Question

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Q-6

North Star is trying to determine its optimal capital structure, which now consists of only common equity. The firm will add debt to its capital structure if it minimizes its WACC, but the firm has no plans to use preferred stock in its capital structure. In addition, the firm’s size will remain the same, so funds obtained from debt issued will be used to repurchase stock. The percentage of shares repurchased will be equal to the percentage of debt added to the firm’s capital structure. (In other words, if the firm’s debt-to-capital ratio increases from 0 to 25%, then 25% of the shares outstanding will be repurchased.) North Star is a small firm with average sales of $25 million or less during the past 3 years, so it is exempt from the interest deduction limitation.

Its treasury staff has consulted with investment bankers. On the basis of those discussions, the staff has created the following table showing the firm’s debt cost at different debt levels:

Debt-to-Capital Equity-to-Capital Ratio Ratio Debt-to-Equity Ratio Before-Tax Cost of Debt Bond Rating (wa) (W ) (D/E) (ra) 0 0.00 0.25 0.50 1. 00 0.75 .0000 0.3333 1.0000 5.0% 6.0 AA A BBB BB 0.50 8.3 0.75 0.25 3.0000 11.0 The firm has total capital of $5 million and 200,000 shares of common stock outstanding. Its EBIT is $500,000 and will not change if debt, at any of the levels shown in the preceding table, is added to the firm's capital structure. North Star uses the CAPM to estimate its cost of common equity,. It estimates that the risk-free rate is 3.5%, the market risk premium is 4.5%, and its tax rate is 25%. North Star's current beta, which is because it has no debt, is 1.25. Calculate the firm's interest expense for each of the capital structures shown in the preceding table. (Wd) (W) (rd) EBIT Interest 0.00 1.00 5.0% 500,000 0.25 0.75 6.0 500,000 0.50 0.50 8.3 500,000 0.75 0.25 11.0 500,000

Answer 1

Wd. WC. WD

Answer 0 (49) (UD) () (EBIT) I 0.00 1.00 50% 500000 - In this case the firm has zero level debt. Hence interest expense is Nil. The firm uses the CAPM to estimate ite loet Common equity CAPM 2 Rp + ß (Rick peremium) 2 3.5%+ 1.95 (4.5%) 29.125% Wa) (We) (rd) 25 .25 6.0% Total Wd 2 og 2 r 2 Canifal - Soooooo 5000000 X.25 2 1250ooo Joooooo 1.25 2 3750000 6.0% Interest Expenses a Wax rd 2 1250000 x 6.0% - 75000

.50 .50 8.3%

Total Capital. =. 5000000

WD = 5000000 X .50 = 2500000

WC = 5000000 X .50 = 2500000

Rd. = 8.3%

Interest Expense = WD X RD

= 2500000 X 8.3% = 207500

WD. WC. Rd

.75 .25 11.0%

Total Capital = 5000000

WD = 5000000 X .75 = 3750000

WC = 5000000 X .25 = 1250000

Rd = 11.0%

Interest Expenses = WD X RD

= 3750000 X 11.0% = 412500

WD. WC. Rd. EBIT. Interest

.00 1.00 5.0% 500000 Nil

.25 .75 6.0% 500000 75000

.50 .50 8.3% 500000 207500

.75 .25 11.0% 500000 412500

Answer 0 (49) (UD) () (EBIT) I 0.00 1.00 50% 500000 - In this case the firm has zero level debt. Hence interest expense is Nil. The firm uses the CAPM to estimate ite loet Common equity CAPM 2 Rp + ß (Rick peremium) 2 3.5%+ 1.95 (4.5%) 29.125% Wa) (We) (rd) 25 .25 6.0% Total Wd 2 og 2 r 2 Canifal - Soooooo 5000000 X.25 2 1250ooo Joooooo 1.25 2 3750000 6.0% Interest Expenses a Wax rd 2 1250000 x 6.0% - 75000