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.