0781) = $1,250,384.00 The total value of the stock in Year 5 with the industry required return will be: Stock value in Year 5 = $1,250,384.00 / (.15 – .0781) = $17,395,308.29 This means the total value of the stock today is: Value of stock today = $720,807.48/1.15 + $811,817.84/1.152 + $914,319.33/1.153 + $1,029,762.82/1.154 + ($1,159,782.41 + 17,395,308.29) / 1.155 Value of stock today = $11,655,749.48 And the value per share of the stock today is: Value per share = $11,655,749.48 / 300,000 Value per share = $38.85 3.

Using the revised industry EPS, the industry PE ratio is: Industry PE = $18.08 / $1.51 = 12.00 Using the original stock price assumption, Ragan’s PE ratio is: Ragan PE (original assumptions) = $44.71 / $5.35 = 8.36 Using the revised assumptions, Ragan’s PE = $38.85 / $5.35 = 7.26 Obviously, Ragan’s PE is lower than the industry average. Given that the growth rate for the company is higher than the industry, this is unexpected. The reason is that the company pays out a higher dividend than the industry.

4.

Here, we must make an assumption. We have two estimates of the required return. Since we are assuming the growth rate follows the growth rate assumption in Question 2, we will use the industry average required return assumed in that question as well. The total earnings of the company which would be paid out as a dividend as a cash cow are: Total earnings = 2(150,000 shares)($5.35) Total earnings = $1,605,000 So, the value of Ragan as a cash cow is: Cash cow value = $1,605,000 / .15 = $10,700,000 The total stock value with growth from Question 2 is $11,655,749.48, so the percentage of the value of the company not attributable to growth opportunities is: Percentage of value not attributable to growth opportunities = $10,700,000 / $11,655,749.48 = .9180 So, the percentage of the company’s value attributable to growth opportunities is: Percentage of value attributable to growth opportunities = 1 – .9180 = .0820, or 8.20%

5.

Again, we will assume the results in Question 2 are correct. The growth rate of the company we calculated in this question was the industry growth rate of 7.81 percent. Since the growth rate is: g = ROE × b If we assume the payout ratio remains constant, the ROE is: .0781 = ROE(.6012) ROE = .1299, or 12.99%

6.

The most obvious solution is to retain more of the company’s earnings and invest in profitable opportunities. This strategy will not work if the return on the company’s investment is lower than the required return on the company’s stock.

CHAPTER 10  A JOB AT EAST COAST YACHTS  1.

The biggest advantage the mutual funds have is instant diversification. The mutual funds have a number of assets in the portfolio.

2.

Both the APR and EAR are infinite. The match is instantaneous, so the number of periods in a year is infinite.

CHAPTER 31 CASE  C­41   3.

The advantage of the actively managed fund is the possibility of outperforming the market, which the fund has done on average over the past ten years. The major disadvantage is the likelihood of underperforming the market. In general, most mutual funds do not outperform the market for an extended period of time, and finding the funds that will outperform the market in the future beforehand is a daunting task. One factor that makes outperforming the market even more difficult is the management fee charged by the fund.

4.

The returns are the most volatile for the small cap fund because the stocks in this fund are the riskiest. This does not imply the fund is bad, just that the risk is higher, and therefore, the expected return is higher. You would want to invest in this fund if your risk tolerance is such that you are willing to take on the additional risk in expectation of a higher return. The higher expenses of the fund are expected. In general, small cap funds have higher expenses, in large part due to the greater cost of running the fund, including researching smaller stocks.

5.

The Sharpe ratio for each of the mutual funds and the company stocks are: Bledsoe S&P 500 Index Fund = (9.18% – 3.2) / 20.43% = .2927 Bledsoe Small-Cap Fund = (14.12% – 3.2) / 25.13% = .4345 Bledsoe Large Company Stock Fund = (8.58% – 3.2) / 23.82% = .2259 Bledsoe Bond Fund = (6.45% – 3.2) / 9.85% = .3299 East Coast Yachts Stock = (16% – 3.2) / 65% = .1969 The Sharpe ratio is most applicable for a diversified portfolio, and is least applicable for the company stock.

6.

This is a very open-ended question. The asset allocation depends on the risk tolerance of the individual. However, most students will be young, so in this case, the portfolio allocation should be more heavily weighted toward stocks. In any case, there should be little, if any, money allocated to the company stock. The principle of diversification indicates that an individual should hold a diversified portfolio. Investing heavily in company stock does not create a diversified portfolio. This is especially true since income comes from the company as well. If times get bad for the company, employees face layoffs, or reduced work hours. So, not only does the investment perform poorly, but income may be reduced as well. We only have to look at employees of Enron or WorldCom to see the potential for problems with investing in company stock. At most, 5 to 10 percent of the portfolio should be allocated to company stock. Age is a determinant in the decision. Older individuals should be less heavily weighted toward stocks. A commonly used rule of thumb is that an individual should invest 100 minus their age in stocks. Unfortunately, this rule of thumb tends to result in an underinvestment in stocks.

CHAPTER 11  A JOB AT EAST COAST YACHTS,  PART 2 1.

There should be little, if any, money allocated to the company stock. The principle of diversification indicates that an individual should hold a diversified portfolio. Investing heavily in company stock does not create a diversified portfolio. This is especially true since income also comes from the company. If times get bad for the company, employees face layoffs, or reduced work hours. So, not only does the investment perform poorly, but income may be reduced as well. We only have to look at employees of Enron or WorldCom to see the potential for problems with investing in company stock. At most, 5 to 10 percent of the portfolio should be allocated to company stock.

2.

This is not the portfolio with the least risk. By adding stocks, a riskier asset, the overall risk of the portfolio will decline. This will be demonstrated in the next questions.

3.

We can use the equations for the expected return of the portfolio, and the portfolio standard deviation, that is: E(RP) = XEE(RE) + XDE(RD) 2

2

2

2

P = (X E  E + X D  D + 2XEXDEDD,E)1/2 Using these equations and equity portfolio weights from zero to 100 percent at intervals of 10 percent, we get the following portfolio expected returns and standard deviations:

CHAPTER 31 CASE  C­43  

Weight of stock fund 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Portfolio E(R) 6.45% 6.66% 6.88% 7.09% 7.30% 7.52% 7.73% 7.94% 8.15% 8.37% 8.58%

Portfolio standard deviation 9.8500% 9.5182% 9.8006% 10.6484% 11.9417% 13.5536% 15.3843% 17.3648% 19.4493% 21.6077% 23.8200%

The graph of the opportunity set of feasible portfolios will look like the following:

Investment Opportunity Set 10% 9% 8% 7% 6% Portfolio Expected Return

5% 4% 3% 2% 1% 0% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% Portfolio Standard Deviation

4.

Now we can use Solver to maximize this expression by changing the weight of the equity input cell. The constraint is that the standard deviation of the portfolio is equal to the standard deviation of the bond fund. Using Solver, the weight of the large cap stock fund and bond fund in this portfolio is: XE = .2082 XD = .7918 So, the expected return and standard deviation of this portfolio is: E(R) = .2082(.0858) + .7918(.0645) E(R) = .0689, or 6.89%  = [.20822(.2382)2 + .79182(.0985)2 + 2(.2082)(.7918)(.2382)(.0985)(.15)]1/2  = .0985, or 9.85% This is the exact same standard deviation as the bond fund, but the expected return is about one-half percent higher.

CHAPTER 31 CASE  C­45   5.

To find the weights of each asset in the minimum variance portfolio, we begin with the equation for the variance of the portfolio. Using S to represent the large company fund and B to represent the bond fund, the variance of a portfolio of two assets equals: 2

2

2

2

2

 P = X S  S + X B  B + 2XSXBS,B Since the weights of the assets must sum to one, we can write the variance of the portfolio as: 2

2

2

2 B

 P = X S  S + (1 – XS)2

+ 2XS(1 – XS)SBS,B

To find the minimum for any function, we find the derivative and set the derivative equal to zero. Finding the derivative of the variance function, setting the derivative equal to zero, and solving for the weight of the stock fund, we find: 2

dσp2/dXS = 2XS S – 2(1 – XS )σB2 + 2σSσB S,B – 4XSσSσBS,B = 0 Solve for XS to get: 2

2

2

XS = ( B – SBS,B) / ( S +  B – 2SBS,B) Using this expression, we find the weight of the stock fund, must be: XS = [.09852 – (.2382)(.0985)(.15)] / [.23822 + .09852 – 2(.2382)(.0985)(.15)] XS = .1041 This implies the weight of the bond fund is: XB = 1 – XS XB = 1 – .1041 XB = .8959 The expected return of this portfolio is: E(R) = .1041(.0858) + .8959(.0645) E(R) = .0667, or 6.67% The variance of the portfolio is: 2

2

2

2

2

 P = X S  S + X B  B + 2XSXBSBS,B 2

 P = (.10412)(.23822) + (.89592)(.09852) + 2(.1041)(.8959)(.2382)(.0985)(.15) 2

 P = .009059 And the standard deviation is:

 = .0090591/2  = .0952, or 9.52%

CHAPTER 31 CASE  C­47   With these returns and variances, the minimum variance portfolio is important because no investor would ever hold a portfolio with a greater weight in bonds. If an investor increases the weight of bonds in the portfolio, the risk of the portfolio increases and the expected return decreases. The result is illustrated in Question 4. 6.

