# Calculating NPV and BEP for cash inflows in the given cases

Break-even cash inflows and risk Pueblo Enterprises is considering investing in either of two mutually exclusive projects, X and Y. Project X requires an initial investment of $30,000; project Y requires $40,000. Each project's cash inflows are 5-year annuities: Project X's inflows are $10,000 per year; project Y's are $15,000. The firm has unlimited funds and, in the absence of risk differences, accepts the project with the highest NPV. The cost of capital is 15%.

a. Find the NPV for each project. Are the projects acceptable?

b. Find the breakeven cash inflow for each project.

c. The firm has estimated the probabilities of achieving various ranges of cash

inflows for the two projects, as shown in the following table. What is the probability

that each project will achieve the breakeven cash inflow found in part b?

Probability of achieving

cash inflow in given range

Range of cash inflow Project X Project Y

$0 to $5,000 0% 5%

$5,000 to $7,500 10 10

$7,500 to $10,000 60 15

$10,000 to $12,500 25 25

$12,500 to $15,000 5 20

$15,000 to $20,000 0 15

Above $20,000

d. Which project is more risky? Which project has the potentially higher NPV? Discuss the risk-return tradeoffs of the two projects.

e. If the firm wished to minimize losses (that is, NPV $0), which project would you recommend? Which would you recommend if the goal was achieving a higher NPV?

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#### Solution Preview

a. Find the NPV for each project. Are the projects acceptable?

Project X

Initial cash flow= Io=-$30,000

Number of periods=n=5

Cost of capital=r=15%

Annual cash inflow=C=$10,000

NPV=Io+C/r*(1-1/(1+r)^n)

Plug in the various values

NPV = -30000+10000/15%*(1-1/(1+15%)^5)=$3521.55

Since NPV is positive, project is acceptable if considered independently.

Project Y

Initial cash flow= Io=-$40,000

Number of periods=n=5

Cost of capital=r=15%

Annual cash inflow=C=$15,000

NPV=Io+C/r*(1-1/(1+r)^n)

Plug in the various values

NPV = -40000+15000/15%*(1-1/(1+15%)^5)=$10,282.33

Since NPV is positive, project is acceptable if considered independently.

Since X and Y are mutually exclusive projects, Project Y should be selected because of higher NPV.

b. Find the break even cash inflow for each project.

Let break Even cash ...

#### Solution Summary

Solution describes the steps to calculate NPV and break even cash inflow for the given projects. It also discusses riskiness of the projects.