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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