We can find the Sharpe optimal portfolio by using Solver. To use Solver, we input the Sharpe ratio in a cell. The Sharpe ratio is:

Sharpe ratio =

E(R)  R f σP

We also need to recognize that the weight of debt in the portfolio is one minus the weight of equity. Substituting the equations for the expected return of the portfolio and the standard deviation of the portfolio, we get: X E E(R E )  (1  X E )E(R D )  R f

Sharpe ratio =

( X E2 σ 2E

 (1  X E ) 2 σ 2D  2 X E (1  X E )σ E σ D ρ E,D )1 / 2

Now we can use Solver to maximize this expression by changing the weight of equity input cell. Doing so, we find the weight of equity in the Sharpe optimal portfolio is 19.76 percent. This question can also be solved directly. The goal is to maximize the Sharpe ratio, so we can use the expression for the Sharpe ratio, set the derivative equal to zero, and solve for the weight of equity (or debt). Doing so, the resulting expression for the weight of equity in the Sharpe optimal portfolio is: [E(R E )  R f ]σ 2D  [E(R D )  R f ]σ E σ D ρ E,D

XE =

[E(R E )  R f ]σ 2D  [E(R D )  R f ]σ 2E  [E(R) E  R f  E(R) D  R f ]σ E σ D ρ E,D

Using this equation, we find the weight of equity in the Sharpe optimal portfolio is: XE =

[.0858  .032].0985 2  [.0645  .0320](.23 82)(.0985) (.15) [.0858  .0320].098 5 2  [.0645  .0310].238 2 2  [.0858  .0320  .0645  .0320](.23 82)(.0985) (.15) XE = .1976 and the weight of debt is: XD = 1 – .1976 XD = .8024

So, the expected return and standard deviation of the Sharpe optimal portfolio is: E(R) = .1976(.0858) + .8024(.0645) E(R) = .0687, or 6.87%  = [.19762(.2382)2 + .80242(.0985)2 + 2(.1976)(.2382)(.8024)(.0985)(.15)]1/2  = .0979, or 9.79% The Sharpe ratio of the Sharpe optimal portfolio is:

.0687  .0320 .0979 Sharpe ratio = Sharpe ratio = .3751 The Sharpe optimal portfolio is the best risky portfolio for all investors because it delivers a greater reward-to-risk ratio than any other portfolio. If a line is drawn from the risk-free rate to the Sharpe optimal portfolio, it shows the best combination of portfolios available to any investor. Investors can change the level of risk by altering the percentage of their investment in the risk-free asset and the Sharpe optimal portfolio. This line is the Security Market Line.

CHAPTER 12  THE FAMA­FRENCH MULTI­FACTOR  MODEL AND MUTUAL FUND RETURNS NOTE: The example below shows the results for returns between October 2010 and September 2015. The actual answer to the case will change based on current market conditions. 1.

For a large-company stock fund, we would expect the beta for the market risk premium to be near one since large company returns account for a large part of the total market return on a market-value basis. We would expect the betas for the SMB and HML risk factors to be low, and possibly negative, since large company stock returns are not highly related to small company stock returns and large company stocks tend to be more oriented toward value stocks.

2.

The following shows the results of the regression estimates for the period between October 2010 and September 2015. The actual answer to the case will change based on current market returns. Fidelity Magellan:

Regression Statistics 0.97626239 Multiple R 4 R Square 0.95308826

CHAPTER 31 CASE  C­49  

Adjusted R Square Standard Error Observations

1 0.95057513 3 0.00871456 3 60

ANOVA df Regression Residual Total

Intercept Mkt-RF SMB HML

3 56 59

SS 0.08640 0.00425 0.09066

Coefficients -0.00216 1.08816 0.06291 -0.13206

Standard Error 0.00120 0.03546 0.05736 0.06311

MS 0.02880 0.00008

F 379.24369

t Stat -1.79745 30.69090 1.09670 -2.09264

P-value 0.07766 0.00000 0.27747 0.04092

Significanc eF 3.6948E-37

Fidelity Low-Priced Stock Fund:

Regression Statistics Multiple R 0.97094 R Square 0.94273 Adjusted R Square 0.93967 Standard Error 0.00868 Observations 60.00000 ANOVA Regression Residual Total

Intercept Mkt-RF SMB HML

df 3.00000 56.00000 59.00000

SS 0.06939 0.00422 0.07361

Coefficient s 0.00065 0.95742 0.11224 0.09351

Standard Error 0.00119 0.03530 0.05711 0.06283

MS 0.02313 0.00008

F 307.29301

t Stat 0.54383 27.12394 1.96550 1.48837

P-value 0.58871 0.00000 0.05432 0.14226

Significanc eF 0.00000

Baron Small Cap Fund:

Regression Statistics Multiple R 0.96584 R Square 0.93284 Adjusted R Square 0.92924 Standard Error 0.01147 Observations 60.00000 ANOVA Regression Residual Total

Intercept Mkt-RF SMB

df 3.00000 56.00000 59.00000

SS 0.10239 0.00737 0.10976

Coefficient s -0.00147 1.01454 0.58630

Standard Error 0.00158 0.04668 0.07552

MS 0.03413 0.00013

F 259.28367

Significance F 0.00000

t Stat -0.92967 21.73473 7.76379

P-value 0.35653 0.00000 0.00000

Lower 95% -0.00463 0.92103 0.43502

CHAPTER 31 CASE  C­51  

HML

-0.12235

0.08308

-1.47266

0.14644

-0.28878

3.

This answer will depend on the returns used by the students.

4.

If the market is efficient, all assets should have an alpha of zero. In this case, none of the three funds has a statistically significant positive alpha at the 5 percent level, so the evidence provided here against market efficiency is limited.

5.

Once adjusting for risk, we cannot say any of these three funds performed better since all three alphas are not significantly different from zero at the 5 percent level of confidence, although the alpha for the Fidelity Magellan Fund is significantly negative at the 10 percent level, so it may have had the worst performance given its level of risk.

CHAPTER 13  COST OF CAPITAL FOR SWAN MOTORS NOTE: The example below shows the results during November 2012. The actual answer to the case will change based on current market conditions. 1.

The book value of the company’s liabilities and equity can be found from a number of sources. We went to http://www.sec.gov and found Tesla’s Form 10q, dated September 30, 2015. Tesla’s Form 10q showed the following:

The book value of equity is $1,315 million on the balance sheet. However, for a more current book value, we multiplied the number of shares outstanding by the book value per share on Yahoo! Finance. For the book value of debt, we used the following note in the 10q:

In the notes, the company issued $800 million of 2019 bond, the issued another $120 million. For the 2021 bond, the company initially issued $1.2 billion, the issued another $180 million. The total numbers do not match the balance sheet debt, but we will use these numbers nonetheless. It is likely

CHAPTER 31 CASE  C­53   that the company has repurchased some of the outstanding debt, but any repurchase is not noted in the 10q. 2.

We need various pieces of information to estimate the cost of equity. We can use the dividend growth model or the CAPM, so we will attempt to use both. The following information is necessary for our calculations. We gathered all the information from finance.yahoo.com. The screen shots below show this information. Market price = $232.26 Market capitalization = $30.16 billion Shares outstanding = 129.80 million Most recent dividend = $0 Beta = 1.40 3-month Treasury bill rate = .06%

CHAPTER 31 CASE  C­55  

Tesla has never paid a dividend so we cannot use the dividend growth model to estimate the cost of equity. We do have the information to estimate the cost of equity with the CAPM. Using the market risk premium of 7 percent from the textbook, we get: RE = Rf + [E(RM) – Rf] RE = .0006 + 1.40[.07] RE = .0986, or 9.86% 3.

Below are the top 10 competitors in the automobile industry by market capitalization at the time: Company

Beta

Ford General Motors Honda Toyota Fiat Chrysler Volkswagen DaimlerChrysler Ford

0.97 1.44 0.74 0.54 0.49 1.97 1.55 0.97

Industry Average

1.10

We should make an important note here: All of the competitors listed may not be direct competitors. First, since Tesla manufactures only electric cars, it could be an entirely different industry. Additionally, Tesla primarily sells only in the United States, so it is largely immune from the currency risk faced by many of the above auto companies. Finally, since several of the companies listed are based overseas and only have ADRs listed on U.S. exchanges, they may not be comparable. In this case, we have chosen to use all the companies listed.

Using the industry average beta, the cost of equity is: RE = Rf + [E(RM) – Rf] RE = .0006 + 1.70[.07] RE = 7.76% Because Tesla’s beta is so different from the industry beta, a decision must be made as to the correct cost of equity. will use the cost of equity using Tesla’s beta. 4.

To get the yield to maturity on Tesla’s bonds, we went to finramarkets.morningstar.com/BondCenter/. We gathered the following information:

Tesla has a convertible bond that matures 06/01/2018. Because the convertible feature is so deep in the money, the bond is priced near the conversion value, resulting in a very large negative yield to maturity. We have chosen to ignore this bond in our analysis. If you click on the link for each bond, the website provides information concerning the bond, including the face amount of the issue. So, the weighted average cost of debt for Tesla using both the book value and the market value is:

3/1/2019 3/1/2021 Total

Book value (millions) $920 1,380 $2,300

Percent of total 0.40 0.60 1.00

Quoted price 94.347 92.625

Market value (millions) $867.992 1,278.225 $2,146.22

Percent of total 0.40 0.60 1.00

Yield to Maturity 2.028% 2.754%

Book values 0.81% 1.65% 2.46%

Market values 0.82% 1.64% 2.46%

It is irrelevant whether we use book or market values to calculate the cost of debt for Tesla. The weighted average cost of debt using book value weights is 2.46 percent, and using market value weights we get 2.46 percent. 5.

Using book value weights, the total value of Tesla is: V = $2,300,000,000 + $1,322,662,000 V = $3,622,662,000 So, the WACC based on book value weights is: WACC = RE(E/V) + RD(D/V)(1 – T) WACC = (.0986)($1,322.662/$3,662.662) + (.0246)($2,300/$3,622.662)(1 – .35) WACC = .0462, or 4.62%

CHAPTER 31 CASE  C­57  

Using the market value weights, the total value of Tesla is: V = $2,146,217,400 + $30,160,328,000 V = $32,306,545,400 So, the WACC based on market value weights is: WACC = RE(E/V) + RD(D/V)(1 – T) WACC = (.0986)($ 30,160,328,000 /$32,306,545,400) + (.0246)($ 2,146,217,400 /$32,306,545,400)(1 – .35) WACC = .0938, or 9.38% The cost of capital for Tesla using book value weights and market value weights is dramatically different since Tesla has a market-to-book ratio of about 22.8. 6.

