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Risky Cash Flows The Bartram-Pulley Company (BPC) must decide between two mutually exclusive investment projects
Risky Cash Flows
The Bartram-Pulley Company (BPC) must decide between two mutually exclusive investment projects. Each project costs $8,000 and has an expected life of 3 years. Annual net cash flows from each project begin 1 year after the initial investment is made and have the following probability distributions:
| PROJECT A | PROJECT B | ||
| Probability | Net Cash Flows |
Probability | Net Cash Flows |
| 0.2 | $6,000 | 0.2 | $ 0 |
| 0.6 | 6,750 | 0.6 | 6,750 |
| 0.2 | 8,000 | 0.2 | 17,000 |
BPC has decided to evaluate the riskier project at a 13% rate and the less risky project at a 8% rate.
- What is the expected value of the annual net cash flows from each project? Round your answers to nearest dollar.
Project A Project B Net cash flow $ $
What is the coefficient of variation (CV)? (Hint: σB = $5,444 and CVB = 0.73.)σ (to the nearest whole number) CV (to 2 decimal places) Project A $ - What is the risk-adjusted NPV of each project? Round your answer to the nearest dollar.
Project A $ Project B $
Expert Solution
a).
Expected value for a probability distribution is a weighted average of individual values. It is calculated as (p1*c1)+(p2*c2)+(p3*c3)
Annual net cashflow of Project A
= (0.2*6000)+(0.6*6750)+(0.2*8000)= 6850
Annual net cashflow of Project B
= (0.2*0)+(0.6*6750)+(0.2*17000)= 7450
b).
Coefficient of variation is calculated as Standard deviation/mean.
Standard deviation with probability distribution is calculated as: sqrt((summation(x^2*p(x)))-Mean^2)
summation(x^2*p(x))= (6000^2*0.2)+(6750^2*0.6)+(8000^2*0.2)= 47337500
Mean= 6850
Standard Deviation= sqrt(47337500-6850^2)= 644.2049 rounded to 644.
Coefficient of variation= 644.2049/6850= 0.09
c).
From the coefficient of variation, we can see that Project B is riskier, as its CV value is high.
So, Project B is evaluated at 13% and Project A by 8%.
Risk adjusted NPV of Project A= -8000+6850/1.08+6850/1.08^2+6850/1.08^3= $9653.
Risk adjusted NPV of Project B= -8000+7450/1.13+7450/1.13^2+7450/1.13^3= $9591.
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