# Cost of Debt question help

Hi all,

I keep getting the wrong outcome in the below question;

A target capital structure of 20% preferred stock, 30% common equity and 50% debt. The company has outstanding a 7% annual coupon-paying, 20-year maturity and \$1,000 par bond. Currently the bond is selling for \$932.5. The company is expected to have the constant growth rate of 10% and its stock is selling for \$100 per share. Next year’s dividend is expected to be \$3 per share. The company’s \$1,000 face value preferred stock currently sells for \$900 and has a dividend rate of 6%. If the company’s marginal tax rate is 35%, what is the after-tax cost of debt?

A. 4.55%

B. 7.99%

C. 5.20%

I believe my error is that I’m using \$70 as the coupon instead of \$35; but my question is why is the Coupon multiplied by 50%?

Whats the answer ? Then I will try to figure it out

It is stated that their bond is paying coupons annually, so I don’t see why you would divide the coupon by 2.

I compute that cost of debt as:

N=20

PV=932.5

PMT=-70

FV=-1000

CTP-> I/Y=7.67%

Then your after-tax cost of debt would be:

(1-0.35)*7.67%=4.9859

That does not seem to be one of the possible answers though.

N = 20

PMT = 70

FV = 1000

PV = -932.5

CPT - I/Y = 7.67

After Tax cost of debt = 7.67 * (1-0.35) = 4.98%. The closest is between A and C, but i will go for C, as it is the closest.

But the answers are actually wrong, the variation between the options and the answers is too wide.

If above both are not correct then 7%(1-0.35)= 4.55%

Where did you get this question? It clearly didn’t come from CFA Institute, nor from one of the major prep providers (Schweser, Wiley, Fitch).

What’s their explanation?

The author of the question has done something wrong.

This was an Apptuto question. I believe it may be a mistake.

I had chosen 4.99% as the answer hence my surprise to be told it’s incorrect.

Here is the solution from Apptuto:

“If the bonds are trading at \$932.5 per \$1000 par, the required yield will be: N = 10*2=20; PV = -932.5 ; FV = 1000; PMT = 1000*7%*0.5 = 35; CPT I / Y = 4.00%. annual rate = 4.00%*2 = 8.00% The after-tax cost of the debt is: 8% x (1-0.35) = 5.20% You might have taken coupon rate instead of yield for the cost of debt.”

Well, they’ve obviously fouled up the answer.

The question says that it’s 20 years to maturity, annual pay. They calculated it as if it were 10 years to maturity, semiannual pay.

E-mail them and let them know that their solution is junk.

Done. Other than this, I am finding their QBank very useful. I don’t know any other views on Apptuto; certainly a major improvement on AllenCFA.