The biggest potential problem with SMI using Tesla’s cost of capital is that SMI operates stores that generate the company’s sales. Tesla generates sales almost exclusively from its internet site. This could potentially be a risk factor that affects the cost of capital. Another factor that could affect the cost of capital is Tesla’s access to capital since it is a public company, while Swan Motors is private.

CHAPTER 14 YOUR 401k ACCOUNT AT EAST COAST  YACHTS 1.

Before the fact, you would expect that mutual funds managers would be able to outperform the market. This is due, in part, to the Darwinian nature of the business. Good performing fund managers are richly rewarded, and poor performing fund managers are fired, often very quickly. In reality, we should expect that less than 50 percent of all equity mutual funds would outperform the market. This does not depend on the level of market efficiency. Consider the following question: What percentage of investors will outperform the market in a given year? Answer: Fifty percent. While there could be one really poor investor who takes all of the losses in a given year, in general, to get the market average we would expect one-half of investors would outperform the market, and one-half would underperform the market. After all, the market average return has to be the average return of all investors’ average return. This is definitely true if we consider the weighted average return, that is, the average return of investors weighted by the dollar amount of the investment. We would expect more than 50 percent of mutual funds would underperform the market because of the expenses charged by the mutual funds. Consider the large-cap stock fund, with an expense ratio of 1.50 percent. The fund must exceed the market return by 1.50 percent before fees in order to achieve a return after fees equal to the market return. Whether the market is efficient or inefficient is irrelevant unless mutual funds managers are the best investors in the market, and all other investors, including private money managers, pension fund managers, individuals, etc. are the bad investors in the market.

CHAPTER 31 CASE  C­59   We should also consider that mutual funds managers may be able to outperform the market before expenses. Whether they can outperform the market on an after-expense basis becomes a question of whether mutual fund managers can extract economic rents from the stock market. The evidence tends to support the idea that they cannot. In general, research has found that mutual fund managers underperform the market after expenses by the average expense ratio. This means that mutual funds as a whole tend to have the market average return before expenses, so they do not appear to be able to outperform the market. 2.

The results in the graph tend to support the idea of market efficiency. Consider the case of the Fidelity Magellan Fund, one of the largest actively managed equity mutual funds at the time this was written. The total assets of the fund at the time this was written was about $22.4 billion. So the question is this: What would Fidelity pay for one year to increase the return of the Magellan Fund by .01 percent? If we multiply the fund assets by .01 percent, we get: $22,400,000,000(.0001) = $2,240,000. So, if Fidelity can increase the return of this one fund by only .01 percent per year, it should be willing to pay up to $2.24 million for that year. Given the amount mutual fund companies would be willing to spend for research, and the Darwinian nature of the industry, we would expect that mutual fund managers should be able to outperform the market. While there have been notable exceptions, such as Peter Lynch’s tenure at Magellan, as a whole, mutual fund managers do not seem to be able to outperform the market. As a result, if the “best” and definitely best-financed investors cannot outperform the market, the results support the concept of market efficiency.

3.

Given that the evidence presented tends to support market efficiency, you should invest in the S&P 500 index fund. However, this is not the entire answer. By investing the entire equity portion of your account in the S&P 500 index, your portfolio is not diversified since the S&P 500 index includes only large-cap stocks. Therefore, part of your equity investment should probably be in the small cap fund for diversification purposes. Note that a small cap index fund may be the best option, but there is no small cap index fund available in the 401k account.

CHAPTER 16 STEPHENSON REAL ESTATE RECAPITALIZATION 1.

If Stephenson wishes to maximize the overall value of the firm, it should use debt to finance the $45 million purchase. Since interest payments are tax deductible, debt in the firm’s capital structure will decrease the firm’s taxable income, creating a tax shield that will increase the overall value of the firm.

2.

Since Stephenson is an all-equity firm with 11 million shares of common stock outstanding, worth $48.50 per share, the market value of the firm is: Market value of equity = $48.50(11,000,000) Market value of equity = $533,500,000 So, the market value balance sheet before the land purchase is:

Assets Total assets 3.

a.

Market value balance sheet $533,500,000 Equity $533,500,000 Debt & Equity

$533,500,000 $533,500,000

As a result of the purchase, the firm’s pre-tax earnings will increase by $10 million per year in perpetuity. These earnings are taxed at a rate of 40 percent. Therefore, after taxes, the purchase increases the annual expected earnings of the firm by: Earnings increase = $10,000,000(1 – .40) Earnings increase = $6,000,000 Since Stephenson is an all-equity firm, the appropriate discount rate is the firm’s unlevered cost of equity, so the NPV of the purchase is: NPV = –$45,000,000 + ($6,000,000 / .105) NPV = $12,142,857

CHAPTER 31 CASE  C­61   b.

After the announcement, the value of Stephenson will increase by $12,142,857, the net present value of the purchase. Under the efficient-market hypothesis, the market value of the firm’s equity will immediately rise to reflect the NPV of the project. Therefore, the market value of Stephenson’s equity after the announcement will be: Equity value = $533,500,000 + 12,142,857 Equity value = $545,642,857

Old assets NPV of project Total assets

Market value balance sheet $533,500,000 12,142,857 Equity $545,642,857 Debt & Equity

$545,642,857 $545,642,857

Since the market value of the firm’s equity is $545,642,857 and the firm has 11 million shares of common stock outstanding, Stephenson’s stock price after the announcement will be: New share price = $545,642,857 / 11,000,000 New share price = $49.60 Since Stephenson must raise $45 million to finance the purchase and the firm’s stock is worth $49.60 per share, Stephenson must issue: Shares to issue = $45,000,000 / $49.60 Shares to issue = 907,187 c.

Stephenson will receive $45 million in cash as a result of the equity issue. This will increase the firm’s assets and equity by $45 million. So, the new market value balance sheet after the stock issue will be:

Cash Old assets NPV of project Total assets

Market value balance sheet $ 45,000,000 533,500,000 12,142,857 Equity $590,642,857 Debt & Equity

$590,642,857 $590,642,857

The stock price will remain unchanged. To show this, Stephenson will now have: Total shares outstanding = 11,000,000 + 907,187 Total shares outstanding = 11,907,187 So, the share price is: Share price = $590,642,857 / 11,907,187 Share price = $49.60

d.

The project will generate $10 million of additional annual pretax earnings forever. These earnings will be taxed at a rate of 40 percent. Therefore, after taxes, the project increases the annual earnings of the firm by $6 million. So, the aftertax present value of the earnings increase is: PVProject = $6,000,000 / .105 PVProject = $57,142,857 So, the market value balance sheet of the company will be:

Old assets PV of project Total assets 4.

a.

Market value balance sheet $533,500,000 57,142,857 Equity $590,642,857 Debt & Equity

$590,642,857 $590,642,857

Modigliani-Miller Proposition I states that in a world with corporate taxes: VL = VU + tCB As was shown in Question 3, Stephenson will be worth $590,642,857 if it finances the purchase with equity. If it were to finance the initial outlay of the project with debt, the firm would have $45 million worth of 7 percent debt outstanding. So, the value of the company if it financed with debt is: VL = $590,642,857 + .40($45,000,000) VL = $308,642,857

b.

After the announcement, the value of Stephenson will immediately rise by the present value of the project. Since the market value of the firm’s debt is $45 million and the value of the firm is $608,642,857, we can calculate the market value of Stephenson’s equity. Stephenson’s marketvalue balance sheet after the debt issue will be:

Value unlevered Tax shield Total assets

Market value balance sheet $590,642,857 Debt 18,000,000 Equity $608,642,857 Debt & Equity

$ 45,000,000 563,642,857 $608,642,857

Since the market value of Stephenson’s equity is $563,642,857 and the firm has 11 million shares of common stock outstanding, Stephenson’s stock price after the debt issue will be: Stock price = $563,642,857 / 11,000,000 Stock price = $51.24 5.

If Stephenson uses equity in order to finance the project, the firm’s stock price will remain at $49.60 per share. If the firm uses debt in order to finance the project, the firm’s stock price will rise to $51.24 per share. Therefore, debt financing maximizes the per share stock price of the firm’s equity.

CHAPTER 31 CASE  C­63  

CHAPTER 17 McKENZIE CORPORATION’S CAPITAL  BUDGETING 1.

We assume the $5,700,000 is spent immediately so we can ignore time value of money considerations. If we include the time value of money, the numerical solutions will change slightly, but the analysis will remain the same. The expected value of the company in one year without expansion is: V = .30($20,000,000) + .50($25,000,000) + .20($43,000,000) V = $27,100,000 And the expected value of the company in one year with expansion is: V = .30($22,000,000) + .50($32,000,000) + .20($52,000,000) V = $33,000,000 The company’s stockholders appear to be better off with expansion since the expected NPV of the project is positive. The difference in the expected value of the company with and without expansion is $5,900,000. If the required investment is $5,700,000, the expansion creates a positive increase in expected value for current shareholders. However, as further analysis will show, stockholders are actually worse off.

2.

The value of the company’s debt with low economic growth is the value of the company because the company value is less than the face value of the debt. In both other economic states, the value of the debt is the face value of the debt. So, the expected value of debt in one year without expansion is: VD = .30($20,000,000) + .50($25,000,000) + .20($25,000,000) VD = $23,500,000 And the value of the company’s debt in one year with expansion is: VD = .30($22,000,000) + .50($25,000,000) + .20($25,000,000) VD = $24,100,000

3.

The value of the company’s equity with low economic growth is zero both with and without expansion since the company value will be less than the face value of the debt. The value of equity with normal growth or high growth is the value of the company minus the $25,000,000 face value of debt. So, the expected value of the equity without expansion is: VE = .30($0) + .50($0) + .20($18,000,000) VE = $3,600,000 And the value of equity with expansion is: VE = .30($0) + .50($7,000,000) + .20($27,000,000) VE = $8,900,000 The value expected for bondholders from the expansion is the difference in the expected value of debt. So, with expansion, the company’s bondholders gain: Bondholder gain = $24,100,000 – 23,500,000 Bondholder gain = $600,000 And the value expected for stockholders is: Stockholder gain = $8,900,000 – 3,600,000 Stockholder gain = $5,300,000 The stockholder value increases by $5,300,000, but the expansion was funded entirely by equity, so the expected NPV of expansion for stockholders is actually: Stockholder NPV = –$5,700,000 + 5,300,000 Stockholder NPV = –$400,000

4.

