Financial Management · Estimating the cost of capital

Yield Curves, Credit Spreads and Cost of Capital for ACCA FM

Updated 11 October 2026 · Fact-checked

A yield curve plots yields on similar bonds against time to maturity. The cost of debt for a company is the risk-free yield for its maturity plus a credit spread that reflects its credit rating. To solve questions, find the right maturity yield, add the spread, then adjust for tax.

Understand Yield Curves, Credit Spreads and Cost of Capital

Interest rates are not the same for every loan term. The term structure of interest rates is the link between the yield on a bond and the time left until it matures. A yield curve is the graph of that link, usually for government bonds, which carry little default risk.

A curve can be upward sloping (normal), flat, or downward sloping (inverted). Three theories explain the shape:

Expectations theory: long-term yields reflect expected future short-term rates. If markets expect rates to rise, the curve slopes up.
Liquidity preference theory: investors want extra yield for locking money away, so long-term yields include a premium. The curve tends to slope up even if rates are not expected to change.
Market segmentation theory: short-term and long-term markets have separate buyers and sellers, so each maturity has its own supply and demand.

A government yield is close to a risk-free rate. A company can default, so lenders ask for more. The extra yield is the credit spread. It depends on the credit rating. A higher rating (such as AAA or AA) means lower default risk and a smaller spread. A lower rating means a bigger spread. A spread is often quoted in basis points: 100 basis points = 1%.

So the pre-tax cost of debt = risk-free yield at the matching maturity + credit spread. The yield to maturity (YTM) of a bond is the discount rate that makes the present value of its interest and redemption payments equal to its market price. For a company, the YTM on its traded debt is the pre-tax cost of debt. Interest is tax deductible, so the after-tax cost = pre-tax cost × (1 − tax rate), provided the company pays tax and gets relief on interest. This after-tax figure goes into the WACC.

A worse rating raises the cost of debt. It can also raise the cost of equity, as shareholders see more financial risk. That pushes up the WACC and lowers the NPV of projects.

Key rules to remember

Pre-tax cost of debt from a spread: Kd (pre-tax) = risk-free yield for the maturity + credit spread; Convert basis points to a percentage first: 150 basis points = 1.50%.
After-tax cost of debt: Kd (after tax) = Kd (pre-tax) × (1 − T); Use only if the company pays tax and interest is deductible. For redeemable debt, find the IRR using after-tax interest.
Yield to maturity (YTM): Market price = Σ interest ÷ (1 + r)^t + redemption value ÷ (1 + r)^n; Solve r by interpolation between two trial rates: r = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L).
Basis points: 1 basis point = 0.01%; 100 basis points = 1%.
Spread implied by a bond: Credit spread = YTM of corporate bond − yield on government bond of the same maturity; Compare bonds with the same maturity and currency.

How to solve Yield Curves, Credit Spreads and Cost of Capital questions

Use this method for questions on yield curves, ratings and the cost of debt.

1Read what is asked: a cost of debt, a spread, a curve shape, or an explanation of a theory.
2Identify the maturity of the debt. Pick the government yield for that maturity from the curve or table given.
3Convert the credit spread from basis points to a percentage and add it to the risk-free yield for the pre-tax cost of debt.
4If the question gives a bond price and cash flows instead, calculate the YTM by trying two discount rates and interpolating.
5Apply tax: multiply by (1 − tax rate) if the company pays tax and interest is deductible. Use after-tax interest in YTM calculations.
6Link the result to the WACC or the investment decision if asked, and state the effect of a rating change.
7For theory parts, name the theory, state what it says about the curve shape, and apply it to the scenario given.

Quickest way: Add, convert, tax

When to use it: Use for OT questions where a spread and a risk-free yield are given and you need the cost of debt fast.

Find the government yield at the right maturity.
Turn basis points into a percentage by dividing by 100.
Add the two to get the pre-tax cost of debt.
Multiply by (1 − tax rate) only if the question asks for the after-tax cost.
Check the answer is bigger than the risk-free yield before tax.

