Cyclone Software Co. is trying to establish its optimal capital structure. Its c
ID: 2649966 • Letter: C
Question
Cyclone Software Co. is trying to establish its optimal capital structure. Its current capital structure consists of 40% debt and 60% equity; however, the CEO believes the firm should use more debt. The risk-free rate, rRF, is 6%; the market risk premium, RPM, is 6%; and the firm's tax rate is 40%. Currently, Cyclone's cost of equity is 15%, which is determined by the CAPM. What would be Cyclone's estimated cost of equity if it changed its capital structure to 50% debt and 50% equity? Round your answer to two decimal places.
Explanation / Answer
When Capital structure consist of 20% Debt and 80% equity
Given in question,
Risk Free rate (rRF) = 5%
Cost of equity (Ke) = 15%
Market risk Premium (RPM)= 7%
Under CAPM Model
Cost of Equity (Ke) = rRF + equity Beta (market risk Premium)
Accordingly,
15 = 5 + equity beta (7)
15 - 5 = equity beta (7)
equity beta = (15-5)/7
= 10/7
= 1.43
i.e .equity beta = 1.43
Overall beta = Debt beta [D (1-tax rate)/ {E+D (1-tax rate)}] + equity beta [E/{E+D (1-tax rate)}]
= 0 *[20 (1-0.40)/ (80+20(1-0.40)] + 1.43 [ 80/(80+20(1-0.40)]
= 0 + 1.43 [ 80/ (80+12)]
= 1.43* (80/92)
= 1.43 * 0.869
= 1.243
i.e. overall beta = 1.243
Now, with the help of overall beta which remains same evenafter change in capital structure, we can findout equity beta of new structure i.e. 50% debt and 50% equity.
Now, when new capital structure consist of 50% debt and 50% equity
Overall beta = Debt beta [D (1-tax rate)/ {E+D (1-tax rate)}] + equity beta [E/{E+D (1-tax rate)}]
1.243 = 0 *[50 (1-0.40)/ (50+50(1-0.40)] + equity beta [ 50/(50+50(1-0.40)]
1.243 = equity beta [50/(50+30)]
1.243 = equity beta (50/80)
equity beta (50/80)= 1.243
equity beta = 1.243/50*80
= 1.989
Ke in new structure = rRF + Equity beta (RPM)
= 5 %+ 1.989 (7%)
= 18.923%
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