Financial Management · Estimating the cost of capital

Cost of Debt: Irredeemable, Redeemable and Convertible Bonds

Updated 11 October 2026 · Fact-checked

The cost of debt is the return lenders require, adjusted for tax relief on interest. For irredeemable debt use after-tax interest ÷ ex-interest market price. For redeemable or convertible debt, find the IRR of the after-tax cash flows using two trial rates and interpolation.

Understand Cost of Debt: Irredeemable, Redeemable and Convertible

Debt holders lend money and want a return. That return is the company's cost of that finance. You find it from the bond's market price, not its nominal value, because the market price shows what investors will pay today for the future cash flows.

Interest is tax-deductible in most questions. So the company's real cost is lower than the interest it pays. This is why you calculate an after-tax cost of debt, written Kd(1 – T). It is the figure that goes into the WACC.

Irredeemable debt never gets repaid. The interest goes on for ever, so it is a perpetuity. The cost is simply annual interest after tax divided by the market price ex-interest.

Redeemable debt is repaid on a set date, usually at par or at a premium. The investor's return is the interest plus the gain or loss on redemption. You need the discount rate that makes the present value of future cash flows equal today's price. That is the IRR. You find it with two trial rates and linear interpolation.

A convertible bond gives the holder a choice on the conversion date: take cash redemption, or convert into a fixed number of shares. Assume the holder picks whichever is worth more. Work out the conversion value (future share price × number of shares), compare it with the redemption value, use the higher, and then find the IRR as for redeemable debt.

Key rules to remember

After-tax cost of irredeemable debt: Kd(1 – T) = i(1 – T) ÷ P0; i = annual interest in $, P0 = current market price ex-interest per bond, T = tax rate. Use the same unit for i and P0 (for example per $100 nominal).
After-tax interest cash flow: Interest × (1 – T); Use this for each year's interest in the IRR calculation. Assume tax relief arrives in the same year unless told otherwise.
IRR by interpolation: IRR = L + [NPV at L ÷ (NPV at L – NPV at H)] × (H – L); L and H are the low and high trial rates. NPV at L is positive and NPV at H is negative, so the bracket must contain the answer.
Conversion value: Current share price × (1 + g)^n × number of shares per bond; g = expected annual share price growth, n = years to conversion. Compare with the redemption value and use the higher.
Cash flows for the IRR: Year 0: – market price; Years 1 to n: after-tax interest; Year n: redemption or conversion value; Cash flows for the bond holder's return; the same rate is the company's cost of debt.

How to solve Cost of Debt: Irredeemable, Redeemable and Convertible questions

Use this order for any cost of debt question, whether irredeemable, redeemable or convertible.

1Read whether the debt is irredeemable, redeemable or convertible, and note the tax rate and when tax is paid.
2Find the market price. Make sure it is ex-interest. Use this as the year 0 outflow, not the nominal value.
3Calculate the annual interest from the coupon rate × nominal value, then multiply by (1 – T).
4If irredeemable, divide after-tax interest by the market price and stop.
5If convertible, work out the conversion value at the conversion date and compare it with the redemption value. Use the higher figure as the final cash flow.
6Set up the cash flows: price at year 0, after-tax interest each year, redemption or conversion value in the final year.
7Choose two trial rates, calculate each NPV, and check one is positive and one negative. Interpolate to find the IRR.
8State the answer as a percentage, labelled as the after-tax cost of debt.

Quickest way: Estimate first, then bracket tightly

When to use it: Use this in Section B objective test cases and in Section C where time is short and the answer is an IRR.

Estimate the rate first: if the price is below redemption value, the cost is above the after-tax coupon yield. If it is above, the cost is lower.
Pick the first trial rate near that estimate, and the second 1 to 3 percentage points away on the other side of the answer.
Use the annuity and discount factor tables provided. Calculate only the NPV at each rate.
Check the signs of the two NPVs differ. If both are positive or both negative, move the rate and try again.
Interpolate once, then sense-check: the answer should sit between the two trial rates.

Common mistakes in Cost of Debt: Irredeemable, Redeemable and Convertible

Using the nominal value instead of the market price as the year 0 figure.
The coupon is quoted on nominal value, so students carry nominal value through the whole calculation.
Fix: Interest comes from the nominal value. The investment (year 0) is always the market price.
Forgetting to deduct tax from interest, or taking tax off the redemption value as well.
Students remember 'tax' but apply it to the wrong cash flow.
Fix: Multiply only the interest by (1 – T). Redemption and conversion values are not taxed in this method.
Using the cum-interest price in the irredeemable formula.
The question gives one price and students do not check whether interest is due shortly.
Fix: Use the ex-interest price. If the price is cum-interest, subtract the interest due first.
Ignoring the conversion choice and always using par as the final cash flow for a convertible.
Convertibles look like normal bonds with extra wording.
Fix: Always calculate the conversion value and compare it with par. Use the higher.
Choosing two trial rates that give NPVs of the same sign, then interpolating anyway.
Students rush and do not check the signs.
Fix: Check the signs before interpolating. If they match, you are extrapolating, so pick a new rate.
Applying the wrong number of years or the wrong discount factors for the annuity.
Tax timing or conversion date is misread.
Fix: Write a short timeline of years and cash flows before you open the tables.

