Estimating the cost of capital

Financial Management (FM) · ACCA · 7 min read · Updated: 2 Nov 2026

Welcome to Estimating the Cost of Capital!

In your Financial Management (FM) journey, you’ve already learned that businesses need money (capital) to grow. But here’s the catch: money isn't free! Whether a company gets money from shareholders or borrows it from a bank, those providers expect a return.

In this chapter, we are going to learn how to calculate exactly how much that expectation costs the company. Think of the Cost of Capital as the "hurdle rate." If a project doesn't earn more than what the capital costs, the company is actually destroying value. Don't worry if this seems a bit mathematical at first—we will break it down step-by-step!

1. The Cost of Equity ($K_e$)

The cost of equity is the return required by the company's ordinary shareholders. Because ordinary shareholders take the highest risk (they hold the residual claim and are the last to get paid in a liquidation), they demand the highest return.

A. The Dividend Valuation Model (DVM)

The simplest way to evaluate equity is by looking at the dividends the company pays. If a company pays a constant dividend forever, the formula is:

$ K_e = \frac{D}{P_0} $

Where:
$D$ = Constant annual dividend
$P_0$ = Current market price of the share (ex-dividend)

What if dividends are growing?
Usually, shareholders expect dividends to increase over time. This is the Dividend Growth Model:

$ K_e = \frac{D_0(1+g)}{P_0} + g = \frac{D_1}{P_0} + g $

Where:
$D_0$ = The dividend just paid (current dividend)
$D_1$ = The dividend expected in one year's time ($D_0(1+g)$)
$g$ = The expected annual constant growth rate of dividends
$P_0$ = Current market price per share (ex-div)

How to find the growth rate ($g$)?

If the exam scenario does not give you $g$, you can estimate it using two syllabus methods:
1. Historical Growth: Comparing the earliest and latest dividends over a number of periods.
2. Gordon’s Growth Approximation: $ g = b \times r_e $
(Where $b$ is the earnings retention rate, and $r_e$ is the accounting rate of return on equity / return on capital employed).

Quick Tip: Always ensure the share price ($P_0$) is "ex-div." If the price quoted is "cum-div" (with dividend), simply subtract the upcoming dividend from the market price before doing your calculation!

B. The Capital Asset Pricing Model (CAPM)

We can also estimate the cost of equity based on systematic risk rather than dividends. Total risk consists of unsystematic (diversifiable) risk and systematic (market-wide) risk. In a well-diversified portfolio, unsystematic risk is eliminated, so investors require compensation only for systematic risk.

The formula provided on the exam formula sheet is:
$ E(r_i) = R_f + \beta_i(E(r_m) - R_f) $

Key Terms:
- $R_f$ (Risk-free rate): Return on a zero-default-risk asset, such as short-dated government securities.
- $\beta_i$ (Equity Beta): A measure of the sensitivity of the company's share returns relative to the overall market portfolio. A beta of 1.0 moves in tandem with the market.
- $E(r_m)$ (Market return): The expected average return of the whole market portfolio.
- $(E(r_m) - R_f)$: The Equity Risk Premium—the excess return demanded by investors for bearing average market risk over safe debt.

Key Takeaway: Equity is the most expensive source of finance because shareholders rank behind all debt holders in the creditor hierarchy.

2. The Cost of Debt ($K_d$) and Preference Shares

Debt is generally cheaper than equity for two reasons:
1. It carries lower risk for the investor (fixed contractual returns and higher claim in liquidation).
2. Tax Relief: Interest payments are tax-deductible! The corporation tax shield reduces the effective cost of debt to the company.

A. Irredeemable Debt

Irredeemable bonds are never repaid; the company pays fixed coupon interest in perpetuity.

Pre-tax cost of debt: $ K_d = \frac{I}{P_0} $

Post-tax cost of debt: $ K_d(1-T) = \frac{I(1-T)}{P_0} $

Where:
$I$ = Annual interest payment per bond (coupon rate $\times$ nominal value)
$T$ = Corporation tax rate
$P_0$ = Current ex-interest market price of the bond (usually per \$100 nominal)

B. Redeemable Debt

Redeemable debt is repaid at a future date (at par, premium, or discount). To calculate its post-tax cost to the issuing company, we use the Internal Rate of Return (IRR) method.

Step-by-Step for Redeemable Debt:
1. Identify relevant company cash flows:
- Year 0: Current market price (ex-interest) = Cash Inflow (net issue proceeds / current bond value)
- Years 1 to $n$: Annual interest after tax $I(1-T)$ = Cash Outflow
- Year $n$: Redemption amount = Cash Outflow
2. Calculate the Net Present Value (NPV) using a lower discount rate $r_a$ (e.g. 5%).
3. Calculate the Net Present Value (NPV) using a higher discount rate $r_b$ (e.g. 10%).
4. Calculate the post-tax cost of debt using linear interpolation:
$ \text{IRR} = r_a + \left[ \frac{\text{NPV}_a}{\text{NPV}_a - \text{NPV}_b} \right] (r_b - r_a) $

C. Convertible Debt

Convertible bonds allow investors to choose at maturity between cash redemption or converting into ordinary shares. To estimate the cost of debt:
1. Calculate the conversion value: $ \text{Conversion value} = \text{Number of shares} \times \text{Expected share price at conversion date} $.
2. Assume rational investors will select whichever is higher: the cash redemption value or the conversion value.
3. Set up the cash flows as with redeemable debt (Inflow at Year 0, post-tax interest outflows Years 1 to $n$, and the higher terminal value outflow at Year $n$), then solve for IRR.

