Cost of Debt

A company that has borrowed money has a cost of debt, but the cost is not the figure printed on the loan agreement.

A bond that pays a 14% coupon on its nominal value but trades below that value yields more than 14% to the person who buys it today; a bank loan with an arrangement fee costs more than its interest rate; and because interest is deductible for tax, what the company really pays is less than what the lender receives.

For investment decisions the right figure is the cost the company would face today for new money of the same kind, measured after tax. This topic explains how to calculate it.

It sets out the difference between the lender’s pre-tax return and the company’s after-tax cost, between the nominal rate and the yield, how to calculate the cost of irredeemable debt, how to calculate the cost of redeemable debt as an internal rate of return (IRR) with the approximate rate as a starting point, the effect of the timing of tax relief, how to value a bond, the cost of a bank loan with fees, and what determines the cost of debt in Nigeria, with worked examples.

The next topic covers the cost of preference shares and convertible bonds.

The cost of a redeemable bond, as the internal rate of return of its cash flows, was needed in May Diet, 2026, Question 2(a) (7 marks), in the calculation of the weighted average cost of capital. Read the capital asset pricing model and arbitrage pricing theory first.

Pre-tax and after-tax cost

The cost of capital for investors is the return they require; for a company it is the return it must earn on its investments to pay them. The two are the same in theory but differ in practice because interest is a tax-deductible expense for the company. So the cost of debt can be seen from two sides.

The lender’s view discounts the pre-tax cash flows at the lender’s required return, the pre-tax cost of debt or yield. The company’s view discounts the cash flows after tax relief at the after-tax cost of debt, which is the rate used in the weighted average cost of capital. For a bank loan at 18% with tax at 30%, the after-tax cost is 18% × (1 − 0.30) = 12.6%.

Different items of debt have different costs because of differences in risk: whether the debt is secured, whether it is senior or subordinated (paid after other lenders), the time to maturity (longer-dated debt normally costs more, because the lender is exposed for longer and the future is less certain), and the credit rating of the borrower.

Nominal rate, yield and market value

The nominal rate (coupon) is the interest as a percentage of the nominal value of the debt: a bond of ₦100 nominal with a 14% coupon pays ₦14 a year whatever its price. The market value is the present value of all its future cash flows, and the yield is the return to the investor on that price.

Suppose ₦1,000m nominal of 10% bonds trade at ₦2,000m. The company still pays ₦100m a year. But the lender earns ₦100m on ₦2,000m, a yield of 5%: the cost of debt is the yield on the market price. The price used is ex-interest, excluding any interest about to be paid, as a share price is taken ex-dividend.

Irredeemable debt

If the debt is never repaid, interest goes on for ever, a perpetuity. The market value is P₀ = interest ÷ K_d, so before tax K_d = interest ÷ P₀ and after tax K_d = interest × (1 − t) ÷ P₀. For a 12% irredeemable bond (₦12 interest per ₦100 nominal) priced at ₦84 ex-interest with tax at 30%: K_d = 12 × 0.70 ÷ 84 = 8.4 ÷ 84 = 10.0%.

Redeemable debt: the cost as an IRR

The cost of redeemable debt is its redemption yield: the internal rate of return of the cash flows from now to redemption, with the market price as the outflow at time 0. The repayment of principal is not a tax-deductible expense, so the after-tax cost cannot be found by multiplying the pre-tax yield by (1 − t); a full IRR is needed. The cash flows are:

• the market value, ex-interest (an outflow at time 0 from the investor’s point of view);
• the annual interest (inflows);
• the tax relief on the interest, which reduces the company’s cost, so the net interest is interest × (1 − t), in the same year as the interest or one year later, as the question states; and
• the redemption value (an inflow), often at par, but sometimes at a premium.

Example: a 14% bond of ₦100 nominal, redeemable at par in 5 years, is priced at ₦92 ex-interest; tax is 30%. Net interest is 14 × 0.70 = ₦9.80.

1. Starting point: the approximate IRR.
   [net interest + (redemption − price) ÷ years] ÷ [(redemption + price) ÷ 2] = [9.80 + (100 − 92) ÷ 5] ÷ 96 = 11.40 ÷ 96 = 11.9%.
2. Try 11%:
   annuity factor 3.696 and year 5 factor 0.593: 9.80 × 3.696 + 100 × 0.593 = 36.22 + 59.30 = 95.52, less 92 gives +3.5.
3. Try 12%:
   factors 3.605 and 0.567: 9.80 × 3.605 + 100 × 0.567 = 35.33 + 56.70 = 92.03, less 92 gives about 0.
4. After-tax cost ≈ 12.0% (the IRR is 12.02%).

Before tax the same bond yields 16.5%, so 16.5% × 0.70 = 11.5% would have understated the after-tax cost, because it gives tax relief on the ₦8 gain on redemption, which is not deductible. For a bond redeemed at par and priced at par the two methods agree, because there is no gain.

