Estimating the cost of capital

Financial Management (FM) · ACCA · 6 min read

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 people 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 losing 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. Since shareholders take the most risk (they are the last to get paid if the company fails), they usually demand the highest return.

A. The Dividend Valuation Model (DVM)

The simplest way to look at 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 $

Where:
$D_0$ = The dividend just paid (current dividend)
$g$ = The expected annual growth rate of dividends
$P_0$ = Current market price (ex-div)

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

If the exam doesn't give you $g$, you usually find it in two ways:
1. Historical Growth: Looking at past dividends.
2. Gordon’s Growth Model: $ g = b \times r $
(Where $b$ is the percentage of profits kept in the business, and $r$ is the return the company earns on those profits).

Quick Tip: Always make sure the share price ($P_0$) is "ex-div." If the price is "cum-div" (with dividend), simply subtract the upcoming dividend from the price before you start your calculation!

B. The Capital Asset Pricing Model (CAPM)

Sometimes, we look at the cost of equity based on risk rather than dividends. CAPM says that shareholders want a "risk-free" return plus a "bonus" for taking on the specific risk of that company.

The formula is:
$ K_e = R_f + \beta(R_m - R_f) $

Key Terms:
- $R_f$ (Risk-free rate): What you’d earn on a totally safe investment, like government bonds.
- $\beta$ (Beta): A measure of how "jumpy" the share price is compared to the whole market. A Beta of 1.0 means the share moves exactly like the market.
- $R_m$ (Market return): The average return of the whole stock market.
- $(R_m - R_f)$: This is called the Equity Risk Premium. It’s the "extra" return required for choosing stocks over safe bonds.

Key Takeaway: The Cost of Equity is the most expensive source of finance because shareholders take the highest risk.

2. The Cost of Debt ($K_d$)

Debt is generally cheaper than equity for two reasons:
1. It is less risky for the lender (they get paid before shareholders).
2. Tax Relief: Interest payments are tax-deductible! This is a huge concept in FM. When a company pays interest, it reduces their tax bill, making the actual cost of debt lower.

A. Irredeemable Debt

This is debt that is never paid back; the company just pays interest forever.

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

Where:
$I$ = Annual interest payment
$t$ = Tax rate (e.g., 30% or 0.30)
$P_0$ = Market price of the debt (usually per $100 block)

B. Redeemable Debt

Most debt has an "expiry date" where the company pays the principal back. To find the cost here, we use the IRR (Internal Rate of Return) method.
Don't panic! You just need to find two "Net Present Values" (NPVs) using two different discount rates and then use the IRR formula.

Step-by-Step for Redeemable Debt:
1. List the cash flows: Year 0 (Market Price - Outflow), Years 1-End (Interest after tax - Outflow), Year End (Redemption value - Outflow).
2. Use a low discount rate (e.g., 5%) to find NPV.
3. Use a higher discount rate (e.g., 10%) to find NPV.
4. Plug the results into the IRR formula.

C. Other Debt Types

- Convertible Debt: Debt that can turn into shares. Treat it like redeemable debt, but for the "Redemption Value," use whichever is higher: the cash payout or the value of the shares it converts into.
- Bank Loans: These don't have a market price. The cost is simply: $ Interest \ Rate \times (1 - t) $.

Common Mistake: Students often forget to apply tax to the cost of debt. Remember: Debt has a tax shield, Equity does not!

3. Weighted Average Cost of Capital (WACC)

Most companies use a mix of both equity and debt. The WACC is the average cost of all these sources, weighted by how much of each the company uses.

The WACC "Smoothie" Analogy:
Think of WACC like a fruit smoothie. If you use 80% strawberries (Equity) and 20% bananas (Debt), the taste (the cost) will be much closer to the strawberries than the bananas. We weight the costs based on their Market Value.

The Formula

$ 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 shares $\times$ Share Price)
$V_d$ = Total Market Value of Debt

Why Market Values?

In FM exams, always use Market Values for weights if they are available. Book Values (from the Statement of Financial Position) are historical and don't represent what the capital actually costs the company today.

Quick Review Box:
1. Calculate $K_e$ (using DVM or CAPM).
2. Calculate $K_d$ (remembering the tax adjustment).
3. Find the Market Value of all Equity ($V_e$).
4. Find the Market Value of all Debt ($V_d$).
5. Plug it all into the WACC formula!

4. Factors Affecting the Cost of Capital

It's not just about math! You need to know why these numbers change:

- Interest Rates: If the central bank raises rates, the cost of both debt and equity usually goes up.
- Risk: If the company takes on a very risky project, shareholders will want a higher return, increasing $K_e$.
- Capital Structure: As a company takes on more debt, it becomes "riskier" to shareholders, which might push $K_e$ up even though debt itself is cheap.

Did you know?
The WACC is only appropriate to use for a new project if the project has the same risk as the current business and doesn't significantly change the capital structure. If the project is totally different (e.g., a bakery opening a rocket ship factory), you'd need a different "marginal" cost of capital!

Final Summary Takeaways

- Equity is found using Dividends (DVM) or Risk (CAPM).
- Debt cost must always be calculated after-tax (post-tax).
- WACC is the average cost of all finance, weighted by Market Values.
- Use ex-div share prices and ex-interest bond prices for all calculations.

Keep practicing these formulas! The more you use them, the more they will feel like second nature. You've got this!

Quick check

Can you answer these now?

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

What is the 'cost of capital' and why is it often called a 'hurdle rate'?

The cost of capital is the return required by investors to provide finance; it acts as a hurdle rate because projects must earn more than this cost to create value for the company.

What is the formula for the cost of equity ($K_e$) when a company pays a constant dividend?

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

How do you calculate the cost of equity ($K_e$) if dividends are expected to grow at a constant rate?

$ K_e = \frac{D_0(1+g)}{P_0} + g $, where $D_0$ is the current dividend and $g$ is the annual growth rate.

What is Gordon's Growth Model (the retention technique) for estimating dividend growth ($g$)?

$ g = b \times r $, where $b$ is the earnings retention rate and $r$ is the return on new investments.

What is the 'cum-div' price and how should it be adjusted for cost of equity calculations?

A 'cum-div' price includes the upcoming dividend; it must be converted to an 'ex-div' price by subtracting the dividend amount before using it in formulas.

How does the Capital Asset Pricing Model (CAPM) define the cost of equity?

$ K_e = R_f + \beta(R_m - R_f) $. It calculates return based on the risk-free rate plus a premium for systematic risk.

Why is the post-tax cost of debt lower than the pre-tax interest rate?

Debt is tax-deductible; the company receives 'tax relief' on interest payments, which reduces the actual cash outflow.

How is the cost of irredeemable debt calculated after tax?

$ K_d(1-t) = \frac{I(1-t)}{P_0} $, where $I$ is the annual interest and $P_0$ is the market price of the debt.

What method is used to calculate the cost of redeemable debt?

The Internal Rate of Return (IRR) method is used, finding the discount rate where the NPV of after-tax cash flows equals zero.

How is the cost of a bank loan calculated?

Cost of bank loan = $ Interest \ Rate \times (1 - t) $.

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

The average of the costs of equity and debt, weighted by their respective market values.

Why must Market Values be used instead of Book Values when calculating WACC weights?

Market values represent the current economic cost and the amount that would need to be paid to attract investors today, whereas book values are based on historical costs.

When is it appropriate to use the current WACC to appraise a new investment project?

WACC is only appropriate if the project has the same business risk as the current operations and the company's capital structure remains unchanged.

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