A company's cost of capital

Welcome to the World of Cost of Capital!

Hello there! Today, we are diving into one of the most critical chapters in the CB1: Business Finance curriculum: A Company’s Cost of Capital. This chapter is a cornerstone of the "Evaluating Projects" section. Think of it this way: before a company decides to build a new factory or launch a product, they need to know how much it "costs" to get the money to pay for it. If the project doesn't earn more than this cost, it’s a "no-go."

Don't worry if this seems a bit technical at first—we’re going to break it down piece by piece. By the end of these notes, you'll see that "Cost of Capital" is just a fancy way of saying "the rent we pay for using money." Let's get started!

1. What Exactly is the "Cost of Capital"?

Imagine you want to start a small lemonade stand. You borrow £50 from your brother (who insists on 10% interest) and you use £50 of your own savings (which could have earned 5% in a bank). Your "Cost of Capital" is the weighted average of these two rates.

In the corporate world, companies get money from two main sources: Debt (loans/bonds) and Equity (shareholders). Each source wants a "return" (payment) for the risk they are taking. The Weighted Average Cost of Capital (WACC) is the overall average rate the company pays to all its security holders to finance its assets.

Key Term: Opportunity Cost

The cost of capital is fundamentally an opportunity cost. It is the return that investors could have earned if they had invested their money in a different project with the same level of risk.

Quick Review:
• Debt holders want interest.
• Equity holders want dividends and share price growth.
• WACC is the average of these two, based on how much of each the company uses.

2. The Cost of Equity (\(r_e\))

This is often the trickiest part because, unlike a bank loan, there is no "set" interest rate for shareholders. We use two main methods to estimate it:

Method A: The Dividend Valuation Model (DVM)

This model assumes the value of a share is the present value of all future dividends. If dividends grow at a constant rate \(g\), the formula for the cost of equity is:
\(r_e = \frac{D_1}{P_0} + g\)
Where:
• \(D_1\) = The dividend expected in one year.
• \(P_0\) = The current market price of the share.
• \(g\) = The constant growth rate of dividends.

Method B: Capital Asset Pricing Model (CAPM)

This is the favorite for IFoA exams! It looks at the risk of the company compared to the whole market.
\(r_e = R_f + \beta(R_m - R_f)\)
Where:
• \(R_f\) = The Risk-Free Rate (usually the return on government bonds).
• \(\beta\) (Beta) = A measure of how much the company’s share price moves compared to the market.
• \(R_m\) = The expected return on the Market Portfolio.
• \((R_m - R_f)\) = The Equity Risk Premium (the extra return required for taking on market risk).

Memory Aid: "Big Bad Beta"
If \(\beta = 1\), the stock moves exactly with the market. If \(\beta > 1\), the stock is "riskier" than the market (like a tech startup). If \(\beta < 1\), it’s "safer" (like a utility company).

Key Takeaway: The Cost of Equity is usually higher than the Cost of Debt because shareholders take more risk (they are paid last if the company goes bust!).

3. The Cost of Debt (\(r_d\))

The cost of debt is simpler: it is the yield to maturity that lenders require. However, there is a massive benefit to debt called the Tax Shield.

The Magic of Tax Deductibility

In most countries, interest payments on debt are tax-deductible expenses. This makes debt "cheaper" for the company. We calculate the post-tax cost of debt as:
Post-tax \(r_d\) = \(r_d \times (1 - t)\)
Where \(t\) is the corporation tax rate.

Example: If a company borrows at 10% interest and the tax rate is 20%, the actual cost to the company is only \(10\% \times (1 - 0.20) = 8\%\). The government is essentially "paying" 2% of the interest for you!

Common Mistake to Avoid: Never forget the \((1 - t)\) for debt! However, never apply tax relief to the Cost of Equity. Dividends are paid out of profits after tax has already been taken.

4. Putting it Together: The WACC Formula

Now we combine the costs using the proportions of Debt and Equity in the company’s market value capital structure.

\(WACC = (\frac{E}{V} \times r_e) + (\frac{D}{V} \times r_d \times (1 - t))\)

Where:
• \(E\) = Market Value of Equity.
• \(D\) = Market Value of Debt.
• \(V\) = Total Value of the company (\(E + D\)).

Step-by-Step Calculation Guide:

1. Find Market Values: Always use Market Value, not "Book Value" (the numbers in the old accounts).
2. Calculate \(r_e\): Use CAPM or the Dividend Model as provided.
3. Calculate \(r_d\): Find the pre-tax interest rate.
4. Adjust for Tax: Multiply \(r_d\) by \((1 - t)\).
5. Weight them: Multiply each cost by its share of the total value and add them up.

Did you know?
If a company has 100% equity, its WACC is simply its cost of equity. As it adds cheaper debt, the WACC usually starts to fall, but if it adds too much debt, the risk of bankruptcy makes both equity and debt holders demand higher returns, and the WACC starts to rise again!

5. Using WACC for Project Evaluation

In the context of evaluating projects, the WACC is often used as the discount rate (or "hurdle rate"). If the project’s internal rate of return (IRR) is higher than the WACC, the project adds value.

When can you use the current WACC for a new project?

You can only use the company's existing WACC if two conditions are met:
1. Business Risk: The new project has the same risk as the company's existing operations.
2. Financial Risk: The company's capital structure (Debt/Equity ratio) stays roughly the same.

What if the project is different?
If a supermarket decides to open a space exploration wing, it shouldn't use the supermarket WACC! It should find the Marginal Cost of Capital or use a Risk-Adjusted Discount Rate based on the "Proxy Beta" of the space industry.

Key Takeaway: WACC is not a "one-size-fits-all" number. It must reflect the specific risk of the project being evaluated.

6. Summary and Final Tips

Summary Quick-Check:
• WACC is the average cost of all financing sources.
• Equity Cost is found via CAPM or DVM.
• Debt Cost must be adjusted for tax: \(r_d(1-t)\).
• Weights must be based on Market Values (\(Price \times Quantity\)).
• Use WACC as a hurdle rate for projects with similar risk.

Final Advice for Struggling Students:
If a question gives you a lot of data, start by identifying what is "Equity" and what is "Debt." Once you have those two piles of information, calculate their individual costs first, then find their weights, and only then try to combine them. Slow and steady wins the race in CB1!

You've got this! Cost of capital is just about understanding who is providing the money and what reward they expect for the risk they are taking. Keep practicing the formulas, and it will become second nature!