Cost of capital
Cost of debt from yields
Estimate what a company pays to borrow today, from its bond yields or from a government yield plus a credit spread.
Learning objectives
- Explain why the cost of debt is today's yield, not the coupon rate
- Calculate a bond's yield to maturity with RATE
- Build a cost of debt from a government yield and a credit spread, including a synthetic rating
- Convert a pre-tax cost of debt to after tax
The cost of debt in a WACC is the return lenders would demand today to lend to the company: the rate at which it could borrow if it raised new debt now. It is not the coupon on old bonds or the rate on a loan signed years ago; those reflect market conditions and credit quality at the time.
There are two common ways to estimate it. If the company has bonds that trade, their yield to maturity is the market's answer. If it doesn't, build the rate up: a government yield for the same maturity plus a credit spread that matches the company's risk, often taken from a rating, or from a 'synthetic rating' based on interest cover.
Kd = YTM = RATE(n, coupon, −price, face) or Kd = government yield + credit spread; after tax: Kd × (1 − t)
- n
- years to maturity (annual coupons)
- price
- the bond's market price per 100 of face value
- credit spread
- the extra yield lenders demand over a government bond of the same maturity
- t
- tax rate; interest is tax-deductible, so debt costs less after tax
What the yield really is. A bond promises fixed cash flows: the coupons and the face value at maturity. The yield to maturity is the single discount rate that makes the present value of those promises equal to today's price. RATE finds it by trial and error, the same way IRR does for a project. So the yield is the return a buyer locks in by paying today's price and holding to maturity, which is exactly what a new lender would expect to earn from the company.
Why after tax. Interest is deducted before profit is taxed. If the company borrowed SAR 100m at the example's 5.71%, it would pay SAR 5.71m of interest a year but save SAR 1.14m of tax, so the net cost is SAR 4.56m. The saving only exists if the company has taxable profits to deduct the interest from; a loss-making company gets little or no shield, and its after-tax cost is closer to the pre-tax rate.
The synthetic-rating method, step by step:
- Calculate interest cover: EBIT ÷ interest expense.
- Look up the rating band that cover falls in, and the spread that goes with it.
- Add the spread to the government yield for a similar maturity.
- Multiply by (1 − t).
When both methods are available, compare them. If the bond's yield and the synthetic estimate are close, you can be confident. If they differ widely, ask why: an illiquid bond, an unusual covenant, or a cover ratio distorted by a one-off year. The after-tax figure is the debt half of the WACC; the next lesson builds the equity half.
Calculate
A private company has no traded bonds. The government yield for its borrowing maturity is 4.00% and companies with a similar credit profile pay a spread of 2.25%. The tax rate is 20% (illustrative). What is its after-tax cost of debt?
Check your understanding
Five years ago a company issued 10-year bonds with a 3% coupon. Rates have risen, and the bonds now trade at 88 per 100. Which is the better estimate of its pre-tax cost of debt for a WACC today?
Challenge: Two estimates of Najd Logistics' cost of debt
Najd Logistics Co. (fictional) has one bond that trades. Estimate its cost of debt two ways: (1) from the bond's yield to maturity, and (2) from a synthetic rating: interest cover, looked up in the illustrative spread table (D1:F6) with an approximate-match VLOOKUP, plus the government yield. Show both after tax.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Assumptions | Value | Cover at least | Rating | Spread | |
| 2 | Bond price (per 100 of face value) | 97.20 | 0.0 | B | 4.50% | |
| 3 | Annual coupon rate | 5.50% | 2.0 | BB | 2.75% | |
| 4 | Years to maturity | 7 | 3.0 | BBB | 1.75% | |
| 5 | Government yield, same maturity | 4.40% | 5.0 | A | 1.10% | |
| 6 | EBIT (SAR m) | 84.0 | 8.0 | AA | 0.70% | |
| 7 | Interest expense (SAR m) | 21.0 | Illustrative spread table | |||
| 8 | Tax rate (illustrative) | 20.0% | ||||
| 9 | ||||||
| 10 | Estimates | Value | ||||
| 11 | Yield to maturity (pre-tax cost of debt) | |||||
| 12 | Credit spread implied by the bond | |||||
| 13 | After-tax cost of debt (from the yield) | |||||
| 14 | Interest cover (EBIT ÷ interest) | |||||
| 15 | Synthetic rating | |||||
| 16 | Synthetic spread | |||||
| 17 | Pre-tax cost of debt (synthetic) | |||||
| 18 | After-tax cost of debt (synthetic) |
You're learning as a guest — exercises are checked, but progress isn't saved. Create a free account to keep it.