# Cost of debt, taxes and WACC

I am studying the cost of debt. Without loss of generality, suppose the debt consists of bonds. On the one hand, some textbooks (e.g. Hillier et al. "Fundamentals of Corporate Finance: 4th European Edition" chapter 13) warn against using coupon rate as the cost of debt, as the coupon rate is relative to the face value, not the market value of the bond. Instead, they suggest using yield to maturity (YTM) which is the compound return calculated relative to the bond's market value, and that makes sense to me. (Berk & DeMarzo "Corporate Finance" 4th ed. includes a similar point among "Common Mistakes" in Chapter 12.)

On the other hand, when calculating the weighted average cost of capital (WACC), the cost of debt is typically multiplied by $$(1-t)$$ where $$t$$ is the tax rate. This is meant to account for the fact that interest payments are tax deductible. This would make sense to me if the cost of debt were the coupon rate but not YTM. Whenever YTM times the market value of the bond is not the same as the coupon, I do not see why the difference should be tax deductible. After all, the actual payments that the tax office gets to see and to give tax deductions for are the coupons, not YTM times the market value of the bond. So multiplication by $$(1-t)$$ does not make sense to me any longer.

It may help to focus on the idea behind WACC calculations. It is supposed to show the return that both bondholders and shareholders demand to provide the company with capital. In the simplest case of only debt (no equity financing), it would be the current yield (determined by interest rates but also perceived credit risk of the entity).

If you run a company you care about current cost, not the past. Yield to maturity is a market metric and a lot more valuable compared to some outdated value. As a somewhat sloppy analogy, it does not matter what your car cost when you bought it if you have a crash. Your insurance company will pay current market value for it.

The cost of debt for a firm is best described as the cost of borrowing each additional dollar of debt:

• Internally, WACC is often used as a hurdle rate, to figure out the suitability of a given project.
• Externally, WACC can be used as a discount rate for future cashflows to determine the fair value of a company

Both are forward looking and do not care about the past.

Even excluding this logic, some bonds (most notable zero coupon bonds) sell at values different from par at issuance. In this case, the coupon does not reflect the true cost of debt even at issuance.

• Thank you. You explain the cost of debt in the case of zero taxes, and to that end I agree with everything you wrote. However, this does not answer my question. If I understand the tax code correctly, the tax deduction is based on coupon payments, not YTM times the market value of debt (MVD). Therefore, I do not see how the WACC formula can be right – unless the coupon equals YTM*MVD (which happens to be the case e.g. when the market value of a bond is equal to its face value). Oct 14, 2022 at 6:10
• I think I am beginning to realize my mistake. The WACC based on existing bonds that were issued in the past might not be appropriate for assessing (the net present value of) new projects. For assessing new projects, we should look at how expensive it would be to borrow money to finance them right now, and that is where the market value of the bonds comes in. It tells us what the coupon would be on hypothetical, newly issued bonds, and that coupon would be tax deductible. So yes, in such a forward-looking exercise, forward-looking WACC is needed. Did I get that right? Oct 14, 2022 at 8:38
• Exactly, since you are interested in the current cost of financing, the current market price of existing bonds is the best estimate. Oct 14, 2022 at 17:00
• By the way, your last paragraph relates to this question of mine. Would you say corporate bonds that do pay coupons typically sell at par value at issuance? Oct 14, 2022 at 17:32
• I am not qualified enough to answer that side question. I may find time to ask at work in the department that deals with that. I general, there are lost of ways bonds can be issued, with underwriters, via auctions ect but I am only involved in valuation in the secondary markets.
– Alex
Oct 15, 2022 at 15:31