Question

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $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 $17,000
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 two decimal places.
A. Project A. $
B. Project B. $
2. Project B's standard deviation (B) is $5,444 and its coefficient of variation (CVB) is 0.73. What are the values of (A) and (CVA)? Round your answer to two decimal places.
A = $
CVA =

Answer 1

Answer:

1) Expected annual cash flow for project A= $6750

Expected annual cash flow for project B= $7450

2)

Standard deviation (σ) for A = $158.11

Coefficient of variation for A = 0.0234

Explanation:

1)

For project A

Expected cash flow 1 = 0.2 × $6500 = $1300

Expected cash flow 2 = 0.6 × $6750 = $4050

Expected cash flow 3 = 0.2 × $7000 = $1400

Expected annual cash flow = sum of expected cash flow = $1300 + $4050 + $1400 = $6750

For project B

Expected cash flow 1 = 0.2 × $0 = $0

Expected cash flow 2 = 0.6 × $6750 = $4050

Expected cash flow 3 = 0.2 × $17000 = $3400

Expected annual cash flow = sum of expected cash flow = $0 + $4050 + $3400 = $7450

2) Deviation from mean = cash flow - expected cash flow

Deviation from mean 1 = 6500 - 6750 = 250

Deviation from mean 2 = 6750 - 6750 = 0

Deviation from mean 3 = 7000 - 6750 = -250

Variance (σ²) = Sum of (Deviation from mean² × Probability)

σ² = (250² × 0.2) + (0² × 0.6) + ((-250)² × 0.2) = 12500 + 12500 = 25000

Standard deviation (σ) = √ variance = √25000 = $158.11

Coefficient of variation = Standard deviation / expected annual cash flow = $158.11 / $6750 = 0.0234