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Cost of Capital

What it costs a firm to raise money, how each source is priced, and how the weighted average sets the hurdle for new projects.

Uses ideas from Sources of Finance. Which ideas

3 conceptsAbout 10 min
Start with the first concept
Part one

The concepts

Concept 1 of 3.

The cost of capital

The minimum return investors need.

Before you read

A firm earns a 9% return on a project funded at a cost of 12%. Is it better off?

Core idea

The cost of capital is the return investors require for supplying funds. A project earning above it adds value; one below it destroys value. Riskier investments need higher returns.

A bank lends at 10%. Shareholders expect more than that for taking the greater risk. A firm that earns less than it costs to raise its money loses value, even if its profit is positive. So what does the money cost?

In plain wordsThe cost of capital is the return investors need in order to supply money to the firm. If a project earns less than this, the firm is worse off.

Exam definitionThe cost of capital is the required rate of return expected by providers of finance for supplying funds to a business. It is the minimum return a firm must earn on its investments to satisfy investors and maintain its market value.

TypeMeaning
Explicit costThe actual cost paid for raising capital, such as interest or dividends
Implicit costThe opportunity cost of using funds, such as earnings kept back
Specific costThe cost of one source of finance, such as debt or equity
Weighted average cost of capital (WACC)The average cost of all sources, weighted by their proportions
Marginal cost of capital (MCC)The cost of the next increment of capital raised
FactorEffect
Risk profileHigher business or financial risk leads to a higher required return
Capital structureDebt may lower the cost, up to an optimal point
Dividend policyHigher dividends may increase reliance on external funds
Tax rateA higher tax rate raises the interest tax shield and lowers the after-tax cost of debt
Market conditionsInterest rates and investor expectations affect the cost of finance
CreditworthinessA better credit rating lowers the borrowing cost

Risk and return. The riskier the investment, the higher the return investors expect, and the higher the cost of capital. A safe lender asks for less than an equity holder.

Why it matters. It is the discount rate for NPV and IRR (Chapter 13). It guides the choice of debt and equity (Chapter 16). It informs the dividend decision, and the valuation of shares, bonds and whole firms.

Don’t think retained earnings are free. Retained profit has no interest and no issue cost, but shareholders could have used the dividend elsewhere. That forgone return is an implicit cost, and it is why the cost of retained earnings is taken as about equal to the cost of equity.

Where it breaks. The cost of equity cannot be seen in a bill; it has to be estimated, and each method (dividend growth, earnings yield, CAPM) gives a different answer. A cost of capital for the whole firm can be wrong for a project that is much riskier than the firm’s usual business.

For exams. Know the types, the factors, the significance for the four financial decisions, and the rule: accept projects earning more than the cost of capital.

Risk up, required return up, cost of capital up.

Go deeper for practitioners

A project-specific rate. A firm that makes tyres and starts an overseas venture should not use its tyre WACC for the new business. The venture’s own risk sets the right discount rate, which may be higher.

A decision. Two firms in the same trade have the same debt, but one has a better credit rating. Whose cost of capital is lower, and what difference does that make to the projects each can accept?

Check yourself

1. The opportunity cost of using retained earnings is called…

Not quite. The answer is “An implicit cost”. Retained profit has no direct payment, but shareholders forgo the return they could have earned on the dividend.

2. A higher tax rate makes the after-tax cost of debt…

Not quite. The answer is “Lower”. Interest is tax-deductible, so a higher rate gives a bigger tax shield and a lower cost.

3. Which statement matches the risk and return rule?

Not quite. The answer is “Higher risk, higher required return, higher cost of capital”. Investors need more compensation for taking more risk.

Reflect & discuss

“Why might a firm’s overall WACC be the wrong discount rate for a project much riskier than its usual work?”

