Financial Management · The valuation of debt and other financial assets

Yield to Maturity and Cost of Debt for ACCA FM

Updated 11 October 2026 · Fact-checked

Yield to maturity (YTM) is the IRR of a bond's cash flows: you pay today's market price and receive interest and redemption value. Solve it by trying two discount rates, finding the NPV at each, then interpolating. The pre-tax YTM is the cost of debt to the investor. For the company, use after-tax interest.

Understand Yield to Maturity and Cost of Debt

A bond promises two things: regular interest (the coupon) and a repayment (the redemption value) on a set date. You buy it at the market price, which is often not the nominal value. So the coupon rate alone does not tell you what you earn.

The yield to maturity is the annual return you earn if you buy at today's market price and hold to redemption. It is the discount rate that makes the present value of all future bond cash flows equal to the market price. That is exactly what an IRR is. The initial outflow is the price, and the inflows are the interest and redemption.

The coupon rate is fixed by the bond terms: interest ÷ nominal value. The YTM moves with the market price. For a bond redeemed at par, if the price is below the nominal value, the YTM is above the coupon rate. If the price is above the nominal value, the YTM is below the coupon rate. If the price equals the nominal value and the bond is redeemed at par, the YTM equals the coupon rate. If redemption is at a premium or discount to nominal value, this shortcut does not hold, so calculate the YTM.

YTM links to the cost of debt. The YTM is the pre-tax cost of the debt to the company, because it is the return lenders require at current market prices. Interest is tax-deductible, so the company's cost of debt for WACC uses the interest after tax relief. You then find the IRR again using the after-tax cash flows.

In the exam you cannot solve for the IRR directly. You calculate the NPV at two rates, one giving a positive NPV and one a negative NPV, and interpolate. The answer is an estimate, and that is accepted.

Key rules to remember

Bond price from YTM: P0 = Σ [Interest ÷ (1 + r)^t] + Redemption value ÷ (1 + r)^n; r is the YTM. Use annuity factors for the interest and a single discount factor for redemption.
Interpolation for IRR / YTM: YTM = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L is the lower rate and H the higher rate. NPV at L must be positive and NPV at H negative. Cash flows must include the price as a negative figure at time 0.
Coupon rate: Coupon rate = Annual interest ÷ Nominal value; Fixed by the bond terms. It does not change when the market price changes.
Current (running) yield: Current yield = Annual interest ÷ Market price; Ignores the gain or loss on redemption, so it differs from YTM for redeemable bonds.
Interest after tax relief: After-tax interest = Coupon × (1 − tax rate); Use for the company's cost of debt. Assume tax is paid in the same year unless told otherwise.
Irredeemable debt cost: Kd = Interest × (1 − T) ÷ P0; Use only if the debt is never redeemed. P0 is the ex-interest market price.
Starting-rate approximation: r ≈ [Interest + (Redemption − Price) ÷ n] ÷ [(Redemption + Price) ÷ 2]; Only a guide for choosing the first trial rate. Do not give it as the final answer.

How to solve Yield to Maturity and Cost of Debt questions

Use this method for any question that asks for a yield to maturity or a cost of redeemable debt.

1Decide what is asked: pre-tax YTM (investor's return) or after-tax cost of debt (company, for WACC). If the question mentions tax, it is usually the after-tax cost.
2List the cash flows. Time 0 is the market price as a negative figure. Then list the interest each year (after tax if needed) and the redemption value in the final year. Note any premium or discount on redemption.
3Pick a first trial rate. Use the coupon rate, or the approximation formula. If the price is below redemption value, the YTM is above the coupon rate. If above, it is below.
4Calculate the NPV at that rate using annuity and discount factors from the tables.
5Choose a second rate on the other side, so that one NPV is positive and one is negative. Keep the two rates 1 to 2 percentage points apart. Calculate the NPV.
6Interpolate with L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L). Use the absolute size of the NPVs so the fraction is positive.
7State the answer to two decimal places or as asked. Say whether it is pre-tax or after tax. Do a quick sense check against the coupon rate.

Quickest way: Approximate first, then bracket

When to use it: Use this in Section A and in Section B OT cases where time is short and the answer options are spaced apart.

Work out the approximation: [Interest + (Redemption − Price) ÷ n] ÷ [(Redemption + Price) ÷ 2].
Round it to a whole percentage as your first trial rate, and take the next whole percentage above or below as the second.
Calculate the NPV at both rates, only the two calculations, with tax applied to interest first if needed.
Interpolate once, then match your result to the closest option. Because the interpolated answer is an estimate, expect small differences from the options.
If both NPVs have the same sign, move one rate further out. Do not extrapolate far.

