# Return on equity in a firm

FIRM A AND FIRM B HAVE DEBT-TOTAL ASSET RATIOS OF 60 PERCENT AND 40 PERCENT AND RETURNS ON TOTAL ASSETS OF 20 PERCENT AND 30 PERCENT, RESPECTIVELY. WHICH FIRM HAS GREATER RETURN ON EQUITY?

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#### Solution Preview

ROE = ROA X Assets/Equity

We are given the Debt/Assets ratio

Now Equity/Assets = ...

#### Solution Summary

The solution explains how to calculate the return on equity

What are earnings if the owners put up the $100?

Firm's weighted-average cost of capital at various combination of debt and equity. What is the firm's optimal capital structure?

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

Construct a pro forma balance sheet that indicates the firm's optimal capital structure.

Firms' weight average cost of capital and other questions:

1. 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?

2. Given the following schedules:

Debt/Assets Cost of Debt Cost of Equity

0% 7% 14%

10 7 14

20 7 14

30 8 14

40 8 16

50 10 18

60 10 20

a. What is firm's cost of capital at the various combinations of debt and equity?

b. What is the firm's optimal capital structure? Construct a balance sheet showing that combination of debt and equity financing.

3. 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?

4. Firm A had $10,000 in assets entirely financed with equity. Firm B also has $10,000, but these assets are financed by $5,000 in debt (with a 10 percent rate of interest) and $5,000 in equity. Both firms sell 10,000 units of output at $2.50 per unit. The variable costs of production are $1, and fixed production costs are $12,000. (to ease the calculation, assume no income tax.)

A. What is the operating income (EBIT) for both firms?

B. What are the earnings after interest?

C. If sales increase by 10 percent to 11,000 units, by what percentage will each firm's earnings after interest income? To answer the question, determine the earnings after taxed and compute the percentage increase in these earnings from the answers you derived in part b.

D. Why are the percentage changes different?

5. A firm's current balance sheet is as follows:

Assets $100 Debt $10

Equity $90

Debt/assets after-tax cost of debt cost of equity cost of capital

0% 8% 12% ?

10 8 12 ?

20 8 12 ?

30 8 13 ?

40 9 14 ?

50 10 15 ?

60 12 16 ?

B. Construct a pro forma balance sheet that indicates the firm's optimal capital structure. Compare this balance sheet with the firm's current balance sheet. What course of action should the firm take?

Assets $100 Debt$?

Equity$?

C. As a firm initially substitutes debt for equity financing, what happens to the cost of capital, and why.

D. If a firm uses too much debt financing, why does the cost of capital rise?

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