Question

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each project has an initial outflow of $6,750 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

Project A			Project B
Probability	Cash Flows		Probability	Cash Flows
0.2	$6,500		0.2	$          0
0.6	6,750		0.6	6,750
0.2	7,000		0.2	18,000

BPC has decided to evaluate the riskier project at 11% and the less-risky project at 8%.

1. What is each project's expected annual cash flow? Round your answers to the nearest cent.

   Project A:	$
   Project B:	$

   
   Project B's standard deviation (σ_B) is $5,798 and its coefficient of variation (CV_B) is 0.76. What are the values of (σ_A) and (CV_A)? Do not round intermediate calculations. Round your answer for standard deviation to the nearest cent and for coefficient of variation to two decimal places.

   σA:	$
   CVA:

2. 
   
3. Based on their risk-adjusted NPVs, which project should BPC choose?
   -Select-Project AProject BItem 5
4. 
   
5. If you knew that Project B's cash flows were negatively correlated with the firm's other cash flow, whereas Project A's flows were positively correlated, how might this affect the decision?
   -Select-This would make Project B more appealing.This would make Project B less appealing.Item 6
   
   If Project B's cash flows were negatively correlated with gross domestic product (GDP), while A's flows were positively correlated, would that influence your risk assessment?
   -Select-This would make Project B more appealing.This would make Project B less appealing.

Answer 1

a). Expected annual cash flow = sum of probability weighted cash flows

Project A expected annual cash flow = 6,750.00

Project B expected annual cash flow = 7,650.00

b). Standard deviation = [sum of (CF - expected CF)^2*P]^0.5

Project A standard deviation = 474.34

Project A coefficient of deviation = 0.07 (calculated as standard deviation/expected annual cash flow)

c). Risk-adjusted NPVs: Since Project B has greater variability in its cash flows, it is the riskier project and so, will have the discount rate of 11%. Project A will have the discount rate of 8%.

Project A NPV: PMT = 6,750; N = 3; rate = 8%, solve for PV. PV = 17,395.40

NPV = 17,395.40-6,750 = 10,645.40

Project B NPV: PMT = 7,650; N = 3; rate = 11%, solve for PV. PV = 18,694.42

NPV = 18,694.42 -6,750 = 11,944.42

Project B should be accepted as it has a higher NPV.

d). If Project B's cash flows were negatively correlated with the other cash flows of the firm then it would reduce overall risk. This would make Project B more appealing.

e). If Project B's cash flows were negatively correlated with GDP then it would again reduce overall risk for the firm. This would make Project B more appealing.

(CF-Expected CF)^2*P 112500 Project A Probability (P) 0.20 0.60 0.20 Total 6750 Cash flow (CF) CFP 6000 1200 4050 7500 1500 6750 Standard deviation Coefficient of variation 1125001 225000 474.34 0.071 Cash flow (CF) CFP Project B Probability (P) 0.20 0.60 0.20 Total 6750 4050 18000 3600 7650 Standard deviation Coefficient of variation (CF-Expected CF)^2*p 11704500 486000 21424500 33615000 5797.84 0.76