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Isabella Construction and Interior Design is an all-equity company in Central Michigan. The CFO John Thornton...

Isabella Construction and Interior Design is an all-equity company in Central Michigan. The CFO John Thornton Jr. is considering moving to a capital structure with 25% debt and 75% equity and using the all the newly raised capital to repurchaseshares of the common stock. The firm’s tax rate is 22%, its current beta is 1.40, and it has 25,000 shares of common stock with a market price of $312 per share. Assume MM propositions hold.
a. How many shares of common stock will remain after the repurchase?
b. If the risk-free rate is 3.5% and the market risk premium is 8.0%, by how much would the cost of equity for the levered firm increase, compared to the cost of equity of the unlevered firm?
c. What will be the change in the WACC, if the company can borrow at 7.25 percent?

Solutions

Expert Solution

Answer a:

Given, target Debt to Capital is 25%

Since, the share repurchase will happen at prevailing market price, the number of shares repurchased by debt will be 25% of total equity shares = 25% of 25,000 = 6,250 shares (as the Capital was all-equity funded initially)

So, number of shares of common stock that will remain after the repurchase = 25,000 - 6,250 = 18,750 shares.

Answer b:

Given, unlevered beta U = 1.40

Original Cost of Equity = Risk-free rate + U * Market risk premium = 3.5% + 1.4 * 8% = 14.70% ...(A)

Let, Levered beta be denoted by L, then

L = U * [ 1 + (1 - T) * (D/E) ]

=> L = 1.40 * [ 1 + (1 - 22%) * (25% / 75%) ] = 1.764

New Cost of Equity = Risk-free rate + L * Market risk premium = 3.5% + 1.764 * 8% = 17.612% ...(B)

The cost of equity for the levered firm as compared to the unlevered firm will increase by (B - A) = 17.612% - 14.700% = 2.912%

Answer c:

Original WACC = Original Cost of Equity = 14.70%

Now, given Cost of Debt = 7.25%

New Cost of Equity = 17.612%, as calculated in answer b.

New WACC = Proportion of Debt * Cost of Debt * (1 - T) + Proportion of Equity * New Cost of Equity

=> New WACC = 25% * 7.25% * (1 - 22%) + 75% * 17.612% = 14.62275%

Change in WACC = New WACC - Original WACC = 14.62275% - 14.70% = -0.07725% = - 0.08% (rounded to two decimal places)

jeff jeffy answered 6 months ago
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