Assuming bondholders are fully informed and they act rationally, they will expect the stockholders to act in their best interest and not expand, so the price of the bonds will not change. If the expansion is announced, the price of the bonds will increase.

5.

If they don’t expand, nothing will happen since it is already priced into the bond. If the company announces the expansion, they signal they are willing to sacrifice for the bondholders, so the company will receive a lower interest rate in the future.

6.

It is a stronger signal that stockholders are not acting in their best interest if the expansion is financed with cash on hand. If the company issues new equity, the expected loss in stock value is shared proportionally by the new investors, so the current stockholders will not bear the entire loss in stock value alone. By expanding with cash on hand, current stockholders are bearing the entire expected loss in stock value.

CHAPTER 18

CHAPTER 31 CASE  C­65  

THE LEVERAGED BUYOUT OF CHEEK  PRODUCTS, INC. In this leveraged buyout, the debt level of the company changes through time. Since the debt level changes through time, the APV method is appropriate for evaluating the LBO. The steps we must undertake are: Step 1: Calculating the present value of unlevered cash flows for the first five years. Step 2: Calculating the present value of the unlevered cash flows beyond the first five years. Step 3: Calculating the present value of interest tax shields for the first five years. Step 4: Calculating the present value of interest tax shields beyond the first five years. Step 1: Calculating the present value of unlevered cash flows for the first five years. The income statement presented does not include interest, so it is the projected unlevered cash flows of the company. To find the cash flows each year, we find the operating cash flow by adding depreciation back to net income. Next, we subtract any capital expenditures, changes in net working capital, and add the asset sales. So, the unlevered cash flows each year will be: Sales Costs Dep EBT Tax Net income Capital expenditures Change in NWC Asset sales Unlevered cash flows

2015 $2,749.00 731.00 485.00 $1,533.00 613.20 $919.80

2016 $3,083.00 959.00 516.00 $1,608.00 643.20 $964.80

2017 $3,322.00 1,009.00 537.00 $1,776.00 710.40 $1,065.60

2018 $3,400.00 1,091.00 564.00 $1,745.00 698.00 $1,047.00

2019 $3,539.00 1,149.00 575.00 $1,815.00 734.00 $1,089.00

$279 $(122) $1,419

$242 $(186) $1,028

$304 $101

$308 $95

$304 $108

$2,666.80

$2,452.80

$1,197.60

$1,208.00

$1,252.00

Since these are unlevered cash flows, we need to discount at the unlevered cost of equity. Because the company currently has no debt, the required return on assets is equal to the cost of equity. So, using this discount rate, we find the present value of the unlevered cash flows for the next five years will be: PV = $2,666.80 / 1.14 + $2,452.80 / 1.142 + $1,197.60 / 1.143 + $1,208 / 1.144 + $1,252 / 1.145 PV = $6,400.48

Step 2: Calculating the present value of the unlevered cash flows beyond the first five years. The assumption given is that the cash flows will grow at 3.5 percent into perpetuity. Again, we discount these cash flows at the unlevered return on equity. So, the value of these cash flows in Year 5 will be: Unlevered CF value in Year 5 = [$1,252(1 + .035)] / (.14 – .035) Unlevered CF value in Year 5 = $12,341.14 The value today of this terminal value is: PV = $12,341.14 / 1.145 PV = $6,409.60 Step 3: Calculating the present value of interest tax shields for the first five years. The interest tax shield each year is the interest paid times the tax rate. To find the present value of the interest tax shield, we need to discount these at the pretax cost of debt, so the present value of the interest tax shield for the first five years is: PV = ($1,927)(.40) / 1.125 + ($1,859)(.40) / 1.1252 + ($2,592)(.40) / 1.1253 + ($2,526)(.40) / 1.1254 + ($2,614)(.40) / 1.1255 PV = $3,211.89 Step 4: Calculating the present value of interest tax shields beyond the first five years. Finally, we must calculate the value of tax shields associated with debt used to finance the operations of the company after the first five years. The assumption given in the case is that debt will be reduced and maintained at 25 percent of the value of the firm from that date forward. Under this assumption it is appropriate to use the WACC method to calculate a terminal value for the firm at the target capital structure. This in turn can be decomposed into an all-equity value and a value from tax shields. Note that we need to use the interest rate on the debt beyond Year 5 in these calculations. If the capital structure changes after the first five years, the levered cost of equity can be found with Modigliani-Miller Proposition II with corporate taxes: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .14 + (.25)(.14 – .08)(1 – .40) RS = .1490, or 14.90% Now, we can calculate the WACC for the company beyond Year 5. The WACC at this point will be: RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS RWACC = [.25](1 – .40)(.08) + [1 / 1.25](.1490) RWACC = .1312, or 13.12% We can use the WACC to calculate the terminal value of the levered company, which will be: VL = [$1,252(1 + .035)] / (.1312 – .035) VL = $13,470.06

CHAPTER 31 CASE  C­67   Using Modigliani-Miller’s valuation of a levered firm: VL = VU + tCB we can value the interest tax shield as: $13,470.06 = $12,341.14 + Interest tax shield Interest tax shield = $1,128.92 This is the value of the interest tax shield beyond Year 5. Discounting this at the cost of debt over the first five years, we find the value today is:1 PV = $1,128.92 / 1.1255 PV = $626.47 We have valued all future cash flows of the company. The value of the unlevered cash flows today is: Value of unlevered CF = $6,400.48 + 6,409.60 Value of unlevered CF = $12,810.08 And the value of the interest tax shield today is: Value of interest tax shield = $3,211.89 + 626.47 Value of interest tax shield = $3,838.36 So, the total value of the company today is: Value of company today = $12,810.08 + 3,838.36 Value of company today = $16,648.44 So, the most the group should offer per share is: Price = $16,648.44 / 425 Price = $39.17

CHAPTER 19 ELECTRONIC TIMING, INC. 1.The value of the company will decline by the amount of the dividend. Ignoring taxes, shareholders wealth will not be affected because the stock price will drop by the amount of the dividend payment.

1 A good argument can be made that since post-2019 debt levels are proportional to firm value, the tax shields are as risky as the firm and should be discounted at the rate R0.

2.

The value of the company could increase or decrease. If the company is over-levered, paying off debt can lower the interest rate on debt, and decrease financial distress costs. If there are no financial distress costs, capital structure theory argues that increasing debt can increase the value of the company because of the interest tax shield.

3.

The PE ratio will fall and the ROA and ROE will increase, but the changes are irrelevant.

4.

A regular dividend payment is something the company should probably not undertake. A company rarely begins regular dividend payments that it will be unable to continue in the future. Cessation of dividend payments is viewed as a negative signal by the market.

5.

The implication is that the company should not retain earnings unless the ROE of the new project is greater than the shareholders required return on equity. This is an intuitive result. Shareholders want the company to retain earnings for future growth if the earnings will earn a greater return than shareholders require. If the return on the retained earnings is lower than shareholders’ required return, the company is lowering shareholder value.

6.     The decision does depend on the organizational form of the company. Money paid to shareholders of a corporation are dividends, and currently taxed at the lower dividend tax rate. Money paid to the owners of an LLC is considered income, and taxed at the applicable personal income tax rate.

CHAPTER 20 EAST COAST YACHTS GOES PUBLIC 1.

The main difference in the costs is the reduced possibility of underpricing in a Dutch auction. As to which is better, we don’t actually know. In theory, the Dutch auction should be better since it should eliminate underpricing. However, as Google shows, underpricing can still exist in a Dutch auction. Whether the underpricing is as severe in a Dutch auction as it would be in a traditional underwritten offer is unknown.

2.

There is no way to calculate the optimum size of the IPO, so whether Dan is correct or Larissa is correct will only be told in time. The disadvantages of raising the extra cash in the IPO include the agency costs of excess cash. The extra cash may encourage management to act carelessly. The extra cash will also earn a small return unless invested in income producing assets. At best, cash and shortterm investments are a zero NPV investment. The advantages of the increased IPO size include the increased liquidity for the company, and the lower probability that the company will have to go back to the primary market in the near term future. The increased size will also reduce the costs of the IPO as a percentage of funds raised, although this may not be a large advantage.

3.

The underwriter fee is 7 percent of the amount raised, or: Underwriter fee = $85,000,000(.07) Underwriter fee = $5,950,000

CHAPTER 31 CASE  C­69  

Since the company must currently provide audited financial statements due to the bond covenants, the audit costs are not incremental costs and should not be included in the calculation of the fees. So, the sum of the other fees is: Total other fees = $1,800,000 + 15,000 + 20,000 + 100,000 + 8,500 + 525,000 + 75,000 Total other fees = $2,543,500 This means the total fees are: Total fees = $5,950,000 + 2,543,500 Total fees = $8,493,500 The net amount raised is the IPO offer size minus the underwriter fee, or: Net amount raised = $85,000,000 – 5,950,000 Net amount raised = $79,050,000 So, the fees as a percentage of the net amount to the company are: Fee percentage = $8,493,500 / $79,050,000 Fee percentage = .1074, or 10.74%

4.

Because of legal repercussions, you should not provide specific advice on which option the employees should choose. There are advantages and disadvantages to each. If the employee tenders the stock to be sold in the IPO, the employee will lose out on any underpricing. This could be a significant cost. However, if the employee retains the stock, he/she must hold the stock for the lockup period, typically 180 days. Additionally, during the lockup period, the employee is legally prohibited from hedging the price risk of the stock with any derivatives. And heavy selling by insiders is considered a negative signal by the market. Another risk in not selling in the IPO is that after the lockup period expires, the employees may be considered insiders, subject to SEC restrictions on selling stock.

