Calculate cost of debt

CFA Level I Corporate Finance
#1

Problem 22 page 33 (L1V42022)
Two years ago, a company issued $20 million in long-term bonds at par value
with a coupon rate of 9%. The company has decided to issue an additional
$20 million in bonds and expects the new issue to be priced at par value with a
coupon rate of 7%. The company has no other debt outstanding and has a tax
rate of 40%. To compute the company’s weighted average cost of capital, the
appropriate after-tax cost of debt is closest to:
A 4.2%.B 4.8%.C 5.4%.

I used the weighted average cost of both issues to calculate the cost of debt. It’s like 0,59%+0,57%=8%
Then I take after-tax cost: 0,6*8%=4,8%

But the solution of Curriculum used 7% of the second issue as the cost of debt and so the after tax-cost they calculated is 0,6*7%= 4,2%

Who can explain me why we use YTM of expected new issue instead of weighted average of all issued as cost of debt ?

#2

For valuation purposes, you always want the current market cost of debt.

In this example, that cost of debt was 9% when the first bond was issued, but is now 7%, presumably because of better performance. As such, the company currently funds its debt at 7%, not 9%, and so WACC should be based on the 7%.

Although this will get you the correct answer at the exam, please note this will in fact give you the wrong valuation. This is for a couple of reasons:.

  1. This 7% only holds for a specifuc maturity. For WACC, you want very long term duration, since you discount at WACC to infinity. And so you would need some term premium to the 7%, else you’d overstate valuation. The question states ‘long term’, usually meant as 10y, to get around that, but in practice you still need to deal with the curve.

  2. If the cost of debt moves so fast from 9% to 7%, then likely leverage / credit risk also goes down fast. Accordingly, you can’t assume the debt / equity ratio is constant. Therefore, you’ll overstate the tax shield, and the valuation, if you use the traditional WACC formula.

Having run DCFs for billion dollar M+A deals, in my experience it is for reasons such as the above that no one really uses DCF to actually value a business. Rather, the DCF is more a negotiating tool.