# calculating after-tax cost of debt

this is example 48-4 of reading 48

valence industries issues a bond to finance a new project. it offers a 10-year, 5% semi-annual coupon bond. upon issue, the bond selss at $1025. what is valence’s before-tax cost of debt? if valence’s marginal tax rate is 35%, what is valence’s after-tax cost of debt?

and in the solution, it says as given

FV = $1000

i am not sure why the future value is $1000

thanks.

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Upon issue, the bond can trade at either a premium or a discount. In this example, the coupon rate on the bond was greater than the prevailing market rate. Investors bid it up until it the C/Y reaches equilibrium with market rates. The question should say that the par value of the debt is $1000. If thats the case, that is the future repayment value, and thus why FV =$1000.

N=20, I/YR = ? PV = 1025 PMT = 25 FV = 1000

Double I/YR and that is your YTM

Multiply that by (1-.35) and viola, after tax cost of debt

Thanks for the reply.

But what I have on that post was all there was on the problem. I am not sure how I would assume that the coupon rate of the bond is greater than market rate. Could you explain that part to me in more detail please?

Also, what can I do if the problem does not tell me the par value of the debt?

Thanks again.

I would almost always assume par value of debt was $1000 unless told otherwise, or if it were a callable bond (can have a call price of say $1025 after 5 years).

Lets say currently the market interest rate is 5% and the bond issued by a corporation was 6%. For $1000 par value, you are getting $60 of coupon payments a year instead of the $50 that is the prevailing rate in the market. People will buy the 6% debt raising the price until these are equal. In this example, the price would be $1200.

60/1200 = 5%

The coupon payment doesn’t change, but the price of the bond will. This is just a simplistic explanation. Hope it helps.

I think your derivation of bond price of $1200 has some problem. You ignored all maturity and duration of this bond. It does not simply take the coupon rate devided by the market yield to come up with bond price.

Haha good point, I thought that looked weird, I should have put it in my calc. Ill make a real example.

Yeah, it’s about 108 give or take a bit.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Sorry about that post, I’ve been consumed with a million things and made a simply horrible mistake.

Ex:

Suppose you have a a market interest rate of 5%

You have a bond that is 10 year semi-annual coupon bond that pays $25 per 6 months, $1000 par value. When you plug that in your calculator you will get 5% (2.5 doubled)

Now suppose you have the similar 10 year bond issued in the same interest rate environment with a semi annual coupon bond that pays $30 every 6 months with a $1000 par value. You put that into your calculator and get $1077.95 rounded.

You are paying more for the higher yielding bond so these are equal now.

107.8 vs 108 - pretty close, huh? Who says you even need a calculator for these exams?

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!