CHAPTER 21 THE DECISION TO LEASE OR BUY AT  WARF COMPUTERS 1.

The decision to buy or lease is made by looking at the incremental cash flows. The incremental cash flows from leasing the machine are the security deposit, the lease payments, the tax savings on the lease, the lost depreciation tax shield, the saved purchase price of the machine, and the lost salvage value. The salvage value of the equipment in four years will be: Aftertax salvage value = $440,000 – $440,000(.35) Aftertax salvage value = $286,000 This is an opportunity cost to Warf Computers since if the company leases the equipment it will not be able to sell the equipment in four years. The lease payments are due at the beginning of each year, so the incremental cash flows are:

Saved purchase Lost salvage value Lost dep. tax shield Security deposit Lease payment Tax on lease payment Cash flow from leasing

Year 0 $3,600,000

–210,000 –935,000 327,250 $2,782,250

The aftertax cost of debt is: Aftertax cost of debt = .11(1 – .35) Aftertax cost of debt = .0715, or 7.15% And the NAL of the lease is:

Year 1

Year 2

Year 3

–$419,958

–$560,070

–$186,606

–935,000 327,250 –$1,027,708

–935,000 327,250 –$1,167,820

–935,000 327,250 –$794,356

Year 4 –$286,000 –93,366 210,000

–$169,366

CHAPTER 31 CASE  C­71   NAL = $2,782,250 – $1,027,708 / 1.0715 – $1,167,820 / 1.07152 – $794,356 / 1.07153 – $169,366 / 1.07154 NAL = $31,753.25 The company should lease the equipment.

2.

The book value of the equipment in Year 2 will be: Book value = $3,600,000 – $3,600,000(.3333 + .4445) Book value = $799,920 So, the aftertax salvage value in Year 2 will be: Aftertax salvage value = $1,144,000 + ($799,920 – 1,440,000)(.35) Aftertax salvage value = $1,215,972 So, the NAL of the lease under the new terms would be:

Saved purchase Lost salvage value Lost dep. tax shield Lease payment Tax on lease payment Cash flow from leasing

Year 0 $3,600,000

–1,650,000 577,500 $2,527,500

Year 1

–$419,958 –1,650,000 577,500 –$1,492,458

Year 2 –$1,215,972 –560,070

–$1,776,042

So, the NAL of the lease under these terms is: NAL = $2,527,500 – $1,492,458 / 1.0715 – $1,776,042 / 1.07152 NAL = –$412,291.60 The NAL of the lease is negative under these terms, so it appears the terms are less favorable for the lessee. However, the lease will likely be classified as an operating lease. The lease is now for two years, which is less than 75 percent of the equipment’s life. Using the company’s cost of debt, the present value of the lease payments is: PV of lease payments = $1,650,000 + $1,650,000 / 1.11 PV of lease payments = $3,136,486.49 This is less than 90 percent of the price of the equipment. As long as the lease contract does transfer ownership to the lessee at the end of the contact, or allow for a purchase at a bargain price, the FAS 13 conditions for a capital lease are not met. As such, the reason for suggesting the revised lease terms is unethical on Nick’s part. Also, notice that the question also states that if the lease is renewed in two years, the lessor will allow for the increased lease payments made over the first two years. This is also an indication that the revision is for less than ethical reasons.

CHAPTER 31 CASE  C­73   3.

4.

a.

The inclusion of a right to purchase the equipment will have no effect on the value of the lease. If the company does not purchase the equipment, it can go on the market and purchase identical equipment at the same price.

b.

The right to purchase the equipment at a fixed price will have increase the value of the lease. If the company can purchase the equipment at the end of the lease at below market value, it will save money, or at a minimum, can purchase the equipment at the fixed price and resell it in the open market. This is a real option, therefore has value to the lessee. It is a call option on the equipment. As such, it must have a value until it expires or is exercised. It is also important to note that this would likely make the lease contract a capitalized lease.

c.

The right to purchase the equipment at a bargain price is also a real option for the lessee, and will increase the value of the lease. It is a call option, and therefore will have value until it expires or is exercised. This contract condition will definitely ensure the lease is classified as a capitalized lease.

The cancellation option is also a real option. The cancellation option is a put option on the equipment. It will increase the value of the lease since the lessee will only exercise the option when it is to the lessee’s advantage.

CHAPTER 22 CLISSOLD INDUSTRIES OPTIONS 1.

Since the Black–Scholes model uses the standard deviation of the underlying asset, and there is only one underlying asset no matter how many strike prices are available, we would only expect to see one implied standard deviation.

2.

To find the implied volatility for an option, you can set up a spreadsheet to calculate the option price. The Solver function in Excel will allow you to input the desired price and will solve for the desired unknown variable. We did this (the spreadsheet is available), and the implied standard deviation for each of the options is: Strike Price $50 55 60 65

3.

Option Price $12.78 10.14 7.99 5.81

Implied Standard Deviation 75.04% 70.96 68.21 63.22

There are two possible explanations. The first is model misspecification. Although the Black– Scholes option pricing model is widely acclaimed, it is possible that the model specifications are incorrect. One potential variable that is incorrectly specified is the assumption of constant volatility.

In fact, the volatility of the underlying stock is itself volatile, and will increase or decrease over time. The Black–Scholes model may also ignore important variables. For example, Fisher Black describes trades he, Myron Scholes, Robert Merton, and others made when the model was first developed (Black, Fisher, 1989, “How we came up with the option pricing formula,” The Journal of Portfolio Management, Winter, 4-8.) As in any potential arbitrage opportunity, they purchased underpriced assets, in this case warrants on National General stock. Unfortunately, soon after they took this position, American Financial announced a tender offer for National General, which sharply reduced the value of the warrants. The market had already priced the potential tender offer in the warrant price, while this variable was not accounted for in the Black–Scholes model. A second possible explanation is liquidity. At- or near-the-money options tend to be more liquid than deep in-the-money or deep out-of-the-money options. Since options that are not near-the-money are less liquid, the price should carry a liquidity premium. 4.

The VIX is a benchmark for stock market volatility. The VIX is based on option prices, which reflect investors' consensus view of future expected stock market volatility. During periods of market turmoil, both option prices and the VIX tend to rise. When the market is calmer, investor fear, option prices, and the VIX decline.

5.

The VIX uses eight different S&P 100 Index (OEX) option series to represent the implied volatility of a hypothetical OEX option with exactly 30 days to expiration.

CHAPTER 23 EXOTIC CUISINES’ EMPLOYEE STOCK  OPTIONS 1.

We can use the Black–Scholes equation to value the employee stock options. We need to use the risk-free rate that is the same as the maturity as the options. So, assuming expiration in three years, the value of the stock options per share of stock is: d1 = [ln($27.15/$40) + (.038 + .602/2)  3] / (.60  d2 = .2564 – (.60 

3 ) = .2564

3 ) = –.7828

N(d1) = .6012 N(d2) = .2169 Putting these values into the Black-Scholes model, we find the option value is: C = $27.15(.6079) – ($40e–.038(3))(.2169)

CHAPTER 31 CASE  C­75   C = $8.58 Assuming expiration in 10 years, the value of the stock options per share of stock is: d1 = [ln($27.15/$40) + (.044 + .602/2)  10] / (.60  d2 = .9764 – (.60 

10 ) = .9764

10 ) = –.9210

N(d1) = .8356 N(d2) = .1785 Putting these values into the Black–Scholes model, we find the option value is: C = $27.15(.8356) – ($40e–.044(10))(.1785) C = $18.09 2.

Whether you should exercise the options in three years depends on several factors. A primary factor is how long you plan to stay with the company. If you are planning to leave next week, you should exercise the options. A second factor is how the option exercise will affect your taxes.

3.

The fact that the employee stock options are not traded decreases the value of the options. A basic way to understand this is to realize that an option always has value since, ignoring the premium, it can never lose money. The right to sell an option also has to have value. If the right to sell is removed, it decreases the price of the option.

4.

The rationale for employee stock options is to reduce agency costs by better aligning employee and shareholder interests. Vesting requires employees to work at a company for a specified time, which means the employee actions are actually part of the company performance. Vesting is also a “golden handcuff”. The employee is less likely to leave the company if in-the-money employee stock options will vest soon.

5.

The evaluation of the argument for or against repricing is open-ended. There are valid reasons on both sides of the discussion. Repricing increases the value of the employee stock option. Consider an extreme: A company announces the employee stock options will be worth a minimum of $10 at expiration. Since all values less than $10 are no longer possible, the value of the option increases.

6.

Employee stock options increase in value if the stock price increases; however, the stock price can increase because of a general market increase. Consider a company of average risk in a bull market that has a large return for several years. The company’s stock should closely mirror the market return, even though most of the stock price increase is due to the general market increase. Similarly, if the market falls, the company’s stock will likely fall as well, even if the company is doing well. A better method of valuing employee stock options might be to reward employees for company performance in excess of the market performance, adjusted for the company’s level of risk.

CHAPTER 24 S&S AIR’S CONVERTIBLE BOND  1.

Chris is suggesting a conversion price of $45 because it means the stock price will have to increase before the bondholders can benefit from the conversion. Even though the company is not publicly traded, the conversion price is important. First, the company may go public in the future. The case does not discuss whether the company has plans to go public, and if so, how soon it might go public. If the company does goes public, the bondholders will have an active market for the stock if they convert. Second, even if the company does not go public, the bondholders could potentially have an equity interest in the company. This equity interest can be sold to the original owners, or someone else. The potential problem with private equity is that the market is not as liquid as the market for a public company. This illiquidity lowers the value of the stock. We can use the PE ratio to estimate the current stock price. Doing so, we get: P/E = Price/EPS 17.50 = Price/$1.75 Price = $30.63

2.

The floor value is the maximum of the conversion value and the intrinsic value. The conversion value of the bond is given as $680.56. The intrinsic value of the bond is: Intrinsic value = $25(PVIFA4%,20) + $1000(PVIF4%,20)

CHAPTER 31 CASE  C­77   Intrinsic value = $703.11 So, the floor value of the bond is $703.11. This means that if the company offered bonds with the same coupon rate and no conversion feature, they would be able to sell them for $703.11. 3.