Common mistakes in Yield to Maturity and Cost of Debt

Treating the coupon rate as the cost of debt or the YTM.
The coupon is the number printed on the bond and is easy to spot.
Fix: The coupon is fixed on nominal value. YTM depends on the market price. Use the market price at time 0 and calculate the IRR.
Using the nominal value instead of the market price as the time 0 flow.
Students confuse what the bond repays with what the investor pays today.
Fix: Time 0 is always the current market price. Nominal value is used only to calculate interest and, if redeemed at par, the redemption.
Applying tax relief to the redemption value or premium.
Students think everything related to the debt is tax adjusted.
Fix: Unless told otherwise, only the interest gets tax relief. Redemption value is not adjusted for tax.
Choosing two trial rates that both give a positive (or both negative) NPV.
The first guess is not checked against the price, and the second guess is too close.
Fix: Use the price to judge direction: price below redemption means YTM above the coupon. Check the signs before interpolating.
Leaving the final-year interest out when adding redemption, or using the wrong factor for redemption.
Students focus on the lump sum and forget the interest still paid in year n.
Fix: Apply the annuity factor to interest for all n years. Apply the single year-n discount factor to the redemption value only.
Giving a pre-tax YTM when the question asks for the company's cost of debt for WACC.
The tax wording is missed.
Fix: If a tax rate is given and the answer feeds into WACC, calculate with after-tax interest and label the answer after tax.

Worked examples

Example 1

A bond has a nominal value of $100 and pays 6% interest annually. It will be redeemed at par in 5 years. The current market price is $95. Estimate the yield to maturity using interpolation. Use 7% and 8%. Annuity factors for 5 years: 7% = 4.100, 8% = 3.993. Discount factors at year 5: 7% = 0.713, 8% = 0.681.

Show the solution

Interest is 6% × $100 = $6 a year. Redemption is $100 in year 5. Price is $95.
At 7%: PV of interest = 6 × 4.100 = 24.60. PV of redemption = 100 × 0.713 = 71.30. Total PV = 95.90.
NPV at 7% = 95.90 − 95.00 = +0.90.
At 8%: PV of interest = 6 × 3.993 = 23.958. PV of redemption = 100 × 0.681 = 68.10. Total PV = 92.058.
NPV at 8% = 92.058 − 95.00 = −2.942.
Interpolate: YTM = 7% + [0.90 ÷ (0.90 + 2.942)] × (8% − 7%) = 7% + 0.2343% = 7.23%.
Check: price is below par, so YTM should be above the 6% coupon. It is.

Answer: The yield to maturity is approximately 7.23% a year (pre-tax).

Example 2

A company has a bond with a nominal value of $100 and an annual coupon of 5%. It will be redeemed in 4 years at $105. The current market price is $98. The tax rate is 25%, paid in the same year as the interest. Estimate the company's after-tax cost of debt using 5% and 6%. Annuity factors for 4 years: 5% = 3.546, 6% = 3.465. Discount factors at year 4: 5% = 0.823, 6% = 0.792.

Show the solution

Interest = 5% × $100 = $5. After tax: 5 × (1 − 0.25) = $3.75 a year.
Cash flows: time 0 = −98. Years 1 to 4 = +3.75. Year 4 also has redemption +105. Redemption is not adjusted for tax.
At 5%: PV of interest = 3.75 × 3.546 = 13.2975. PV of redemption = 105 × 0.823 = 86.415. Total = 99.7125.
NPV at 5% = 99.7125 − 98 = +1.7125.
At 6%: PV of interest = 3.75 × 3.465 = 12.99375. PV of redemption = 105 × 0.792 = 83.16. Total = 96.15375.
NPV at 6% = 96.15375 − 98 = −1.84625.
Interpolate: 5% + [1.7125 ÷ (1.7125 + 1.84625)] × 1% = 5% + 0.4812% = 5.48%.

Answer: The after-tax cost of debt is approximately 5.48%.

Exam tips

Read whether the question wants a pre-tax yield or an after-tax cost of debt. Many OT questions test only this distinction.
Write the cash flow layout first: price at time 0, interest, redemption. This protects you from missing a flow and helps in Section C marking.
In Section C, show both NPV calculations and the interpolation formula with numbers. Marks are given for method even if one factor is misread.
OT questions score all or nothing, so check that your two NPVs have opposite signs before interpolating, and check your answer against the coupon rate.
Know the link to WACC: the after-tax cost of debt from this topic is the figure you use for debt in the weighted average calculation, weighted by market value.

Practice questions from The valuation of debt and other financial assets

Yield to Maturity and Cost of Debt in other exams

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

Yield to Maturity and Cost of Debt: frequently asked questions

What is the difference between coupon rate and yield to maturity?

The coupon rate is the fixed interest divided by nominal value and does not change. The yield to maturity is the return you earn from today's market price, including interest and the gain or loss at redemption. They are equal when the bond is priced at nominal value and redeemed at par (nominal value).

How do I calculate yield to maturity using IRR in ACCA FM?

Set up the cash flows with the market price as a negative at time 0, then interest and redemption as positives. Calculate the NPV at two rates that give opposite signs. Then interpolate to estimate the rate where NPV is zero.

Is yield to maturity the same as the cost of debt?

The pre-tax YTM is the cost of debt before tax relief, from the lender's view. For the company's WACC, you calculate the IRR using interest after tax relief, which gives a lower figure. Always state which one you have calculated.

Why does my interpolated answer differ slightly from the exact YTM?

Interpolation assumes the NPV changes in a straight line between the two rates, but the real relationship is a curve. The closer your two rates are to the true answer, the smaller the error. ACCA accepts the interpolated figure.