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One-page summary
The cost of capital
  • Cost of capital: the required return of providers of finance.
  • Explicit: paid in cash. Implicit: opportunity cost. Specific: one source. WACC: all, weighted.
  • Factors: risk, capital structure, dividend policy, tax, market conditions, credit rating.
  • Accept projects that earn more than the cost of capital.
Remember

Risk up, required return up, cost of capital up.

Concept 2 of 3.

Specific costs of capital

Pricing debt, preference, equity and retained earnings one at a time.

Before you read

A ₹100 debenture pays 10% interest and nets ₹95 after issue costs. What does it cost, before tax?

Core idea

Kd = I(1 − T) ÷ NP; Kp = Dp ÷ NP; Ke = D1 ÷ P0 + g, or E1 ÷ P0, or Rf + β(Rm − Rf); Kr ≈ Ke.

Before averaging the costs of different sources, each one has to be priced alone. Debt has a visible interest rate, and equity has no rate at all. The formulas bridge the gap.

In plain wordsEach source has its own cost: debt after tax, preference on its fixed dividend, and equity estimated from what shareholders expect. Retained earnings cost about the same as equity.

Exam definitionCost of debt Kd = I(1 − T) ÷ NP. Cost of preference capital Kp = Dp ÷ NP. Cost of equity Ke may be estimated by the dividend growth model D1 ÷ P0 + g, the earnings yield E1 ÷ P0, or CAPM: Rf + β(Rm − Rf). Cost of retained earnings Kr ≈ Ke.

SourceFormulaWhere
Debt (before tax)Kd = I ÷ NPI = interest, NP = net proceeds
Debt (after tax)Kd = I(1 − T) ÷ NPT = tax rate
PreferenceKp = Dp ÷ NPDp = preference dividend
Equity: dividend growthKe = D1 ÷ P0 + gD1 = next dividend, P0 = price, g = growth
Equity: earnings yieldKe = E1 ÷ P0E1 = expected earnings per share
Equity: CAPMKe = Rf + β(Rm − Rf)Rf = risk-free return, β = beta, Rm = market return
Retained earningsKr ≈ KeOpportunity cost to shareholders

Worked examples (tax rate 25%).

Debt: a ₹100 debenture at 10% interest, with net proceeds of ₹95. Before tax Kd = 10 ÷ 95 = 10.53%. After tax Kd = 10 × (1 − 0.25) ÷ 95 = 7.89%
Preference: ₹100 share at 12%, net proceeds ₹96. Kp = 12 ÷ 96 = 12.5%
Equity, dividend growth: next dividend ₹6, price ₹100, growth 4%. Ke = 6 ÷ 100 + 0.04 = 10%
Equity, earnings yield: expected earnings ₹10 on a ₹100 share. Ke = 10 ÷ 100 = 10%
Equity, CAPM: risk-free 7%, β = 1.2, market return 12%. Ke = 7 + 1.2 × (12 − 7) = 13%

The three estimates of equity cost differ because they assume different things. CAPM includes the share’s own risk through beta, while the dividend growth model needs a reliable forecast of growth.

Don’t use the pre-tax interest rate in WACC. Interest is tax-deductible, so the firm bears only the after-tax cost. Preference dividends and equity dividends are paid from profit after tax, and do not get a tax saving. Using 10% where 7.9% belongs overstates the cost of debt.

Where it breaks. Net proceeds are the price less issue costs and discount, so they change the cost. The dividend growth model fails for a firm that pays no dividend. CAPM depends on a good beta and a market risk premium, and neither is certain. The earnings yield ignores growth.

For exams. Learn each formula and what each symbol stands for, and use net proceeds, not the face value, as the denominator.

Debt after tax, preference on net proceeds, equity by one of three routes.

Go deeper for practitioners

Beta. A beta above 1 means the share moves more than the market, and so demands a higher return. A beta below 1 means it moves less. A defensive firm such as a power utility has a low beta, and a fast-growing technology firm a high one.

