Question

Asked Apr 28, 2019

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Hankins Corporation has 8.9 million shares of common stock outstanding, 640,000 shares of 7.4 percent preferred stock outstanding, and 189,000 of 8.6 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $65.40 per share and has a beta of 1.34, the preferred stock currently sells for $106.60 per share, and the bonds have 13 years to maturity and sell for 89 percent of par. The market risk premium is 7 percent, T-bills are yielding 5.7 percent, and the firm’s tax rate is 35 percent.

If the firm is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows

1 Rating

Step 1

Calculating the value of after-tax cost of capital. We have,

Cost of debt is calculating by the calculation of yield-to- maturity of bond. So, we are calculating the value of YTM of the bond. We have,

Price of bond = C [1 – (1 / (1+r)^{n }] / r + FV / (1+r)^{n }

Here,

FV = Face value of bond = $ 1,000

Price of bond = 89% of par value of bond = $1,000 x 89% = $ 890

C = Coupon payment (Semi-annual) = $1,000 x 8.6%/2 = $43

n = Number of periods (Semi-annual) = 13 x 2 = 26

r = YTM (Semi-annual) = 5.07% (assume)

By substituting these value in the above formula. We get;

Price of bond = $43 [1 – (1 / (1.0507)^{26 }] / 0.0507 + $1,000 / (1.0507)^{26 }

Price of bond = $43 [1 – 0.27641] / 0.0507 + $ 1,000 x 0.27641

Price of bond = $43 [0.723590] / 0.0507 + $ 276.41

Price of bond = $ 613.70 + $ 276.41

Price of bond = $ 890

Since at 5.07% semi-annual YTM, the calculated price of bond is equal to the current price of bond. Therefore, the YTM of the bond is 10.14% (5.07%*2) annually. As we know, the value of YTM is the before-tax cost of debt.

After-tax cost of debt = Before-tax cost of debt x (1 – tax rate)

After-tax cost of debt = 10.14% (1 – 0.35) = 6.59 %

Step 2

Calculating the value of cost of equity using the formula of capital asset pricing model (CAPM). We have,

Required return = Risk-free rate + Beta x Market risk premium

Here,

Risk-free rate = 5.7%

Beta = 1.34

Market risk premium = 7%

By substituting these value in the above formula. We get;

Required return = 5.7 % + 1.34 x 7.00 %

Required return = 5.7% + 9.38 %

Required return = 15.08%

Since, the required return on equity is equal to the cost of equity. So, the cost of equity is 15.08%

Step 3

Calculating the value of cost of preferred stock. We have,

Cost of preferred stock = Dividend per share / Market price of preferred stock

Here,

Dividend per share = Face value of preferred stock x Dividend rate

Dividend per share = $ 100 x 7.4 % = $ ...

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