The problem requires us to calculate the weighted average cost of capital (WACC) for a firm, given the target capital structure proportions and the costs of debt, preferred stock, and common equity.

1. Problem Description

The problem requires us to calculate the weighted average cost of capital (WACC) for a firm, given the target capital structure proportions and the costs of debt, preferred stock, and common equity.

2. Solution Steps

First, calculate the cost of debt.

The firm can sell a 20-year bond with a $1,000 par value and a 9$

9

7

5. The flotation cost is 3% of the face value, which is $0.03 * 1000 = $

3

0.

The net price received by the firm is $975 -$30 = $

9

4

5. The discount of $25 has already been taken into consideration when calculating the sales price of $

9

7

5.

The before-tax cost of debt ($r_d$) can be approximated using the following formula.

$r_d = \frac{Coupon Payment + (Face Value - Net Price) / Years}{ (Face Value + Net Price) / 2}$

$r_d = \frac{90 + (1000 - 945) / 20} { (1000 + 945) / 2} = \frac{90 + 55 / 20}{1945 / 2} = \frac{90 + 2.75}{972.5} = \frac{92.75}{972.5} = 0.09537$

$r_d = 9.537\%$

Alternatively, the YTM of debt can be calculated using financial calculator, using PV = -945, FV=1000, PMT=90, N=

2

0. We get the yield of 9.64%, which is more accurate.

The after-tax cost of debt is calculated as:

$r_d(1 - Tax Rate) = 0.09537 (1 - 0.35) = 0.09537 * 0.65 = 0.06199$

The after tax cost of debt is 6.199%. Using the yield of 9.64% we get 9.64% * 0.65 = 6.266%.

Second, calculate the cost of preferred stock.

The firm can issue preferred stock at $68 per share, and the stock will pay an$8.00 annual dividend. The cost of issuing and selling the stock is $3 per share.

The net price received is $68 -$3 = $

6

5.

The cost of preferred stock ($r_p$) is calculated as:

$r_p = \frac{Dividend}{Net Price} = \frac{8}{65} = 0.12308$

$r_p = 12.308\%$

Third, calculate the cost of common equity.

The firm's common stock is currently selling for $45 per share. The dividend expected to be paid at the end of the coming year is$5.

0

7. Its dividend payments have been growing at a constant rate for the last five years. Five years ago, the dividend was $3.

4

5. A new stock issue must be underpriced at $1 per share, and the firm must pay $2 per share in flotation costs.

First, calculate the growth rate ($g$) of the dividends.

$3.45 (1 + g)^5 = 5.07$

$(1 + g)^5 = 5.07 / 3.45 = 1.4696$

$1 + g = (1.4696)^{1/5} = 1.0798 \approx 1.08$

$g = 0.0798$ or $7.98\%$

The net price for new shares is $45 -$1 - $2 =$

4

2.

The cost of equity ($r_e$) is calculated as:

$r_e = \frac{D_1}{P_0} + g$

where $D_1$ is the expected dividend, $P_0$ is the net price of the stock, and $g$ is the growth rate.

$r_e = \frac{5.07}{42} + 0.0798 = 0.12071 + 0.0798 = 0.20051$

$r_e = 20.051\%$

Finally, calculate the WACC.

WACC = $(w_d * r_d * (1 - Tax Rate)) + (w_p * r_p) + (w_e * r_e)$

where $w_d$ is the weight of debt, $w_p$ is the weight of preferred stock, and $w_e$ is the weight of common equity.

$WACC = (0.30 * 0.06199) + (0.05 * 0.12308) + (0.65 * 0.20051) = 0.018597 + 0.006154 + 0.13033 = 0.15508$

$WACC = 15.508\%$

If we use the yield 9.64% instead of the approximation:

$WACC = (0.30 * 0.06266) + (0.05 * 0.12308) + (0.65 * 0.20051) = 0.018798 + 0.006154 + 0.13033 = 0.155282$

$WACC = 15.5282\%$

3. Final Answer

The firm's weighted average cost of capital (WACC) is approximately 15.51%.