Hamada equation Cyclone Software Co. is trying to establish its optimal capital
ID: 2649946 • Letter: H
Question
Hamada equation
Cyclone Software Co. is trying to establish its optimal capital structure. Its current capital structure consists of 35% debt and 65% equity; however, the CEO believes the firm should use more debt. The risk-free rate, rRF, is 3%; the market risk premium, RPM, is 5%; and the firm's tax rate is 40%. Currently, Cyclone's cost of equity is 16%, 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
Facts as given: Current capital structure: 30% debt, 70% equity; rRF = 3%; rM – rRF = 7%; T = 40%;
rs = 16%.
Step 1: Determine the firm’s current beta.
rs = rRF + (rM – rRF)b
16% = 3% + (7%)b
13% = 7%b
1.714 = b.
Step 2: Determine the firm’s unlevered beta, bU.
bU = bL/[1 + (1 – T)(D/E)]
= 1.714/[1 + (1 – 0.4)(0.30/0.70)]
= 1.36
Step 3: Determine the firm’s beta under the new capital structure.
bL = bU[1 + (1 – T)(D/E)]
= 1.36[1 + (1 – 0.4)(0.5/0.5)]
= 2.18
Step 4: Determine the firm’s new cost of equity under the changed capital structure.
rs = rRF + (rM – rRF)b
= 3% + (7%)2.18
= 18.26%.
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