Question

Calculation of individual costs and WACC Lang Enterprises is interested in measuring its overall cost of capital. Current investigation has gathered the following data. The firm is in the 24 % tax bracket.

Debt The firm can raise debt by selling $1000 -par-value, 9 % coupon interest rate, 17 -year bonds on which annual interest payments will be made. To sell the issue, an average discount of $30 per bond would have to be given. The firm also must pay flotation costs of $30 per bond.

Preferred stock The firm can sell 8.5 % preferred stock at its $90 -per-share par value. The cost of issuing and selling the preferred stock is expected to be $4 per share. Preferred stock can be sold under these terms.

Common stock The firm's common stock is currently selling for $90 per share. The firm expects to pay cash dividends of $4.5 per share next year. The firm's dividends have been growing at an annual rate of 6 %, and this growth is expected to continue into the future. The stock must be underpriced by $6 per share, and flotation costs are expected to amount to $ 4 per share. The firm can sell new common stock under these terms.

Retained earnings When measuring this cost, the firm does not concern itself with the tax bracket or brokerage fees of owners. It expects to have available $150,000 of retained earnings in the coming year; once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.

a. Calculate the after-tax cost of debt.

b. Calculate the cost of preferred stock.

c. Calculate the cost of common stock.

d. Calculate the firm's weighted average cost of capital using the capital structure weights shown in the following table,

Source of capital	Weight
Long-term debt	20 %	​
Preferred stock	25
Common stock equity	55
Total	100%

Answer 1

a. Calculate the after-tax cost of debt.

The firm can raise debt by selling $1000 -par-value, 9 % coupon interest rate, 17 -year bonds on which annual interest payments will be made. To sell the issue, an average discount of $30 per bond would have to be given. The firm also must pay flotation costs of $30 per bond.

We will have to find the yield to maturity on this bond. We will use excel function "RATE" to calculate the yield. Inputs of RATE function = RATE (nper, payment, PV, FV)

Face Value = Future Value = FV = $ 1,000

nper = numbers of periods = 17 years

Payment = annual coupon once a year = 9% x 1,000 = $ 90

PV = - Current effective price of bond = -(Face value - discount - flotation cost) = -(1,000 - 30 - 30) = - $ 940

Hence, pre tax cost of debt, K_d = Yield to maturity on the bond = RATE (nper, payment, PV, FV) = RATE (17, 90, -940, 1000) = 9.74%

Tax rate, T = 24%

After tax cost of debt = K_d x (1 - T) = 9.74% x (1 - 24%) = 7.40%

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b. Calculate the cost of preferred stock.

The firm can sell 8.5 % preferred stock at its $90 -per-share par value. The cost of issuing and selling the preferred stock is expected to be $4 per share. Preferred stock can be sold under these terms.

Expected Dividend, D_s = 8.5% x Par value = 8.5% x 90 = $ 7.65

Effective price, P_s = Par Value - cost of issue = 90 - 4 = 86

Cost of preferred stock, K_s = D_s /  P_s = 7.65 / 86 = 8.90%

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c. Calculate the cost of common stock.

The firm's common stock is currently selling for $90 per share. The firm expects to pay cash dividends of $4.5 per share next year. The firm's dividends have been growing at an annual rate of 6 %, and this growth is expected to continue into the future. The stock must be underpriced by $6 per share, and flotation costs are expected to amount to $ 4 per share. The firm can sell new common stock under these terms.

The two components of common stock namely Retained earnings and fresh issuance of common shares will have different cost of equity associated with them. Let's calculate each one of them one by one.

Retained Earnings:

Expected dividend next year = D₁ = $ 4.50

Price per share = P = $ 90

g = growth rate in dividends = 6%

Hence, cost of retained earnings, K_RE = D₁ / P + g = 4.50 / 90 + 6% = 11.00%

Fresh issuance of common stock:

Effective Price per share, P_e = P - Underpricing - flotation cost = 90 - 6 - 4 = $ 80

Cost of freshly issued common equity, K_e = D₁ / P_e + g = 4.5 / 80 + 6% = 11.63%

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d. Calculate the firm's weighted average cost of capital

Proportion of different source of capital:

• Long-term debt, W_d = 20%
• Preferred stock, W_s = 25%
• Common stock equity, W_e = 55%

Expected retained earnings this year = $ 150,000

Since retained earning is a type of common equity with 55% proportion in capital structure, a total capital requirement of up to $ 150,000 / 55% = $  272,727 will get funded by a mix of debt - 20%, preferred stock - 25% and retained earnings - 55%.

So the WACC for capital up to $ 272,727 will be given by:

WACC = W_d x K_d x (1 - T) + W_s x K_s + W_e x K_RE = 20% x 7.40% + 25% x 8.90% + 55% x 11.00% =  9.76%

And the WACC for marginal capital beyond $ 272,727 will be given by:

WACC = W_d x K_d x (1 - T) + W_s x K_s + W_e x K_e = 20% x 7.40% + 25% x 8.90% + 55% x 11.63% =  10.10%