Worked examples

Example 1

A company has 6% redeemable bonds with a nominal value of $100. They are redeemable at par in 5 years and trade at $95 ex-interest. The tax rate is 25%, paid in the same year as the interest. Estimate the after-tax cost of debt.

Show the solution

After-tax interest = 6 × (1 – 0.25) = $4.50 per year.
Cash flows: year 0 = –$95; years 1 to 5 = +$4.50; year 5 = +$100.
Try 5%: annuity factor (5 years) = 4.329 and discount factor (year 5) = 0.784. PV = 4.50 × 4.329 + 100 × 0.784 = 19.48 + 78.40 = 97.88. NPV = 97.88 – 95 = +2.88.
Try 6%: annuity factor = 4.212 and discount factor = 0.747. PV = 4.50 × 4.212 + 100 × 0.747 = 18.95 + 74.70 = 93.65. NPV = 93.65 – 95 = –1.35.
Interpolate: IRR = 5% + [2.88 ÷ (2.88 + 1.35)] × 1% = 5% + 0.68% = 5.68%.

Answer: The after-tax cost of debt is about 5.7%.

Example 2

A company has 8% convertible bonds with a nominal value of $100, trading at $100 ex-interest. In 4 years holders can redeem at par or convert into 45 shares. The current share price is $2.00 and is expected to grow by 5% a year. The tax rate is 20%. Estimate the after-tax cost of the convertible.

Show the solution

Share price in 4 years = 2.00 × 1.05^4 = 2.00 × 1.2155 = $2.431.
Conversion value = 2.431 × 45 = $109.40. This is higher than par ($100), so holders convert. Use $109.40.
After-tax interest = 8 × (1 – 0.20) = $6.40 per year.
Cash flows: year 0 = –$100; years 1 to 4 = +$6.40; year 4 = +$109.40.
Try 8%: annuity factor (4 years) = 3.312 and discount factor = 0.735. PV = 6.40 × 3.312 + 109.40 × 0.735 = 21.20 + 80.41 = 101.61. NPV = +1.61.
Try 10%: annuity factor = 3.170 and discount factor = 0.683. PV = 6.40 × 3.170 + 109.40 × 0.683 = 20.29 + 74.72 = 95.01. NPV = –4.99.
Interpolate: IRR = 8% + [1.61 ÷ (1.61 + 4.99)] × 2% = 8% + 0.49% = 8.49%.

Answer: The after-tax cost of the convertible bond is about 8.5%.

Exam tips

In objective test questions, an answer is all or nothing. Check the units and whether the question asks for before-tax or after-tax cost.
Quote the interpolation clearly in Section C. Show both trial rates, both NPVs and the formula, so you earn method marks even if a table value slips.
Look for the words ex-interest, cum-interest, redeemable at a premium, and the date tax is paid. They change the cash flows.
For convertibles, write one line comparing conversion value with redemption value. Examiners look for that decision.
Link the answer to WACC. If the next part asks for WACC, use the after-tax cost of debt and market values for the weights.

Practice questions from Estimating the cost of capital

Cost of Debt: Irredeemable, Redeemable and Convertible in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Cost of Debt: Irredeemable, Redeemable and Convertible: frequently asked questions

How do I calculate the after-tax cost of irredeemable debt?

Multiply the annual interest by (1 – tax rate) and divide by the ex-interest market price. For example, 8% debt with a $100 nominal value priced at $80 ex-interest and 25% tax gives 8 × 0.75 ÷ 80 = 7.5%.

Why do I use IRR for redeemable debt?

Redeemable debt pays interest and then a lump sum on a fixed date. The return is the discount rate that equates those cash flows to today's price. That rate is the IRR, and interpolation gives a good estimate.

How do I decide whether a convertible bond will be converted?

Calculate the conversion value, which is the future share price × the number of shares per bond. If it is higher than the redemption value, assume holders convert and use it as the final cash flow. If it is lower, use the redemption value.

Should I use the nominal value or the market price in the cost of debt?

Use the market price as the year 0 figure. Use the nominal value only to calculate the interest and, where relevant, the redemption amount.