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Q1. Olsen Engineering is considering including two pieces of equipment—a truck and an overhead pulley system—in this year’s capital budget. The projects are independent. The cash outlay for the truck is $22,430, and for the pulley system it is $17,100. Each piece of equipment has an estimated life of five years. The annual after-tax cash flow expected to be provided by the truck is $7,500, and for the pulley it is $5,100. The firm’s required rate of return is 14 percent. Calculate the NPV, IRR, MIRR, the traditional payback (PB) period, and the discounted payback (DPB) period for each project. Indicate which project(s) should be accepted. See the excel file for excel solution Pulley System:  1

NPV  $17,100  $5,100   



1 (1.14 ) 5

  $17,100  $5,100(3.43308) 

0.14 

 $17,100  $17,508.71  $408.71

The Pulley System project is acceptable. IRR  15%.

Cost 

(Accept)

TV (1  MIRR) n

MIRR Pulley

 (1.14 ) 5  1  0.14  

5,100   17,100 

 33,711 .53    17,100  

1 5

(1  MIRR ) 5

 33,711 .53

 1.0  0.145  14.5% 

Year



Expected CF  Cumulative PV of CF 0 $(17,100) 1 5,100 2 5,100 3 5,100 4 5,100 5 5,100

PV of CF r = 14% $(17,100) 4,474 3,924 3,442 3,020 2,649

DPBPulley = 4 + 2,240/2,649 = 4.85 years PBPulley = $17,100/$5,100 = 3.35 years

$(17,100) (12,626) ( 8,702) ( 5,260) ( 2,240) 409

Truck:  1

NPV  $22,430  $7,500  



1 (1.14 ) 5

  $22, 430  $7,500(3.43308) 

0.14 



 $22,430  $25,748.10  $3,318.10

The Truck Project is acceptable. IRR = 20%. (Accept)

Cost 

TV (1  MIRR) n

MIRR Truck

 (1.14 ) 5  1  0.14  

7,500   22,430 

 49,576     22,430 

1 5

(1  MIRR) 5

 49,575.78

 1.0  0.172  17.2% 

Year



Expected CF  Cumulative PV of CF 0 $(22,430) 1 7,500 2 7,500 3 7,500 4 7,500 5 7,500

PV of CF r = 14% $(22,430) 6,579 5,771 5,062 4,441 3,895

DPBTruck = 4 + 577/3,895 = 4.15 years PBTruck = $22,430/$7,500 = 2.99  3 years

$(22,430) (15,851) (10,080) ( 5,018) ( 577) 3,318

Q2. Your company is considering two mutually exclusive projects—C and R— whose costs and cash flows are shown in the following table:

The projects are equally risky, and their required rate of return is 12 percent. You must make a recommendation concerning which project should be purchased. To determine which is more appropriate, compute the NPV and IRR of each project. NPVC  $14,000 

$8,000 $6,000 $2,000 $3,000    (1.12)1 (1.12) 2 (1.12) 3 (1.12) 4

 $14,000  $8,000(0.89286)  $6,000(0.79719)  $2,000(0.71178 )  $3,000(0.63552)  $14,000  $7,142.88  $4,783.14  $1,423.56  $1,906.56  $14,000  $15,256.14  $1,256.14

IRRC = 17.3%

NPVR

 $22,840  $8,000 

 1 





1 (1.12 ) 4

0.12

  $22,840  $8,000(3.03735)  $1,458.80  

IRRR = 15.0% NPVR > NPVC, so Project R should be accepted.

Q3. The Chaplinsky Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $40 million on a large scale, integrated plant that will provide an expected cash flow stream of $6.4 million per year for 20 years. Plan B calls for the expenditure of $12 million to build a somewhat less efficient, more labor-intensive plant that has an expected cash flow stream of $2.72 million per year for 20 years. Chaplinsky’s required rate of return is 10 percent. a. Calculate each project’s NPV and IRR. b. Construct the NPV profiles for Plan A and Plan B. Using the NPV profiles, approximate the crossover rate. See the excel file for solution. Q4.The Cordell Coffee Company is evaluating the within-plant distribution system for its new roasting, grinding, and packing plant. The two alternatives are (1) a conveyor system with a high initial cost but low annual operating costs and (2) several forklift trucks, which cost less but have considerably higher operating costs. The decision to construct the plant has already been made, and the choice here will have no effect on the overall revenues of the project. The required rate of return for the plant is 9 percent, and the projects’ expected net costs are listed in the following table:

a. What is the present value of costs of each alternative? Which method should be chosen? (Hint: Be careful—these cash flows are outflows.) b. What is the IRR of each alternative? See the excel file. a.

The PV of costs for the conveyor system is –$556,717, while the PV of costs for the forklift system is –$493,407. Thus, the forklift system is expected to be –$493,407 – (–$556,717) = $63,310 less costly than the conveyor system, and hence the forklifts should be used.  1

PV costs of conveyor  300,000  (66,000) 

1 (1.09 ) 5



 0.09     300,000  (66,000)(3.88965)  556,716.90 

b. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow stream must include both cash inflows and outflows.

CHAPTER 11 Cost of Capital: Follow the problem on pg. 482 and 483.