The conversion ratio of the bonds is: Conversion ratio = $1,000/$45 = 22.22 So, each bond can be converted to 22.22 shares of stock.

4.

The conversion premium is the increase in stock price necessary to make the conversion option possible. Since the stock is currently selling for $30.63, and the conversion price is $45, the conversion premium of the bond is: Conversion premium = ($45 – 30.63) / $30.63 Conversion premium = .4694 or 46.94%

5.

The option value of a convertible bond is defined as the difference between the market value of the bond and the maximum of its straight value and conversion value. Since the bond is sold at par value, the option value is: Option value = Market value – Max[Straight value, Conversion value] Option value = $1,000 – Max[$703.11, $680.56] Option value = $1,000 – 703.11 Option value = $296.89

6.

Todd’s argument is wrong because it ignores the fact that if the company does well, bondholders will be allowed to participate in the company’s success. If the stock price rises to $50, bondholders are effectively allowed to purchase stock at the conversion price of $45.

7.

Mark’s argument is incorrect because the company is issuing debt with a lower coupon rate than they would have been able to otherwise. If the company does poorly, it will receive the benefit of a lower coupon rate.

8.

Reconciling the two arguments requires that we remember our central goal: to increase the wealth of the existing shareholders. Thus, with 20–20 hindsight, we see that issuing convertible bonds will turn out to be worse than issuing straight bonds and better than issuing common stock if the company prospers. The reason is that the prosperity has to be shared with bondholders after they convert. In contrast, if a company does poorly, issuing convertible bonds will turn out to be better than issuing straight bonds and worse than issuing common stock. The reason is that the firm will have benefited from the lower coupon payments on the convertible bonds. Both of the arguments have a grain of truth; we just need to combine them. Ultimately, which option is better for the company will only be known in the future and will depend on the performance of the company. The table below illustrates this point.

Convertible bonds issued instead of straight bonds Convertible bonds issued instead of common stock 9.

If the company does poorly Low stock price and no conversion Cheap financing because coupon rate is lower (good outcome). Expensive financing because firm could have issued common stock at high prices (bad outcome).

If the company prospers High stock price and conversion Expensive financing because bonds are converted, which dilutes existing equity (bad outcome). Cheap financing because firm issues stock at high prices when bonds are converted (good outcome).

The call provision allows the company to redeem the bonds at the company’s discretion. If the company’s stock appears to be poised to rise, the company can call the outstanding bonds. It could be possible that the bondholders would benefit from converting the bonds at that point, but it would eliminate the potential future gains to the bondholders.

CHAPTER 31 CASE  C­79  

CHAPTER 25 WILLIAMSON MORTGAGE, INC. 1.

Jerry’s mortgage payments form a 25-year annuity with monthly payments, discounted at the longterm interest rate of 5.5 percent. We can solve for the payment amount so that the present value of the annuity equals $500,000, the amount of principal that he plans to borrow. The monthly mortgage payment will be: $500,000 = C(PVIFA5.5%/12,300) C = $3,070.44

2.

The most significant risk that she faces is interest rate risk. If the current market rate of interest rises between today and the date the mortgage is sold, the fair value of the mortgage will decrease, and Max will only be willing to purchase the mortgage for a price less than $500,000. If this is the case, she will not be able to loan Jerry the full $500,000 promised.

3.

Treasury bond prices have an inverse relationship with interest rates. As interest rates rise, Treasury bonds become less valuable; as interest rates fall, Treasury bonds become more valuable. Since Jennifer will be hurt when interest rates rise, she is also hurt when Treasury bonds decrease in value. In order to protect herself from decreases in the price of Treasury bonds, she should take a short position in Treasury bond futures to hedge this interest rate risk. Since three-month Treasury bond futures contracts are available and each contract is for $100,000 of Treasury bonds, she would take a short position in five 3-month Treasury bond futures contracts in order to hedge her $500,000 exposure to changes in the market interest rate over the next three months

4.

a.

If the market interest rate is 6.2 percent on the date that Jennifer meets with the Max, the fair value of the mortgage is the present value of an annuity that makes monthly payments of $3,070.44 for 25 years, discounted at 6.2 percent, or: Mortgage value = $3,070.44(PVIFA6.2%/12,300) Mortgage value = $467,639.54

b.

5.

An increase in the interest rate will cause the value of the T-bond futures contracts to decrease. The long position will lose and the short position will gain. Since Jennifer is short in the futures, the futures gain will offset the loss in value of the mortgage.

a. If the market interest rate is 4.6 percent on the date that Jennifer meets with Max, the fair value of the mortgage is the present value of an annuity that makes monthly payments of $3,070.44 for 25 years, discounted at 4.6 percent, or: Mortgage value = $3,070.44(PVIFA4.6%/12,300) Mortgage value = $546,804.59

b.

6.

An increase in the interest rate will cause the value of the Treasury bond futures contracts to increase. The long position will gain and the short position will lose. Since Jennifer is short in the futures, the futures loss will be offset by the gain in value of the mortgage.

The biggest risk is that the hedge is not a perfect hedge. If interest rates change, the fact that Treasury bond interest is semiannual, while the mortgage payments are monthly, may affect the relative value of the two. Additionally, while a change in one of the interest rates will likely coincide with a change in the other interest rate, the change does not have to be the same. For example, the Treasury rate could increase 20 basis points, and the mortgage rates could increase by 40 basis points. The fact that this is not a perfect hedge simply means that the gain/loss from the futures contracts may not exactly offset the loss/gain in the mortgage. We would expect, especially given the short-term nature of the hedge, that the loss in one instrument would be similar to the gain in the other instrument.

CHAPTER 26 KEAFER MANUFACTURING WORKING  CAPITAL MANAGEMENT 1.

The cash flow each quarter will consist of the sales collection, minus the suppliers paid, expenses, dividends, interest, and capital outlays. The cash flows for each quarter will be:

Collections from previous quarter Collections from current quarter sales Payments to suppliers for previous quarter Payments to suppliers for current quarter Expenses Dividends and interest Outlay Net cash flow

Cash Flow Q1 Q2 $607,500.00 $753,768.00

Q3 $780,444.00

Q4 $769,500.00

436,392.00

451,836.00

445,500.00

420,948.00

–350,436.00

–362,838.00

–357,750.00

–338,034.00

–253,302.00 –297,540.00 –185,000.00

–249,750.00 –308,070.00 –185,000.00

–264,215.52 –287,010.00 –185,000.00

–$42,386.00

$99,946.00

–235,986.00 –303,750.00 –185,000.00 –390,000.00 –$246,542.00

Cash Balance Q1 Q2

Q3

$116,188.48

Q4

CHAPTER 31 CASE  C­81   Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus –deficit

$210,000.00 –42,386.00 $167,614.00 135,000.00 $32,614.00

$167,614.00 99,946.00 $267,560.00 135,000.00 $132,560.00

$267,560.00 –246,542.00 $21,018.00 135,000.00 –$113,982.00

$21,018.00 116,188.48 $137,206.48 135,000.00 $2,206.48

The short-term financial plan looks like this:

Target cash balance Net cash inflow New short-term investments Income on short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus –deficit Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt

Short-term Financial Plan $135,000.00 $135,000.00 –42,386.00 99,946.00 0 –100,321.00 375.00 375.00 42,011.00 0 0 0 0 0 0 0 $135,000.00 $135,000.00 –135,000.00 –135,000.00 $0 $0 $75,000.00 75,000.00 0 $0

$75,000.00 175,321.00 0 $0

$135,000.00 –246,542.00 0 876.61 175,321.00 70,344.40 0 0 $135,000.00 –135,000.00 $0

$135,000.00 116,188.48 –44,999.95 0 0 0 –844.13 –70,344.40 $135,000.00 –135,000.00 $0

$175,321.00 0 0 $70,344.40

$0 44,999.95 70,344.40 $0

The interest calculations for each quarter and the net cash cost are: Q1: Q2: Q3: Q4:

Excess funds at start of quarter of Excess funds at start of quarter of Excess funds at start of quarter of Shortage of funds at start of quarter of Net cash cost Q1 Q2 Q3 Q4 Cash generated by short-term financing

$75,000.00 $75,000.00 $175,321.00 $70,344.40

$375.00 375.00 876.61 –844.13 $782.47

earns earns earns costs

$375.00 $375.00 $876.61 $844.13

in income. in income. in income. in interest.

CHAPTER 31 CASE  C­83   2.

If Keafer reduces its target cash balance to $90,000, the cash flows each quarter will remain the same, so they will not be repeated here. The cash balance and short-term financial plan will be: Cash Balance Q1 Q2 $210,000.00 $167,614.00 –42,386.00 99,946.00 $167,614.00 $267,560.00 90,000.00 90,000.00 $77,614.00 $177,560.00

Q3 $267,560.00 –246,542.00 $21,018.00 90,000.00 –$68,982.00

Q4 $21,018.00 116,188.48 $137,206.48 90,000.00 $47,206.48

Short-term Financial Plan $90,000.00 $90,000.00 –42,386.00 99,946.00 0 –100,546.00 600.00 600.00 41,786.00 0 0 0 0 0 0 0 $90,000.00 $90,000.00 –90,000.00 –90,000.00 $0 $0

$90,000.00 –246,542.00 0 1,102.73 220,546.00 24,893.27 0 0 $90,000.00 –90,000.00 $0

$90,000.00 116,188.48 –90,996.49 0 0 0 –298.72 –24,893.27 $90,000.00 –90,000.00 $0

$220,546.00 0 0 $24,893.27

$0 90,996.49 24,893.27 $0

Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus –deficit

Target cash balance Net cash inflow New short-term investments Income on short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus –deficit Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt Q1 : Q2 : Q3 : Q4 :

$120,000.00 120,000.00 0 $0

$120,000.00 220,546.00 0 $0

Excess funds at start of quarter of

$120,000.00

earns

$600.00

in income.

