Cost of debt using YTM approach

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One of many examples (from EOC questions) :
Dot.Com has determined that it could issue $1,000 face value bonds with an 8 percent coupon paid semi-annually and a five-year maturity at $900 per bond. If Dot.Com’s marginal tax rate is 38 percent, its after-tax cost of debt is closest to:
  1. 6.2 percent.
  2. 6.4 percent.
  3. 6.6 percent.
Answer: C (solving for I/Y > 5.315% x2 = 10.63% > 10.63% x (1-0.38) = 6.6%)
I have always wondered, why do we use the YTM quoted on a semi annual basis?
Shouldn’t we convert the YTM to an annual YTM ?
(1.05315^2) -1 = 10.91% > 10.91% x (1-0.38) = 6.77% after-tax cost of debt
Thanks!
 
YTM for bonds is quoted as a bond equivalent yield (BEY), which is twice the semiannual effective yield. It’s done that way because most bonds pay coupons semiannually, so their annual coupon rate is twice their semiannual yield.
The method you propose converts the effective semiannual yield into an effective annual yield. There’s nothing wrong with that, but it’s simply not how bond yields are quoted.
 
Assuming a company financed only with bonds paying semi annual coupons, with an after-tax cost of debt of 8%:
If the cost of debt of 8% is based on the BEY, the company would technically have a higher cost of fund than a company with an 8% cost of equity?
And also, if a company is financed with bonds paying annual payments, should we convert the annual YTM to a BEY?
I entirely agree that bonds are quoted on a semi annual basis (BEY), what I don’t get is why we use the BEY to calculate the cost of debt. We can’t really compare our costs in this case can we?
Thanks again,
 
I agree that the WACC calculation combines various methods of yield, but the differences are small; certainly smaller than the error in estimating the cost of common equity, for example.
I wouldn’t give it another thought.
 
Ok great. I just wanted to make sure I was not missing something here.
Thank you.
 
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