this is what i have done for this problem.

the general formula for calculating the WACC is:

rwacc = [E / (E + D)] x rE + [D / (E + D)] x rD (1 - Tc)

where

E is the market value of equity

D is the market value of debt

rE is the equity cost of capital

rD is the debt cost of capital

Tc is the corporate tax rate

for this problem,

rwacc =

[E1 / (E1 + E2 + D)] x rE1

[E2 / (E1 + E2 + D)] x rE2

[D / (E1 + E2 + D)] x rD (1 - Tc)

let E1 be the market value of preferred stock and E2 be the market value of common stocks. let rE1 and rE2 be the corresponding costs of capital.

because you have 43,000 shares of preferred stock valued at $60.00 each,

E1 = 43,000 x $60.00 = $2,580,000

this stock pays a dividend of $7.50 and is priced at $60.00

using the zero-growth Dividend Discount Model,

Price = dividend amount / cost of capital

cost of capital = divident amount / price = $7.50 / $60.00 = .125

thus,

E1 = $2,580,000

rE1 = .125

because you have 300,000 shares of common stocks trading at $40.00 each,

E2 = 300,000 x $40.00 = $12,000,000

you are given that

stock beta = 0.7

risk-free rate = 0.065

market risk premium = 0.0625

using the Capital Asset Pricing Model,

rE2 = risk-free rate + stock beta x market risk premium

rE2 = .065 + 0.7 x 0.0625 = .10875

the problem gives that Tc = 0.40, so you just need to calculate the market value of debt and the cost of debt.

for D, you know that the face-value is $1,000, and at par, the price of the bond equals its face value. since you have 10,000 bonds each with a face-value of $1,000 trading at 105.5% of par value,

D = 10,000 x 1,000 x 1.055 = $10,550,000

to find the cost of debt, you will need to use the bond pricing formula and solve for the yield rate, letting P = $1,055 (the price of each bond)

P = (F x r)an + C x v^n

where

F = face value of the bond

r = coupon rate

n = number of periods.

an = annuity-immediate of annual payments of 1 lasting for n periods and with rate of interest i

C = redemption value of the bond

v = (1 + i)^(-1)

given that you have semi-annual bonds that matures in 5 years,

n = 5 x 2 = 10 (there are 10 half-years in 5 years)

r = .076 / 2 = .038

(you need to divide by 2 because the coupons are paid semi-annually)

1055 = (1,000 x .038)a10|i + 1,000 x (1 + i)^(-10)

using brute force, i is approximately .0315027 per half year.

or .0630054 per year.

going back to the rwacc formula, with

E1 = $2,580,000

rE1 = .125

E2 = $12,000,000

rE2 = .10875

D = $10,550,000

rD = .0630054

Tc = .40

results in rwacc = .091213966 or 9.12%

the answer seems reasonable to me, but it’s best to see confirmation that others also arrived (or not) at this result. if someone found mistake in my reasoning, i would be thankful if they could share on where i made said mistake. thanks!

as a sanity check, because this is the weighted average cost of capital, i certainly know that rwacc can be no higher than the highest cost of capital calculated, and no smaller than the smallest cost of capital. that is,

rwacc >= min (rE1, rE2, rD)

and rwacc <= max (rE1, rE2, rD)

in my solution, rwacc = 9.12% certainly passes this requirement: it is a value between the two extremes. if i obtained 20% as an answer, i know i made a mistake, since it would be impossible to get such a high cost of capital when the highest cost of capital calculated is less than that.