Excess funds at start of quarter of

$120,000.00

earns

$600.00

in income.

Excess funds at start of quarter of

$220,546.00

earns

$1,102.73

in income.

Shortage of funds at start of quarter of

$24,893.27

costs

$298.72

in interest.

Net cash cost Q1 Q2 Q3 Q4

$600.00 600.00 1,102.73 –298.72

Cash generated by short-term financing

$2,004.01

CHAPTER 31 CASE  C­85   3.

If the sales growth rate is 11 percent, the cash flows for each quarter will be:

Collections from previous quarter Collections from current quarter sales Payments to suppliers for previous quarter Payments to suppliers for current quarter Expenses Dividends and interest Outlay Net cash flow

Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus –deficit

Cash Flow Q1 Q2 $607,500.00 $774,706.00

Q3 $802,123.00

Q4 $790,875.00

448,514.00

464,387.00

457,875.00

432,641.00

–360,170.33

–372,916.83

–367,687.50

–347,423.83

–260,338.17 –305,805.00 –185,000.00

–256,687.50 –316,627.50 –185,000.00

–279,098.03 –294,982.50 –185,000.00

–$55,299.50

$107,861.17

–242,541.17 –312,187.50 –185,000.00 –390,000.00 –$237,418.17

Cash Balance Q1 Q2 $210,000.00 $154,700.50 –55,299.50 107,861.17 $154,700.50 $262,561.67 135,000.00 135,000.00 $19,700.50 $127,561.67

Q3 $262,561.67 –237,418.17 $25,143.50 135,000.00 –$109,856.50

Q4 $25,143.50 117,011.64 $142,155.14 135,000.00 $7,155.14

$135,000.00 –237,418.17 0 916.18 183,236.17 53,265.82 0 0 $135,000.00 –135,000.00 $0

$135,000.00 117,011.64 –63,106.63 0 0 0 –639.19 –53,265.82 $135,000.00 –135,000.00 $0

$183,236.17 0 0 $53,265.82

$0 63,106.63 53,265.82 $0

$117,011.64

The short-term financial plan looks like this:

Target cash balance Net cash inflow New short-term investments Income on short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus –deficit Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt

Short-term Financial Plan $135,000.00 $135,000.00 –55,299.50 107,861.17 0 –108,236.17 375.00 375.00 54,924.50 0 0 0 0 0 0 0 $135,000.00 $135,000.00 –135,000.00 –135,000.00 $0 $0 $75,000.00 75,000.00 0 $0

$75,000.00 183,236.17 0 $0

CHAPTER 31 CASE  C­87   The interest calculations for each quarter and the net cash cost are: Q1: Q2: Q3: Q4:

Excess funds at start of quarter of Excess funds at start of quarter of Excess funds at start of quarter of Shortage of funds at start of quarter of

$75,000.00 $75,000.00 $183,236.17 $53,265.82

Net cash cost Q1 Q2 Q3 Q4 Cash generated by short-term financing

earns earns earns costs

$375.00 $375.00 $916.18 $639.19

in income. in income. in income. in interest.

$375.00 375.00 916.18 –639.19 $1,026.99

If the sales growth rate is 5 percent, the cash flows for each quarter will be:

Collections from previous quarter Collections from current quarter sales Payments to suppliers for previous quarter Payments to suppliers for current quarter Expenses Dividends and interest Outlay Net cash flow

Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus –deficit

Cash Flow Q1 Q2 $607,500.00 $732,830.00

Q3 $758,765.00

Q4 $748,125.00

424,270.00

439,285.00

433,125.00

409,255.00

–340,701.67

–352,759.17

–347,812.50

–328,644.17

–246,265.83 –289,275.00 –185,000.00

–242,812.50 –299,512.50 –185,000.00

–249,740.75 –279,037.50 –185,000.00

–$29,472.50

$92,030.83

–229,430.83 –295,312.50 –185,000.00 –390,000.00 –$255,665.83

Cash Balance Q1 Q2 $210,000.00 $180,527.50 –29,472.50 92,030.83 $180,527.50 $272,558.33 135,000.00 135,000.00 $45,527.50 $137,558.33

Q3 $272,558.33 –255,665.83 $16,892.50 135,000.00 –$118,107.50

Q4 $16,892.50 114,957.58 $131,850.08 135,000.00 –$3,149.92

$114,957.58

The short-term financial plan looks like this:

Target cash balance Net cash inflow New short-term investments Income on short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus –deficit Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt

Short-term Financial Plan $135,000.00 $135,000.00 –29,472.50 92,030.83 0 –92,405.83 375.00 375.00 29,097.50 0 0 0 0 0 0 0 $135,000.00 $135,000.00 –135,000.00 –135,000.00 $0 $0 $75,000.00 75,000.00 0 $0

$75,000.00 167,405.83 0 $0

$135,000.00 –255,665.83 0 837.03 167,405.83 87,422.97 0 0 $135,000.00 –135,000.00 $0

$135,000.00 114,957.58 –26,485.54 0 0 0 –1,049.08 –87,422.97 $135,000.00 –135,000.00 $0

$167,405.83 0 0 $87,422.97

$0 26,485.54 87,422.97 $0

The interest calculations for each quarter and the net cash cost are: Q1: Q2: Q3: Q4:

Excess funds at start of quarter of Excess funds at start of quarter of Excess funds at start of quarter of Shortage of funds at start of quarter of Net cash cost Q1 Q2 Q3 Q4 Cash generated by short-term financing

$75,000.00 $75,000.00 $167,405.83 $87,422.97

$375.00 375.00 837.03 –1,049.08 $537.95

earns earns earns costs

$375.00 $375.00 $837.03 $1,049.08

in income. in income. in income. in interest.

CHAPTER 31 CASE  C­89   4.

Since the only period in which there is borrowing is the third period, we can set the ending shortterm debt in Quarter 3 equal to zero and use Solver. Doing so, we find the necessary sales growth rate is 21 percent. The short-term financial plan would be:

Collections from previous quarter Collections from current quarter sales Payments to suppliers for previous quarter Payments to suppliers for current quarter Expenses Dividends and interest Outlay Net cash flow

Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus –deficit

Cash Flow Q1 Q2 $607,500.00 $844,499.33

Q3 $874,386.33

Q4 $862,125.00

488,920.67

506,223.67

499,125.00

471,617.67

–392,618.11

–406,512.94

–400,812.50

–378,723.28

–283,792.06 –333,355.00 –185,000.00

–279,812.50 –345,152.50 –185,000.00

–331,651.19 –321,557.50 –185,000.00

–$98,344.50

$134,245.06

–264,391.72 –340,312.50 –185,000.00 –390,000.00 –$207,005.39

Cash Balance Q1 Q2 $210,000.00 $111,655.50 –98,344.50 134,245.06 $111,655.50 $245,900.56 135,000.00 135,000.00 –$23,344.50 $110,900.56

Q3 $245,900.56 –207,005.39 $38,895.17 135,000.00 –$96,104.83

Q4 $38,895.17 116,810.70 $155,705.87 135,000.00 $20,705.87

$116,810.70

The short-term financial plan looks like this:

Target cash balance Net cash inflow New short-term investments Income on short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus –deficit

Short-term Financial Plan $135,000.00 $135,000.00 –98,344.50 134,245.06 0 –134,620.06 375.00 375.00 97,969.50 0 0 0 0 0 0 0 $135,000.00 $135,000.00 –135,000.00 –135,000.00 $0 $0

Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt

$75,000.00 75,000.00 0 $0

$75,000.00 209,620.06 0 $0

$135,000.00 –207,005.39 0 1,048.10 205,957.29 0 0 0 $135,000.00 –135,000.00 $0

$135,000.00 116,810.70 –116,829.02 18.31 0 0 0 0 $135,000.00 –135,000.00 $0

$209,620.06 3,662.77 0 $0

$3,662.77 120,491.78 0 $0

The interest calculations for each quarter and the net cash cost are: Q1: Q2: Q3: Q4:

Excess funds at start of quarter of Excess funds at start of quarter of Excess funds at start of quarter of Excess funds at start of quarter of Net cash cost Q1 Q2 Q3 Q4 Cash generated by short-term financing

$75,000.00 $75,000.00 $209,620.06 $3,662.77

earns earns earns earns

$375.00 $375.00 $1,048.10 $18.31

in income. in income. in income. in income.

$375.00 375.00 1,048.10 18.31 $1,816.41

CHAPTER 27 CASH MANAGEMENT AT RICHMOND  CORP.

CHAPTER 31 CASE  C­91  

1.

The amount the company will have available is the future value of the transfers, which are an annuity. The amount of each transfer is one minus the wire transfer cost, times the number of transfers, which is four since there are four banks, times the amount of each transfer. So, the total available in two weeks will be: Amount available = (1 – .002){4[$185,000(FVIFA.068%,14)]} Amount available = $10,385,104.15

2.

The bank will accept the ACH transfers from the four different banks, so the company incurs a transfer fee from each collection center. The future value of the deposits will now be: Value of ACH = [4($185,000 – 200)(FVIFA.075%,14)]/1.00075 Value of ACH = $10,391,608.36 The company should go ahead with the plan since the future value is higher.

3.