D. Preference Shares and Bank Debt

- Preference Shares: Irredeemable preference shares pay a fixed dividend ($D_p$). Because preference dividends are paid out of post-tax profit and do not receive tax relief, the cost of preference share capital is:
$ K_p = \frac{D_p}{P_0} $
- Bank Debt: Non-traded loans carry no market price quotation. The after-tax cost is simply the contractual interest rate multiplied by $(1 - T)$.

Common Mistake: Forgetting that debt interest receives tax relief, whereas preference dividends and ordinary dividends do not.

3. Weighted Average Cost of Capital (WACC)

The WACC is the average cost of all sources of long-term finance, weighted according to the proportions used by the company.

The WACC Analogy:
Think of WACC like a fruit smoothie. If you blend 80% strawberries (Equity) and 20% bananas (Debt), the final flavor reflects that weighting. We calculate the company's average cost of capital by weighting each source's cost by its market value.

The Formula

As provided on the ACCA formulae sheet:
$ \text{WACC} = \left( \frac{V_e}{V_e + V_d} \right) k_e + \left( \frac{V_d}{V_e + V_d} \right) k_d(1-T) $

Where:
$V_e$ = Total market value of equity (number of ordinary shares $\times$ ex-div share price)
$V_d$ = Total market value of debt (nominal value $\times$ ex-interest market price / \$100)
$k_e$ = Cost of equity
$k_d(1-T)$ = Post-tax cost of debt

If preference shares exist, add their market value $V_p$ to total capital in the denominator and include $\left(\frac{V_p}{V_e + V_d + V_p}\right) k_p$ in the equation.

Market Values vs Book Values

Always use market value weightings when available. Book values reflect historical accounting costs, whereas market values reflect the true economic opportunity cost of capital to current and future investors.

Average vs Marginal Cost of Capital

- Average Cost of Capital (WACC): The weighted average cost of existing capital employed by the firm.
- Marginal Cost of Capital: The cost of raising the next increment of capital for a new investment.
Existing WACC can only be used as the discount rate for evaluating a new project when:
1. The new project carries the same business risk as current operations.
2. The project size will not significantly disrupt the existing capital structure (financial gearing).
3. The financing method does not alter existing capital proportions.

Final Summary Takeaways

- Equity cost is calculated using the Dividend Growth Model ($DGM$) or the Capital Asset Pricing Model ($CAPM$).
- Debt interest yields tax relief, so bank debt and bonds enter WACC at their after-tax cost.
- Preference share dividends receive no tax relief, so their cost is $K_p = \frac{D_p}{P_0}$.
- Redeemable debt post-tax cost is calculated via IRR with Year 0 as an inflow and post-tax interest plus redemption as outflows.
- WACC uses market values rather than book values, and represents the appropriate project hurdle rate only when business and financial risks remain unchanged.

References

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the Dividend Valuation Model formula for the cost of equity with constant dividends?

$ K_e = \frac{D}{P_0} $, where $D$ is the constant annual dividend and $P_0$ is the current ex-dividend share price.

How is the cost of equity calculated using the Dividend Growth Model when dividends grow at a constant rate?

$ K_e = \frac{D_0(1+g)}{P_0} + g = \frac{D_1}{P_0} + g $, where $D_0$ is current dividend, $D_1$ is next year's dividend, and $g$ is constant growth rate.

What is Gordon's Growth Approximation formula for estimating the dividend growth rate?

$ g = b \times r_e $, where $b$ is the earnings retention rate and $r_e$ is the accounting rate of return on equity.

How is the cost of equity calculated under the Capital Asset Pricing Model (CAPM)?

$ E(r_i) = R_f + \beta_i(E(r_m) - R_f) $, where $R_f$ is the risk-free rate, $\beta_i$ is equity beta, and $(E(r_m) - R_f)$ is equity risk premium.

What is the post-tax cost of irredeemable debt for a company?

$ K_d(1-T) = \frac{I(1-T)}{P_0} $, where $I$ is annual coupon interest, $T$ is tax rate, and $P_0$ is ex-interest market price.

How is the post-tax cost of redeemable debt calculated?

It is calculated as the Internal Rate of Return (IRR) of Year 0 market value (inflow), post-tax annual interest payments (outflows), and redemption amount (outflow).

How is the redemption cash flow determined when estimating the cost of convertible debt?

Compare the cash redemption value with the conversion value (shares $\times$ expected price) and take the higher of the two.

Why is there no tax adjustment when calculating the cost of preference share capital?

Preference dividends are paid out of post-tax profits and are not tax-deductible expenses, so $ K_p = \frac{D_p}{P_0} $.

What is the standard formula for the Weighted Average Cost of Capital (WACC)?

$ \text{WACC} = \left( \frac{V_e}{V_e + V_d} \right) k_e + \left( \frac{V_d}{V_e + V_d} \right) k_d(1-T) $

Why should market values rather than book values be used as weights in calculating WACC?

Market values reflect the current economic opportunity cost of capital and current expectations, whereas book values only show historical accounting costs.

Under what conditions is a company's existing WACC suitable for appraising a new investment project?

When the new project shares the same business risk as existing operations and does not significantly alter the company's financial capital structure.

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