Weighted average cost of debt

Two years ago, a company issued $20 million in long-term bonds at par value with a coupon rate of 9 percent. 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 percent. The company has no other debt outstanding and has a tax rate of 40 percent. 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%.

The relevant cost is the marginal cost of debt. The before-tax marginal cost of debt can be estimated by the yield to maturity on a comparable outstanding. After adjusting for tax, the after-tax cost is 7(1 − 0.4) = 7(0.6) = 4.2%.

If the question is weighted average cost of debt why would I use 7 % for the calculation? I would think that relevant would be 7+9=8%

Thanks for the help!

You are trying to derive the weighted average cost of capital, not debt.

In this case, the WACC used the marginal cost of debt and equity. Which in this case, Kd = 7% (1-t).

The weighted-average cost of capital is the average cost (today) of raising new capital. You use today’s cost of common equity, today’s cost of preferred equity, and today’s cost of debt.

The easiest one is today’s cost of debt: it’s just the current YTM on the company’s outstanding bonds.

It’s not the most accurate either, well depending on the situation. The implied marginal cost of debt should be the YTM for a newly issued LTM bond. Unless the current YTM is a company estimate for today.

Don’t forget who your audience is here.

For Level I CFA candidates, unless they’re told explicitly to add an additional risk premium, the value to use for the cost of new long-term debt is the YTM on that company’s existing long-term debt.

Ah, you’re right.

It’s just so difficult to ignore these small nuisances after reading more advanced academia. I’d certainly wouldn’t have minded to learn proper theory and practice at the go. But for exam purposes, I guess that’s enough to keep busy.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions. - Felix Klein

Alright, makes sense. So assuming the weighted average term has been used just to confuse us newbies… well played

Good to hear.

Not really: the term weighted average means an average of (today’s) common equity cost, preferred equity cost, and debt cost.

I have a hard time understanding why we interpret the term weighted average as “today’s” cost. Since it is a weighted average, shouldn’t we be including both the past cost and today’s cost when calculating the weighted average?

We’re trying to determine what it will cost to finance projects today.

Oh, I see. So basically it is the weighted average cost of today only… And we ignore the past. Thank you for the clarification!

My pleasure.