To find the cost at which the company is indifferent, we set the amount available we found in Question 1 equal to the cost equation we used in Question 2. Setting up this equation where X stands for the ACH transfer cost, we find: [4($185,000 – $X)(FVIFA.075%,14)]/1.00075 = $10,385,104.15 X = $315.67

CHAPTER 28 CREDIT POLICY AT BRAAM  INDUSTRIES To decide on the optimal credit policy, we need to calculate the NPV of each policy. We will begin with the calculation of the NPV of the current policy. Current Policy First, we need to calculate the average daily sales which are: Average daily sales = $116,000,000/365 Average daily sales = $317,808.22 Now, we need to calculate the daily interest rate: Daily interest rate = (1 + .06)1/365 – 1 = .01597%

Next, we need the average daily costs. We will begin with the average daily variable costs, which are 45 percent of sales. So, the average daily variable costs are: Average daily variable costs = .45($116,000,000/365) Average daily variable costs = $143,013.70 Under the current policy, the default rate is 2.1 percent, so the average daily defaults will be: Average daily defaults = .021($116,000,000/365) Average daily defaults = $6,673.97 The current policy has administrative costs equal to 1.6 percent of sales, so the average daily administrative costs are: Average daily administrative costs = .016($116,000,000/365) Average daily administrative costs = $5,084.93 We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest rate, the periodic rate for the 38 day collection period is: Interest rate = (1 + .0001597 / 365)38 – 1 Interest rate = .00609, or .609% Since the credit policy will exist into perpetuity, the NPV is: NPV = –$143,013.70 + ($317,808.22 – 143,013.70 – 6,673.97 – 5,084.93) / .00609 NPV = $26,650,947.25

CHAPTER 31 CASE  C­93   Option 1 Under Option 1, the average daily sales are: Average daily sales = $130,000,000/365 Average daily sales = $356,164.38 The average daily variable costs will be: Average daily variable costs = .45($130,000,000/365) Average daily variable costs = $160,273.97 Under the Option 1, the default rate is 2.6 percent, so the average daily defaults will be: Average daily defaults = .026($130,000,000 / 365) Average daily defaults = $9,260.27 Option 1 has administrative costs equal to 2.4 percent of sales, so the average daily administrative costs are: Average daily administrative costs = .024($130,000,000/365) Average daily administrative costs = $8,547.95 We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest rate, the periodic rate for the 41 day collection period is: Interest rate = (1 + .0001597 / 365)41 – 1 Interest rate = .00657, or .657% Since the credit policy will exist into perpetuity, the NPV is: NPV = –$160,273.97 + ($356,164.38 – 160,273.97 – 9,260.27 – 8,547.95) / .00657 NPV = $26,958,531.53 Option 2 Under Option 2, the average daily sales are: Average daily sales = $129,000,000/365 Average daily sales = $353,424.66 The average daily variable costs will be: Average daily variable costs = .45($129,000,000/365) Average daily variable costs = $159,041.10 Under the Option 2, the default rate is 2.2 percent, so the average daily defaults will be: Average daily defaults = .022($129,000,000/365) Average daily defaults = $7,775.34

Option 2 has administrative costs equal to 1.9 percent of sales, so the average daily administrative costs are: Average daily administrative costs = .019($129,000,000/365) Average daily administrative costs = $6,715.07 We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest rate, the periodic rate for the 51 day collection period is: Interest rate = (1 + .0001597/365)51 – 1 Interest rate = .00818, or .818% Since the credit policy will exist into perpetuity, the NPV is: NPV = –$159,041.10 + ($353,424.66 – 159,041.10 – 7,775.34 – 6,715.07) / .00818 NPV = $21,846,461.54 Option 3 Under Option 3, the average daily sales are: Average daily sales = $132,000,000/365 Average daily sales = $361,643.84 The average daily variable costs will be: Average daily variable costs = .45($132,000,000/365) Average daily variable costs = $162,739.73 Under the Option 3, the default rate is 2.5 percent, so the average daily defaults will be: Average daily defaults = .025($132,000,000/365) Average daily defaults = $9,041.10 Option 3 has administrative costs equal to 2.1 percent of sales, so the average daily administrative costs are: Average daily administrative costs = .021($132,000,000/365) Average daily administrative costs = $7,594.52 We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest rate, the periodic rate for the 49 day collection period is: Interest rate = (1 + .0001597/365)49 – 1 Interest rate = .00785, or .785% Since the credit policy will exist into perpetuity, the NPV is: NPV = –$162,739.73 + ($361,643.84 – 162,739.73 – 9,041.10 – 7,594.42 / .00785 NPV = $23,047,081.08

CHAPTER 31 CASE  C­95  

The company should choose Option 1 since it has the highest NPV. The default rate and administrative costs of Option 2 are below those of Option 3. This is plausible. Option 2 extends the credit period, while Option 3 extends the credit period and relaxes the credit policy. The relaxation of the credit policy will increase the default rate since it will include companies with lower credit ratings who are less likely to pay. This in turn will increase the administrative costs of managing the delinquent accounts.

CHAPTER 29 THE BIRDIE GOLF–HYBRID GOLF  MERGER 1.

As with any other merger analysis, we need to examine the present value of the incremental cash flows. The cash flow today from the acquisition is the acquisition cost plus the dividends paid today, or: Acquisition of Hybrid Dividends from Hybrid Total

–$352,000,000 96,000,000 –$256,000,000

Using the information provided, the cash flows to Birdie Golf from acquiring Hybrid Golf for the next five years will be:

Dividends from Hybrid Tax-loss carryforwards Terminal value of equity Terminal value of debt Total

Year 1 $24,864,000

Year 2 Year 3 Year 4 $8,192,000 $18,624,000 $26,496,000 16,000,000 16,000,000

$24,864,000 $24,192,000 $34,624,000 $26,496,000

Year 5 $36,512,000

576,000,000 –192,000,000 $804,512,000

To discount the cash flows from the merger, we must discount each cash flow at the appropriate discount rate. The additional cash flows from the tax-loss carry forwards and the proposed level of debt should be discounted at the cost of debt because they are determined with very little uncertainty. The terminal value of the company is subject to normal business risk and must be discounted at a normal rate. The current weight of debt and weight of equity in Hybrid’s capital structure is: wD = .50 / (1 + .50) wD = .33 wE = 1 – .33 wE = .67 The beta for Hybrid’s debt is: D = (.08 – .06) / (.13 – .06) D = .29

CHAPTER 31 CASE  C­97   Thus, the overall beta for Hybrid is: H = (.33 × .29) + (.67 × 1.30) H = .96 Now, we can calculate the required return for normal operations of Hybrid, which is: E(RH) = .06 + .96(.13 – .06) E(RH) = .1273, or 12.73% To find the discount rate for dividends, we need to find the new beta of equity for the merged Hybrid. The new debt–equity ratio is 1, which implies a weight of debt and a weight of equity equal to 50 percent. The new beta for equity must be: New = [Old – (wD–new × wD–old] / wE–new New = [.96 – (.50 × .33)] / .50 New = 1.59 So, the discount rate for the dividends to be paid in future is: E(RDiv) = .06 + 1.59(.13 – .06) E(RDiv) = .1713, or 17.13% Now we can find the present value of the future cash flows. The present value of each year’s cash flows, along with the appropriate discount rate for each cash flow, is: Discoun t rate 17.13% Dividends Tax-loss TV of equity TV of debt Total

Year 1 $21,227,09 2

8% 12.73% 8%

Year 2

Year 3

$5,970,751 13,717,421

$11,588,613 12,701,316

Year 4 $14,075,32 1

Year 5 $16,558,962 316,344,830 –130,671,974

$21,227,09 2

$19,688,17 2

$24,289,92 9

$14,075,32 1

$202,231,818

And the NPV of the acquisition is: NPV = –$256,000,000 + 21,227,092 + 19,688,172 + 24,289,929 + 14,075,321 + 202,231,818 NPV = $25,512,330.96

2.

Since the acquisition is a positive NPV project, the most Birdie would offer is to increase the current cash offer by the current NPV, or: Highest offer = $352,000,000 + 25,512,330.96 Highest offer = $377,512,330.96 The highest share price is the total high offer price, divided by the shares outstanding, or: Highest share price = $337,512,330.96 / 5,200,000 shares Highest share price = $72.60

3.

To determine the current exchange ratio which would make a cash offer and a share offer equivalent, we need to determine the new share price under the original cash offer. The new share price of Birdie after the merger will be: PNew = [$94 × 11,600,000 + $25,512,330.96] / 11,600,000 PNew = $96.20 So, the exchange ratio which would make the cash offer and share offer equivalent is: Exchange ratio = $68.75 / $96.20 Exchange ratio = .7147

4.

The highest exchange ratio Birdie would accept is an exchange ratio that results in a zero NPV acquisition. This implies the share price of Birdie remains unchanged after the merger, so the exchange ratio is: Exchange ratio = $68.75 / $94 Exchange ratio = .7314

CHAPTER 31 EAST COAST YACHTS GOES  INTERNATIONAL  1.

The biggest advantage is the increased sales, while the biggest risk is exchange rate risk.

2.

If the dollar strengthens, the profit will decline. Conversely, if the dollar weakens, the profit will increase.

3.

The company will pay the sales commission out of gross sales, so the after-commission sales in euros is: After-commission sales = €8,000,000(1 – .05)

CHAPTER 31 CASE  C­99   After-commission sales = €7,600,000 At the current exchange rate of $1.34/€, the EBT in euros will be converted to dollars in the amount of: Dollar EBT = €7,600,000($1.34/€) Dollar EBT = $10,184,000 East Coast Yachts has production costs equal to 80 percent of dollar sales at this exchange rate. The total sales in dollars are: Total sales = €8,000,000($1.34/€) Total sales = $10,720,000 And the production costs are: Production costs = $10,720,000(.80) Production costs = $8,576,000 So, the profit at the current exchange rate is: Profit = $10,184,000 – 8,576,000 Profit = $1,608,000 If the exchange rate changes to $1.25/€, the euros will convert to: Dollar sales = €7,600,000($1.25/€) Dollar sales = $9,500,000 Since the production costs are fixed, the profit at this exchange rate will be: Profit = $9,500,000 – 8,576,000 Profit = $924,000

The breakeven exchange rate is the exchange rate that will allow the after-commission costs in euros to convert to a dollar amount that covers the production costs, so: Breakeven exchange rate = $8,576,000/€7,600,000 Breakeven exchange rate = $1.1284/€ 4.

The company could use options, futures, or forwards. The downside to all three hedging vehicles is the cost. Over time, the company will gain on some contracts and lose on others.

5.

At the current exchange rate, the company will make a profit unless the exchange rate moves dramatically. So, it is likely that hedging is not required at this point. Taking this into account, the company should probably pursue international sales further.