Financial Management · Sources of finance and their relative costs

Cost of Debt, Preference Shares and Convertibles in ACCA FM

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 I(1 − T) ÷ P0. For redeemable debt find the IRR of the post-tax cash flows. Preference shares cost D ÷ P0 with no tax relief. Convertibles use the IRR with the higher of redemption or conversion value.

Understand Cost of Debt, Preference Shares and Convertibles

A company's cost of capital is the return its investors demand. Lenders, preference shareholders and bondholders each want a return, and the company must earn at least that to keep them satisfied. In FM you calculate each cost separately, then blend them in the WACC.

Debt is cheaper than equity for two reasons. Lenders have a prior claim on cash flows, so their risk is lower. Interest is also usually tax-deductible. So you calculate the post-tax cost of debt by taking the tax saving into account. The market price of the debt is the starting point, not its nominal value, because the market price reflects what investors would pay today for the future cash flows.

Irredeemable debt pays interest forever, so it works like a perpetuity. Cost = post-tax interest ÷ market price. Redeemable debt pays interest and then a repayment at a set date. The cost is the discount rate that makes the present value of those cash flows equal today's market price. That rate is an IRR, often called the yield to maturity when you ignore tax. For the WACC you use the post-tax version.

Preference shares pay a fixed dividend. Dividends are paid out of post-tax profit, so there is no tax relief. Treat them as irredeemable: cost = dividend ÷ market price (ex-dividend).

Convertible bonds let the holder swap the bond for shares on a set date instead of taking cash. Work out the expected conversion value at that date. Assume the holder takes whichever is higher, conversion value or redemption value. Then calculate the IRR using that final cash flow.

Key rules to remember

Irredeemable debt, post-tax: Kd = I × (1 − T) ÷ P0; I is annual interest, T is the tax rate, P0 is the ex-interest market value of the debt. Use the market price, not nominal value.
Redeemable debt, IRR: P0 = Σ [I(1 − T) ÷ (1 + r)^t] + Redemption ÷ (1 + r)^n; Solve for r. Cash flows at time 0 are −P0. Use ex-interest prices. Tax is assumed paid in the same year unless the question says otherwise.
IRR by interpolation: IRR = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L and H are two trial rates. One NPV should be positive and one negative. Keep the trial rates close together, ideally 1 to 2 points apart.
Preference shares: Kp = D ÷ P0; D is the annual preference dividend, P0 is the ex-dividend market price. No tax adjustment.
Bank loan, post-tax: Kd = Interest rate × (1 − T); Use when the loan is at par and the interest rate is the cost. Without issue costs or a discount this needs no IRR.
Convertible conversion value: Conversion value = P0 × (1 + g)^n × number of shares per bond; Here P0 is the current share price and g is the share price growth rate. Compare this with the redemption value and use the higher in the IRR.

How to solve Cost of Debt, Preference Shares and Convertibles questions

Use this method for any question on the cost of debt, preference shares or convertibles.

1Identify the instrument: irredeemable, redeemable, preference share or convertible. This decides the formula.
2Find the market price. Check that it is ex-interest or ex-dividend. If it is cum-interest, deduct the interest about to be paid.
3Work out the annual interest or dividend from the nominal value and coupon rate, not from the market price.
4For debt, deduct tax: interest × (1 − T). Do not do this for preference dividends.
5For irredeemable debt or preference shares, divide by the market price and finish.
6For redeemable debt, lay out cash flows: −P0 at time 0, post-tax interest for each year, and redemption in the final year. Include any premium on redemption.
7For convertibles, calculate the future conversion value, compare it with the redemption value, and use the higher one as the final cash flow.
8Try two discount rates, calculate the NPV at each, and interpolate. State the answer to one decimal place and say which instrument it is.

Quickest way: Fast estimate and sensible trial rates

When to use it: Use under time pressure for redeemable debt and convertibles, where the IRR needs two trial rates.

Pick your first trial rate from a quick estimate: post-tax interest plus the annual gain or loss to redemption, divided by the average of price and redemption value.
Use the annuity factor for the interest and the single discount factor for the redemption. Do not discount each year separately.
Choose the second trial rate 1 to 2 points away, on the other side of zero NPV.
If both NPVs have the same sign, you have not bracketed the IRR. Move the second rate further.
Sense-check: if the debt trades below par, the IRR should be above the post-tax coupon rate. If it trades above par, it should be below.

