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 firms 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 firms capital structure. (In other words, if the firms 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 firms debt cost at different debt levels:

Debt-to-Capital Ratio (Wd)	Equity-to-Capital Ratio (Wc)	Debt-to-Equity Ratio (D/E)	Bond Rating	Before-Tax Cost of Debt (rd)
0.00	1.00	0.0000	AA	5.0%
0.25	0.75	0.3333	A	6.0
0.50	0.50	1.0000	BBB	8.3
0.75	0.25	3.0000	BB	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 firms 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 Stars current beta, which is because it has no debt, is 1.25.

Calculate the beta for each of the capital structures shown in the preceding table.

(W_d) (W_c) (D/E) (r_d) b_L

0.00 1.00 0.0000 5.0%

0.25 0.75 0.3333 6.0

0.50 0.50 1.0000 8.3

0.75 0.25 3.0000 11.0

Note: enter results with four (4) decimal places