Question

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $6,500 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	$6,250		0.2	$0
0.6	$6,500		0.6	$6,500
0.2	$6,750		0.2	$19,000

BPC has decided to evaluate the riskier project at 13% and the less-risky project at 9%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Open spreadsheet

1. What is each project's expected annual cash flow? Round your answers to two decimal places.

   Project A: $  

   Project B: $  

   Project B's standard deviation (σ_B) is $6,185.47 and its coefficient of variation (CV_B) is 0.80. What are the values of (σ_A) and (CV_A)? Round your answers to two decimal places.

   σ_A = $  

   CV_A =

2. Based on the risk-adjusted NPVs, which project should BPC choose?

   _________Project AProject B

3. If you knew that Project B's cash flows were negatively correlated with the firm's other cash flow, but Project A's cash flows were positively correlated, how might this affect the decision?

   _________This would make Project B more appealing.This would make Project B less appealing.

   If Project B's cash flows were negatively correlated with gross domestic product (GDP), while A's cash flows were positively correlated, would that influence your risk assessment?

Answer 1

a). Expected annual cash flow = sum of {probability*annual cash flow}

Expected annual cash flow for Project A = (0.2*6,250) + (0.6*6,500) + (0.2*6,750) = 6,500.00

Expected annual cash flow for Project B = (0.2*0) + (0.6*6,500) + (0.2*19,000) = 7,700.00

b). Standard deviation = {sum of [probability*(Cash flow - expected annual cash flow)^2]}^0.5

Coefficient of variation = standard deviation/expected annual cash flow

Project A: standard deviation = 158.11; CV = 0.02

Cash flow (CF) Probability (P) (CF-Expected CF)^2*P CF P 6250 0.20 1250 12500 0.60 6500 3900 0 6750 0.20 1350 12500 Total 6500.00 25000 Standard deviation 158.11 Coefficient of variation 0.02

c). NPV = sum of present values of all future cash flows - initial investment

Project A NPV = 9.953.42

Using NPV function with cash flows & 9% discount| NPV P Formula rate NPV Prob Probability (P) Time T 0 1 NPV 0.20 -6500 6250 6250 6250 9320.59 1864.12 0.60 6500 -6500 6500 6500 9953.42 5972.05 0.20 6750 10586.24 -6500 6750 6750 2117.25 Expected NPV 9953.42

Project B NPV = 11,680.88

Using NPV function with cash flows & 13% Formula discount rate NPV Prob -1300.00 Probability (P) 0.20 Time T 0 1 2 NPV -6500 -6500.00 0 0 0 6500 5308.50 0.60 -6500 6500 6500 8847.49 0.20 19000 7672.38 -6500 19000 19000 38361.90 Expected NPV 11680.88

Based on risk-adjusted NPVs, Project B should be chosen as it has higher NPV.

d). If project B's cash flows are negatively correlated with the firm's other cash flow, then it will make project B more appealing as it would mean that the project has positive cash flows when the firm's other cash flows are negative.

Similarly, if project B's cash flows are negatively correlated with the GDP, it would make it more appealing.