 # Need help solving a problem involving Weighted Average Cost of Capital (WACC)

Hi everyone. I need help with an assignment for class. I’m try to solve the problem while using a ba ii plus calculator and I’m not sure if I’m doing it correctly.

Cost of Debt:

30 year Bonds

Current Price 105.5%

7.6% Coupon Rate

Semi Annual Bond

5 years to Maturity

Tax Rate is 40%

What is the cost of debt?

In the calculator, I put…

N = 10

I/Y = ?

PV = -1055

Pmt = 38

FV = 1,000

For I/Y, got 3.1503 then multiplied it by .2 and got 0.6301. Then multiplied 0.6301 by .6 and got 0.3780.

Preferred Stock:

Dividend \$7.50

Current Price \$60.00

What is the cost of Preferred?

The calculations I did:

7.50/60.00 = 0.1250

Equity:

Risk Free Rate 6.50%

Stock Beta 0.7

What is the Cost of Equity?

The answer I got for this was 6.33. Not sure if thats correct or not.

Lastly, I need to calculate the WACC (Weighted average cost of capital). Not sure how to do that though.

Thanks

For your cost of debt you need to tax effect it, so it’s 6.3% x (1-0.4)

Your cost of equity is 10.875 which is Re = Rf + beta (MRP) = 6.5 + 0.7 x 6.25

I don’t know what the WACC is here because you haven’t provided the amount of debt, prefereed stock, and equity.

To calculate the weight you do Wd(Re) + Wp(Rp) + We(Re), where the weights equal the proportion of each source to total capital.

So for example if you have \$100 of debt and you have \$400 of total capital, then your Wd is 0.25.

Hope that helps.

Oh I forgot to include the Market Value info:

10,000 Bonds Outstanding Selling @ 105.5% of Par Value

43,000 Preferred Stock @ 60.00

300,000 Shares of Common Stock @ 40.00 per share

Calculations:

I multiplied 10,000 x 1,055 = 10,550,000 (Debt)

then 43,000 x 6,000 = 258,000,000 (Preferred Stock)

Lastly I multiplied 300,000 x 4,000 = 1200000000 (Equity)

I added 10,550,000 + 258,000,000 + 1200000000 and got 1468550000.

After that I divided 10,550,000 by 1468550000 and got 0.0071 (Debt)

I divided 258,000,000 by 1468550000 and got 0.1756 (Preferred Stock)

Lastly, I did 1200000000 by 1468550000 and got 0.8171 (Equity)

WACC Calculations:

Then for debt I did: .3780 x 0.71 and got 0.26838

For Preferred Stock I did: .1250 x 17.56 and got 2.195

For Equity I did: 10.8750 x 0.8171 and got 8.8859

For the WACC, I got 11.34928 but I’m not sure if that is correct

Why are you being inconsistent with your decimal places?

Common stock is at 40.00 per share but you’re multiplying it by 4,000 below? Are you paying attention to your numbers at all?

Your output makes no sense because you’re moving decimal places all the time.

Honestly I’m not 100 % sure what I’m doing. I thought the correct way was to multiply 10,000 and change the 40.00 to 4,000 to make it easier to multiply. I don’t know if I have to multiply the two market value numbers with the decimal points or without the decimal points. My instructor also instructed me to use four decimal places as well. I was wondering if someone could show me the correct way to compute the market values since I’m so confused on how to do it.

I’m sorry your instructor told you to change it to 4,000 because your instructor is clueless. Keep everything consistent.

10,000 Bonds Outstanding Selling @ 105.5% of Par Value = 10,000 x 1,055 = 10,550,000

43,000 Preferred Stock @ 60.00 = 43,000 x 60 = 2,580,000

300,000 Shares of Common Stock @ 40.00 per share = 300,000 X 40 = 12,000,000

Do you see how reasonable these numbers look now? Divide each by the total sum and you get the weights.

Okay now I see how reasonable the numbers are and it makes total sense to me now. Thanks.

Here’s the calculations that I did:

10,550,000 + 2,580,000 + 12,000,000 = 25130000

Then I divided the two numbers:

(Debt) 10,550,000 / 25130000 = 0.4198

(Preferred Stock) 2,580,000 / 25130000 = 0.1027

(common Stock) 12,000,000 / 25130000 = 0.4775

Then I did:

(Debt) 37.80 x 0.4198 = 15.86844 (Preferred Stock) 12.50 x 0.1027 = 1.2825

(Common Stock) 10.8750 x 0.4775 = 5.192812

I added those numbers together and got the WACC which is 22.343752. Hopefully that is the correct answer.

[quote=“ecstaticrose45”]

Cost of Debt:

For I/Y, got 3.1503 then multiplied it by .2 and got 0.6301. Then multiplied 0.6301 by .6 and got 0.3780./quote]

3.1503 means 3.1505% per semiannual period.

Why did you multiply it by 0.2?

My professor instructed me to multiply by 0.2 then also multiply by 0.6 to get a final answer (0.3780). I’m just solving the problem the way my professor instructed me too.

With all due respect, your professor is wrong.

You should multiply by 2.

If you want to change it to a decimal, then multiply by 0.01 after that.

In any case, 0.2 makes no sense.

Ohh okay I understand it now. Thanks for explaining the correct way to do it.

Now I’m not sure if the WACC is correct or not…

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

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.

edit: (i would edit in the same post, but for whatever reason, the site wont let me)