Common mistakes in Cost of Debt, Preference Shares and Convertibles

Using nominal value instead of market price as P0.
The coupon is given on nominal value, so students use nominal value throughout.
Fix: Interest comes from nominal value. The cost is measured against the market price. Always put the market price at time 0.
Applying tax relief to preference dividends.
Preference shares are often grouped with debt as fixed-return finance.
Fix: Preference dividends are paid from post-tax profit. Kp = D ÷ P0 with no (1 − T).
Calculating the IRR on pre-tax interest and then adjusting the answer by (1 − T).
Students copy the irredeemable formula into a redeemable question.
Fix: For redeemable debt, put post-tax interest into the cash flows. The redemption payment is not tax-affected, so you cannot adjust the final rate.
Leaving the interpolation with both NPVs positive or both negative.
Students choose trial rates too close, or do not check the signs.
Fix: Check the signs before interpolating. If they match, change one rate. Extrapolating gives a poor estimate.
Always assuming a convertible will be redeemed.
Students treat it like ordinary redeemable debt.
Fix: Calculate the conversion value first. If it exceeds the redemption value, use it as the final cash flow.
Using a cum-interest price without adjustment.
The word 'cum' is overlooked.
Fix: Deduct the interest due from a cum-interest price to get the ex-interest P0.

Worked examples

Example 1

A company has 6% redeemable bonds with a nominal value of $100. The bonds are redeemable at par in 5 years. The current ex-interest market price is $95. The tax rate is 25%, paid in the same year as the interest. Calculate the post-tax cost of debt.

Show the solution

Annual interest = 6% × $100 = $6; post-tax = 6 × 0.75 = $4.50.
Cash flows: time 0 = −$95; years 1 to 5 = $4.50; year 5 also = $100 redemption.
Try 5%: annuity factor 4.3295 × 4.50 = 19.48; discount factor 0.7835 × 100 = 78.35. PV = 97.83. NPV = 97.83 − 95 = +2.83.
Try 6%: annuity factor 4.2124 × 4.50 = 18.96; discount factor 0.7473 × 100 = 74.73. PV = 93.69. NPV = 93.69 − 95 = −1.31.
Interpolate: IRR = 5% + [2.83 ÷ (2.83 + 1.31)] × 1% = 5% + 0.68% = 5.68%.

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

Example 2

A company has 7% convertible loan notes with a nominal value of $100, with an ex-interest market price of $95. They are redeemable at par in 4 years, or convertible then into 50 ordinary shares per note. The current share price is $2.00 and is expected to grow by 5% a year. The tax rate is 20%. Calculate the post-tax cost of the convertible.

Show the solution

Post-tax interest = 7 × (1 − 0.20) = $5.60 a year.
Share price in 4 years = 2.00 × 1.05^4 = 2.00 × 1.2155 = $2.431.
Conversion value = 50 × 2.431 = $121.55. This is above the $100 redemption value, so assume conversion.
Cash flows: time 0 = −$95; years 1 to 4 = $5.60; year 4 also = $121.55.
Try 10%: annuity factor 3.1699 × 5.60 = 17.75; discount factor 0.6830 × 121.55 = 83.02. PV = 100.77. NPV = +5.77.
Try 12%: annuity factor 3.0373 × 5.60 = 17.01; discount factor 0.6355 × 121.55 = 77.25. PV = 94.26. NPV = −0.74.
Interpolate: IRR = 10% + [5.77 ÷ (5.77 + 0.74)] × 2% = 10% + 1.77% = 11.77%.

Answer: The post-tax cost of the convertible is about 11.8%.

Exam tips

Objective test questions are all or nothing, so read whether the price is cum or ex-interest before you start calculating.
In Section C, show the cash flow table, both NPVs and the interpolation. Marks are given for method even if the arithmetic slips.
Convertible questions nearly always ask you to compare conversion and redemption values. Show the comparison explicitly.
Check whether the question gives tax as paid in the same year or a year later. A one-year lag shifts the tax saving and changes the cash flows.
Finish by using the cost in the WACC if the question asks for it. Use market values as the weights.

Practice questions from Sources of finance and their relative costs

Cost of Debt, Preference Shares and Convertibles 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, Preference Shares and Convertibles: frequently asked questions

How do I calculate the cost of redeemable debt using IRR?

Set up cash flows with the market price as an outflow at time 0. Add post-tax interest each year and the redemption value in the final year. Calculate the NPV at two discount rates and interpolate to find the rate where NPV is zero.

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

Yield to maturity is the pre-tax IRR of the debt. The cost of debt used in the WACC is the post-tax version, where the interest cash flows are reduced by the tax rate.

What is the formula for the cost of preference shares?

Cost of preference shares = annual preference dividend ÷ ex-dividend market price. There is no tax adjustment because dividends are paid after tax.

How do I know whether a convertible will convert?

Calculate the expected share price at the conversion date and multiply by the number of shares per bond. If this is higher than the redemption value, assume conversion. Otherwise assume redemption.