When the tax relief comes a year late

If the company receives the tax relief on interest one year after paying it, the relief on year 1’s interest (₦4.20) arrives in year 2, and the relief on year 5’s interest arrives in year 6. The cash flows are −92, +14, then +9.80 in years 2 to 4, +9.80 + 100 in year 5, and −4.20 in year 6, and the IRR is 12.5%, higher than the 12.0% when relief is received in the same year.

A delay in receiving the relief makes debt a little more expensive for the company.

The value of a bond

The value of redeemable debt is the present value of its future cash flows, discounted at the lender’s required return (before tax). If lenders require 15% on the bond above, its value is 14 × 3.352 + 100 × 0.497 = 46.93 + 49.72 = ₦96.65 per ₦100 nominal. The relationship is the reverse of the cost calculation: a higher required return gives a lower price.

Bank loans and floating rates

The cost of a bank loan is the after-tax rate, but the arrangement fee and similar costs must be included, since they reduce the money received. Example: a loan of ₦200m for 5 years at 21% a year, repaid at the end, with a 1.5% arrangement fee (₦3m) that is not tax-deductible. Tax is 30%. The after-tax interest is 200 × 0.21 × 0.70 = ₦29.4m a year.

The company receives 200 − 3 = ₦197m and pays ₦29.4m a year plus ₦200m at the end: the IRR is 15.15%, compared with 14.7% (21% × 0.70) without the fee. The pre-tax cost including the fee is 21.5%.

Where the rate is floating (tied to a benchmark such as the Central Bank of Nigeria’s Monetary Policy Rate, which was 23% from 22 September 2026), the cost today is the current rate. It will change when the benchmark changes. In an appraisal the current rate, or the expected average, is used, and the sensitivity to rate changes is noted.

What sets the cost of debt in Nigeria

The cost of debt is built up from the risk-free rate (the yield on Federal Government of Nigeria bonds or treasury bills of matching term, which move with the Monetary Policy Rate and the expected rate of inflation) plus a credit spread for the borrower’s risk: its credit rating, security offered, leverage and track record.

In 2026 corporate bond coupons ranged from about 12.5% on older issues of the strongest names to 20% on a first issue by a smaller issuer. Bank lending rates for most borrowers were higher still. For a decision, use the rate the company would pay now, not what it paid in the past.

The ideas in more depth

Why the market value, not the nominal value

The cost of capital is the return that investors require today on the money they could have received today. A bond trading below its nominal value offers a gain at redemption as well as interest; one trading above it offers a loss at redemption.

The market price captures all this, so the cost is the yield on the market price, and the historical coupon is only one of the cash flows.

Why tax relief is only on the interest

A company deducts interest in arriving at taxable profit, but repaying the amount borrowed is not an expense. That is why the cash flows are interest net of tax and the full redemption value, and why the cost is the IRR of these flows rather than a simple adjustment of the pre-tax yield.

Tax relief only helps if the company has taxable profit: a company making losses cannot use it, and its true cost of debt is the pre-tax rate.

Sources and references

• No accounting standard governs the calculation of the cost of debt. The tax relief on interest follows the Nigeria Tax Act 2025 (company tax of 30% for companies other than small companies). The Monetary Policy Rate is set by the Central Bank of Nigeria.

These points are stated as at 5 November 2026.

Worked examples

1. Net interest.
   12 × 0.70 = ₦8.40.
2. Cost.
   8.40 ÷ 84 = 10.0%.

1. Numerator.
   9.80 + (100 − 92) ÷ 5 = 11.40.
2. Denominator.
   (100 + 92) ÷ 2 = 96; 11.9%.

1. Interest.
   200 × 0.21 × 0.70 = ₦29.4m a year.
2. Proceeds.
   200 − 3 = ₦197m; the IRR is 15.15%.

How to answer in the exam

• List the cash flows by year and use the ex-interest market value.
• Compute net interest and keep the redemption untaxed.
• Use the approximate IRR as the first trial and interpolate between two rates on either side of the answer.
• State the timing of tax relief you assume and the result as the after-tax cost.

Common mistakes in the exam

• Using the coupon as the cost of debt.
• Multiplying a redemption yield by (1 − t) when there is a redemption payment.
• Using a cum-interest price.
• Leaving out the arrangement fee in the cost of a loan.
• Using two trial rates on the same side of the IRR.
• Applying tax relief to a company that has no taxable profit.

Quick revision

• After-tax cost of a loan = rate × (1 − t); irredeemable: interest × (1 − t) ÷ price.
• Redeemable: IRR of − price, net interest, redemption (untaxed).
• Late tax relief raises the cost; fees raise the cost.
• Use the market value ex-interest and today’s rates.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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