Common mistakes in Yield Curves, Credit Spreads and Cost of Capital

Using the wrong maturity yield from the curve
Students take the first or the highest yield in the table.
Fix: Match the yield to the remaining life of the debt. Underline the maturity in the question first.
Treating 150 basis points as 150% or 15%
Unfamiliarity with the unit.
Fix: Divide basis points by 100 to get a percentage. 150 basis points = 1.5%.
Applying tax to the risk-free yield only or twice
Rushing the order of steps.
Fix: Add the spread first to get the pre-tax cost, then apply (1 − T) once.
Saying a downward sloping curve always means recession
Memorised as a rule.
Fix: Say it usually signals that markets expect short-term rates to fall. Link it to expectations theory and avoid stating it as certain.
Mixing up expectations and liquidity preference theory
Both explain an upward slope.
Fix: Expectations is about forecasts of future rates. Liquidity preference is about a premium for lending long even with no change expected.
Using coupon rate as the cost of debt
The coupon is easy to see.
Fix: Use the YTM based on the market price. The coupon is only the interest paid on nominal value.

Worked examples

Example 1

A company wants to issue 5-year bonds. The 5-year government yield is 3.2%. Because of its credit rating, the spread over government bonds is 180 basis points. The tax rate is 25%. Calculate the pre-tax and after-tax cost of debt.

Show the solution

Convert the spread: 180 basis points = 1.80%.
Pre-tax cost of debt = 3.2% + 1.8% = 5.0%.
After-tax cost = 5.0% × (1 − 0.25) = 5.0% × 0.75 = 3.75%.

Answer: Pre-tax cost of debt is 5.0%. After-tax cost of debt is 3.75%.

Example 2

A company's 2-year bond has a nominal value of ₹100, pays 6% interest annually, and is redeemed at par. It trades at ₹96.30. The 2-year government yield is 4%. Estimate the YTM using trial rates of 8% and 9%, and the credit spread. Ignore tax.

Show the solution

At 8%: PV = 6 × 1.783 + 100 × 0.857 = 10.698 + 85.7 = 96.398, using the 8% two-year annuity factor 1.783 and discount factor 0.857. NPV = 96.398 − 96.30 = +0.098.
At 9%: PV = 6 × 1.759 + 100 × 0.842 = 10.554 + 84.2 = 94.754, using the 9% two-year annuity factor 1.759 and discount factor 0.842. NPV = 94.754 − 96.30 = −1.546.
The NPVs have opposite signs, so the YTM lies between 8% and 9%. Interpolate: YTM = 8% + [0.098 ÷ (0.098 + 1.546)] × (9% − 8%) = 8% + 0.0596% = about 8.06%.
Credit spread = 8.06% − 4% = about 4.06%, or about 406 basis points.

Answer: YTM is about 8.06%. The credit spread is about 4.06% (roughly 406 basis points) over the government yield.

Exam tips

In OT questions, read the maturity and the unit of the spread before any calculation. Most lost marks come from these two items.
Objective questions are all or nothing, so write down each step even if you can do it mentally.
For theory questions, link each theory to the shape of the curve and to the scenario. Do not just list definitions.
In constructed response, state that a rating downgrade raises the spread, the cost of debt and the WACC, and may lower project NPV.
When interpolating YTM, choose trial rates that give one positive and one negative NPV. If both have the same sign, pick a new rate.

Practice questions from Estimating the cost of capital

Yield Curves, Credit Spreads and Cost of Capital in other exams

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

Yield Curves, Credit Spreads and Cost of Capital: frequently asked questions

What is a yield curve in ACCA FM?

It is a graph of yields against time to maturity for bonds of similar risk, usually government bonds. It shows the term structure of interest rates. Its shape can be upward, flat or downward sloping.

How does a credit rating affect the cost of debt?

A lower rating means a higher chance of default, so lenders demand a bigger credit spread. The pre-tax cost of debt rises as a result. A higher rating gives a smaller spread and cheaper debt.

What is yield to maturity?

It is the discount rate that equates the present value of a bond's future interest and redemption payments to its current market price. It is the IRR of the bond cash flows. For a company, it is the pre-tax cost of its traded debt.

What is the difference between expectations theory and liquidity preference theory?

Expectations theory says long-term yields reflect expected future short-term rates. Liquidity preference theory says investors need a premium for tying up money for longer. The second explains why curves usually slope upwards.