Financial Management · The valuation of debt and other financial assets

Valuing Preference Shares and Zero Coupon Bonds

Updated 11 October 2026 · Fact-checked

Value any financial asset as the present value of its future cash flows, discounted at the investor's required return. Preference shares pay a fixed dividend forever, so value = dividend ÷ required return. Zero coupon and deep discount bonds pay only a redemption sum, so value = redemption ÷ (1 + r)^n.

Understand Valuing Other Financial Assets

Every financial asset is worth what its future cash flows are worth today. You forecast the cash, then discount it at the return investors require for that level of risk. The answer is the fair market value.

The cash flows differ by instrument, so the formula changes, but the method does not. Ask three questions. What cash will the holder receive? When will it arrive? What discount rate fits the risk?

Irredeemable preference shares pay a fixed dividend every year with no end date. This is a perpetuity. Because the dividend is fixed, there is no growth term. Value = annual dividend ÷ required return.

Zero coupon bonds pay no interest. The investor receives one payment, the redemption value, at maturity. They are issued below that value, so the gain is the difference. Deep discount bonds are the same idea but may pay a very low coupon. Their value is the present value of that small coupon plus the redemption value.

The required return is often the yield to maturity (also called the gross redemption yield). If you know the price and redemption value, you can work backwards to find the yield. If you know the yield, you can work forward to find the price.

Key rules to remember

Irredeemable preference share value: P₀ = D ÷ k; D is the fixed annual dividend (rate × nominal value). k is the investor's required return. No growth.
Zero coupon bond value: P₀ = R ÷ (1 + r)^n; R is the redemption value, r the required annual yield, n the years to maturity.
Yield of a zero coupon bond: r = (R ÷ P₀)^(1/n) − 1; Use when price and redemption value are given. This is the pre-tax yield.
Deep discount bond value: P₀ = Σ [Coupon ÷ (1 + r)^t] + R ÷ (1 + r)^n; Use annuity factors for the coupon stream and a single discount factor for the redemption.
Redeemable preference share value: P₀ = Σ [D ÷ (1 + k)^t] + Redemption ÷ (1 + k)^n; Dividends form an annuity, redemption is a lump sum.

How to solve Valuing Other Financial Assets questions

Use this routine for any question on valuing preference shares, zero coupon or deep discount bonds.

1Identify the instrument and whether it is redeemable or irredeemable.
2List every cash flow: dividends or coupons, and any redemption payment. Note nominal value versus market value.
3Calculate the annual dividend or coupon as rate × nominal value, not market value.
4Choose the discount rate: the required return, yield or cost of capital given in the question.
5Pick the right method: perpetuity for irredeemable shares, single discount factor for zero coupon, annuity plus lump sum for coupons with redemption.
6Discount the cash flows and add them up to get the value.
7If the question gives a price and asks for a yield, use the formula backwards or interpolate between two trial rates.
8Check the result is sensible: a zero coupon bond must be worth less than its redemption value.

Quickest way: Fast value check

When to use it: Use in Section A and OT cases where you have about three minutes per question.

Preference shares: compute dividend in currency, divide by the required return as a decimal.
Zero coupon: raise (1 + r) to the power n on your calculator, then divide the redemption value by it.
Yield: divide redemption by price, take the nth root using the x^(1/n) key, subtract 1.
Sanity check: price below redemption, and higher yield means lower price.
Only use discount tables if the question gives coupons; otherwise the calculator is quicker and more accurate.

Common mistakes in Valuing Other Financial Assets

Calculating the preference dividend on market value instead of nominal value.
Students see a share price in the question and apply the rate to it.
Fix: Dividend = dividend rate × nominal value. Market value is only used as the price or in the yield calculation.
Using the dividend growth formula for preference shares.
The dividend valuation model is fresh in mind.
Fix: Preference dividends are fixed, so use D ÷ k with no growth term.
Forgetting to discount the redemption value of a deep discount bond.
Students focus on the coupon annuity and treat the final payment as already in today's money.
Fix: Always add R × discount factor at year n to the present value of the coupons.
Using the wrong number of years or the wrong rate in the power.
Rushing, or mixing up half-yearly and annual periods.
Fix: Write n and r beside the formula. Check whether the question states annual yield and annual compounding.
Entering the rate as a whole number, for example 8 instead of 0.08.
Calculator slips under time pressure.
Fix: Convert the percentage first and check the answer is lower than the redemption value.
Applying tax relief to preference dividends or to a zero coupon yield when valuing.
Students confuse valuation with after-tax cost of debt.
Fix: Valuation uses the investor's required return. Preference dividends get no tax relief. Only adjust for tax if the question asks for the company's cost.

Worked examples

Example 1

A company has 6% irredeemable preference shares with a nominal value of $1 each. Investors require a return of 8%. Calculate the market value of one share.

Show the solution

Dividend per share = 6% × $1 = $0.06.
Required return k = 8% = 0.08.
Value = D ÷ k = 0.06 ÷ 0.08 = $0.75.

Answer: The value of each preference share is $0.75.

Example 2

A company issues a zero coupon bond redeemable at $100 in 5 years. Investors require a yield of 6%. (a) Calculate the value of the bond. (b) If the bond is instead priced at $70 today, calculate the yield.

Show the solution

(a) Discount factor = 1.06^5 = 1.3382.
Value = 100 ÷ 1.3382 = $74.73.
(b) Redemption ÷ price = 100 ÷ 70 = 1.4286.
Take the fifth root: 1.4286^(1/5) = 1.0743.
Yield = 1.0743 − 1 = 7.43%.

Answer: (a) $74.73. (b) About 7.4%. A lower price gives a higher yield, as expected.

Exam tips

Read whether shares are redeemable. Irredeemable means perpetuity; redeemable means annuity plus lump sum.
Always compute the dividend or coupon from nominal value, and show this line in Section C for method marks.
In objective tests, one wrong figure gives zero, so check n, r and the decimal conversion before you select an answer.
Link this topic to cost of capital: the yield you calculate here is the investor's return, and the company's cost of preference shares uses the same formula in reverse.
State a one-line conclusion in written answers, such as whether the bond looks under or overvalued against its market price.

Practice questions from The valuation of debt and other financial assets

Valuing Other Financial Assets in other exams

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

Valuing Other Financial Assets: frequently asked questions

How do you value a zero coupon bond in ACCA FM?

Divide the redemption value by (1 + required yield) raised to the number of years to maturity. There are no interest payments to include. The result must be less than the redemption value.

What is the difference between a zero coupon bond and a deep discount bond?

A zero coupon bond pays no interest at all. A deep discount bond is issued well below its redemption value and may pay a small coupon. Both are valued by discounting all their cash flows.

How do you value preference shares?

For irredeemable shares, divide the fixed annual dividend by the required return. For redeemable shares, discount the dividends and the redemption payment at the required return. Dividends are based on nominal value.

Do I need discount tables for these questions?

For zero coupon bonds and irredeemable preference shares, a calculator is enough. For bonds with coupons you can use annuity tables, or a calculator, if the exam provides them.