Whispering Pines, Inc. (WPI) is considering a leveraged recapitalization and wan

Question

Whispering Pines, Inc. (WPI) is considering a leveraged recapitalization and wants to know the value of the firm subsequent to the recap.

After the recapitalization they will have $23.8 million in perpetual par value debt with a 6% coupon.They are currently forecasted to produce free cash flows of $2.8 million, $7.7 million, and $10.9 million in each of the next three years. After year three, the unlevered cash flows are expected to grow at a constant rate of 3% per year. The marginal corporate tax rate is 40%.

WPI’s closest competitor, a pure-play firm in the same business with similar risk, profitability, and growth prospects, has a debt-to-equity ratio of 0.5 and an equity beta of 1.25. Ten-year treasuries currently yield 2.3% and the expected return on the S&P 500 is 10.0% per annum.

Using the information above regarding Whispering Pines and if you discount the interest tax shields at the unlevered cost of equity, what is the value of the enterprise (market value of assets) using the APV method? Enter your response in millions, rounded to two decimal places.

Explanation / Answer

In the problem, the company is asked to be valued at unlevered cost of equity which indicates the valuation without the impact of the debt capital.

The cash flows that are generated are unlevered in nature which again indicates the valuation without the impact of debt in it.

So we need to calculate the cost of equity which is unlevered in nature.

From the information of WPI’s closest competitor we can find out the levered Beta of the company which is 1.25 (since equity beta = levered beta)

Again we need to unlevered it to adjust the and find out the unlevered cost of equity

Beta (Unlevered) = Beta (Levered)/ [1+ Debt/Equity (1-Tax rate)]

Beta (Unlevered) = 1.25/ [1+0.5*(1-0.4)] (since tax rate is 40%)

Or, Beta (Unlevered) = 1.25/(1.3) = 0.962

Again unlevered cost of equity = Risk Free Rate + Beta (unlevered)* [Market Return - Risk Free rate]

Or, Risk Free Rate = 2.3% (Ten-year treasuries)

Market Return = 10% (S&P 500)

Or, unlevered cost of equity = 2.3% + 0.962 (10-2.3) % = 9.70% (approx)

So value of the firm under the APV Method = Free cash Flow 1st Year/ (1+ unlevered cost of equity) + Free cash Flow 2nd Year/ (1+ unlevered cost of equity) ^2 +

Free cash Flow 3rd Year/ (1+ unlevered cost of equity) ^3 + Free cash Flow 3rd Year * (1+ growth rate)/ (unlevered cost of equity – growth rate) * 1/ (1 + unlevered cost of equity) ^3

Or, value of the firm under the APV Method = 2.8/ (1.097) + 7.7/ (1.097) ^2 + 10.9/ (1.097)^3 + 10.9* (1.03)/(0.097-0.03)* 1/ (1.097)^3

Or, value of the firm under APV Method = $2.55 + $6.40 + $8.25 + $126.95 = $144.15

Hence the value of the firm under APV Method will be $144.15

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