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# Present Value, Break-Even Analysis, Leverage

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A firm has three investment opportunities. Each costs \$1,000, and the firm's cost of capital is 10 percent. The cash inflow of each investment is as follows:

Cash Inflow A B C
Year
1 300 500 100
2 300 400 200
3 300 200 400
4 300 100 500

a. If the net present value method is used, which investment(s) should the firm make?

b. What is the internal rate of return of investment A? The internal rate of return of investment B is 10.22% and 6.15% for investment C. Which investment(s) should the firm make?

c. What is the payback period for each investment?

A firm needs \$100 to start and expects:

Sales \$200
Expenses \$185
Tax rate 33% of earnings

a. What are earnings if the owners put up the \$100?

b. If the firm borrows \$40 of the initial at 10%, what are the profits received by the owner?

c. What is the return on the owners' investment in each case? Why do the returns differ?

d. If expenses rise to \$194, what will be the returns in each case?

e. In which case did the returns decline more?

f. What generalization can you draw form the above?

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#### Solution Preview

Hello!

Question 1

a. The NPV of a project is calculated as:

C0 + C1/(1+r) + C2/(1+r)^2 + ...

where
C0, C1, C2... are the cash flows from period 0, period 1, period 2, etc.
r is the interest rate in decimal form (in this case, 0.10, because the cost of capital is 10%)

Let's calculate it for project A:
NPV(A) = -1000 + 300/1.10 + 300/1.10^2 + 300/1.10^3 + 300/1.10^4 = -49.04

Notice that the cash flow in perdiod 0 is -\$1,000, because that's the cost of the investment, which is paid "today". We've thus found that the NPV of project A is -\$49.04.

Using the same formula for the other projects, we get:

NPV(B) = \$3.69

NPV(C) = -\$101.77

Since project B has the highest NPV, then the firm should make this investment.

b. The IRR of an investment is the discount rate that makes its NPV equal to zero. We thus have to solve:

0 = -1000 + 300/(1+r) + 300/(1+r)^2 + 300/(1+r)^3 + 300/(1+r)^4

Usually, the IRR cannot be found analytically, so some software must ...

#### Solution Summary

Benefits of leverage are noted. Present Value, Break-Even Analysis, and Leverage notes are also assessed.

\$2.19

## Break Even Point and Capital Budgeting

2. (Payback period, net present value, profitability index, and internal rate of return calculations) You are considering a project with an initial cash outlay of \$160,000 and expected free cash flows of \$40,000 at the end of each year for 6 years. The required rate of return for this project is 10 percent.

a.) What is the project's payback period?
b.) What is the project's NPV?
c.) What is the project's PI?
d.) What is the project's IRR?

3. What would be the discounted payback for the period for the project in problem #2?

4. (Break-even point) Roberto Martinez is the chief financial analyst at New Wave Pharmaceuticals (NWP), a company that produces a vitamin claimed to prevent the common cold. Roberto has been asked to determine the company's break-even point in units. He obtained the following information from the company's financial statements for the year just ended. In addition, he found out the NWP'S production manager that the company produced 40 million units in that year. What will Roberto determine the break-even point to be?

Sales \$20,000,000
Variable cost 16,000,000
Revenue before fixed cost \$ 4,000,000
Fixed costs 2,400,000
EBIT \$ 1,600,000

5. (Leverage analysis) New Wave Pharmaceuticals (see description and data in problem #4) is concerned that recent unfavorable publicity about the questionable medicinal benefits of other vitamins will temporarily hurt NWP's sales even though such assertions do not apply to NWP's vitamin. Accordingly, Roberto has been asked to determine the company's level of risk based on the financial information for the year just ended. In addition to the data described in Problem #2 Roberto learned form the company's financial statements that the company incurred \$800,000 of interest expense in the year just ended. What will Roberto determine the (a) degree of operating leverage, (b) degree of financial leverage, and (c) degree of combined leverage to be?

6. (Operating leverage) the B.H. Williams Company manufactures an assortment of wood-burring stoves. The average selling price for the various units is \$475.00. The associated variable cost is \$350 per unit. Fixed costs for the firm average \$200,000 annually.

a.) What is the break-even point in units for the company?
b.) What is the dollar sales volume the firm must achieve to reach the break-even point?
c.) What is the degree of operating leverage for a production and sales level of \$6,000 units for the firm? (Calculate to three decimal places.)

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