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Charlotte's Crochet Shoppe has 17,300 shares of common stock outstanding at a price per share of $85 and a rate of return of 12.01 percent. The company also has 380 bonds outstanding, with a par value of $2,000 per bond. The pretax cost of debt is 6.33 percent, and the bonds sell for 100.2 percent of par. What is the firm's WACC if the tax rate is 40 percent?

Answer :

The WACC for Charlotte's Crochet Shoppe is 7.23%.

Weighted average cost of capital (WACC) is the weighted average of the cost of equity and the cost of debt for a company, taking into account the relative weights of each source of capital. It is calculated as follows:

WACC = (E/V x Re) + [(D/V x Rd) x (1-T)]

where

E = market value of the company's equity,

V = total market value of the company's capital,

D = market value of the company's debt,

Re = cost of equity,

Rd = cost of debt, and

T = tax rate.

Let's now calculate the WACC for Charlotte's Crochet Shoppe.

Step 1: Calculation of the cost of equity using the Capital Asset Pricing Model (CAPM)CAPM = Rf + β(Rm-Rf)

where Rf = risk-free rate, β = beta, and Rm = expected market return.

The beta for Charlotte's Crochet Shoppe is not given in the problem. Let's assume a beta of 1.2, the risk-free rate as 2.5%, and the expected market return as 10%.

CAPM = 2.5% + 1.2(10% - 2.5%) = 11%

Therefore, the cost of equity is 11%.

Step 2: Calculation of the cost of debtThe pretax cost of debt is 6.33%. The bonds sell for 100.2% of par, which means that the market value of each bond is $2,000 x 100.2% = $2,004. The market value of the debt is therefore $2,004 x 380 = $761,520. The after-tax cost of debt is:6.33% x (1 - 40%) = 3.80%Therefore, the cost of debt is 3.80%.

Step 3: Calculation of the weights of equity and debt

The market value of the equity is 17,300 x $85 = $1,469,500.

The total market value of the capital is therefore $1,469,500 + $761,520 = $2,231,020.

The weight of equity is: $1,469,500 / $2,231,020 = 65.85%

The weight of debt is: $761,520 / $2,231,020 = 34.15%

Step 4: Calculation of the WACCWACC = (E/V x Re) + [(D/V x Rd) x (1-T)]

WACC = (0.6585 x 0.11) + [(0.3415 x 0.038) x (1-0.40)]

WACC = 0.0723 or 7.23%

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