A decision. Your three estimates of Ke are 10%, 10% and 13%. Which would you use for a firm that pays regular dividends, and which for a start-up that pays none?

Check yourself

1. A ₹100 debenture pays ₹10 interest and nets ₹95. At a 25% tax rate, the after-tax cost of debt is…

Not quite. The answer is “7.9%”. ₹10 × (1 − 0.25) ÷ ₹95 = 7.9%. The 10.5% figure is before tax.

2. Next dividend ₹6, price ₹100, growth 4%. The cost of equity by the dividend growth model is…

Not quite. The answer is “10%”. 6 ÷ 100 + 0.04 = 10%. The 6% is only the dividend yield.

3. Risk-free rate 7%, beta 1.2, market return 12%. Ke under CAPM is…

Not quite. The answer is “13%”. 7 + 1.2 × (12 − 7) = 13%. Using 12% would ignore the share’s own risk.

Reflect & discuss

“Three methods give three different costs of equity. What does each one assume, and which would you trust for a firm that pays no dividend?”

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One-page summary
Specific costs of capital
  • Kd after tax = I(1 − T) ÷ NP; Kp = Dp ÷ NP.
  • Ke by dividend growth, earnings yield or CAPM.
  • Kr ≈ Ke: retained profit has an opportunity cost.
  • Use net proceeds (after issue costs) in the denominator.
Remember

Debt after tax, preference on net proceeds, equity by one of three routes.

Concept 3 of 3.

Weighted average cost of capital

One average rate for all the firm’s money.

Before you read

A firm has debt at 10%, preference capital at 12% and equity at 15%. Is its average cost the middle figure, 12%?

Core idea

WACC = Σ (weight × cost). With debt ₹2,00,000 at 10%, preference ₹50,000 at 12% and equity ₹2,50,000 at 15%, the weights are 0.40, 0.10 and 0.50, and WACC = 4.0% + 1.2% + 7.5% = 12.7%.

A firm has borrowed some money, issued preference shares and used equity, each at a different cost. A single rate is needed to judge a project, and that is the average, weighted by how much each source supplies.

In plain wordsWACC is the average cost of all the money in the firm, where each source counts in proportion to how much of the total it supplies.

Exam definitionWACC = wdKd + wpKp + weKe + wrKr, where the w are the weights of debt, preference, equity and retained earnings in the capital structure and the K are their costs. It is the minimum average return that investors require.

WACC = (weight of debt × cost of debt) + (weight of preference × cost of preference) + (weight of equity × cost of equity)

Worked example. A firm has debt of ₹2,00,000 costing 10%, preference capital of ₹50,000 costing 12%, and equity of ₹2,50,000 costing 15%. The costs are taken after tax.

SourceAmountCostWeightWeighted cost
Debt₹2,00,00010%0.404%
Preference₹50,00012%0.101.2%
Equity₹2,50,00015%0.507.5%
Total₹5,00,0001.0012.7%
WACC = 4.0% + 1.2% + 7.5% = 12.7%

The decision rule. A project earning more than the WACC creates value, and one earning less destroys it. A project that returns 14% will add value for this firm, and one that returns 11% will not.

Marginal cost of capital. The WACC describes the money already raised. The marginal cost of capital is the cost of the next rupee, which can be higher once cheap sources are used up, for example when the firm has used all its retained earnings and must issue new shares.

Don’t use book values and market values as if they were the same. Weights can be taken at book value (as above, from the balance sheet) or at market value. Market values are better, because they show what investors currently demand, but they are harder to obtain for debt and unlisted firms. State which you use.

Where it breaks. The weights change as the firm raises new money, so the WACC changes too. The result depends on the cost estimates, which are uncertain, especially for equity. Using one firm-wide rate for projects of very different risk can lead to wrong accept or reject decisions.

For exams. Show the table with source, amount, cost, weight and weighted cost, and a total of weights equal to 1.

Weight each cost by its share, then add.

Go deeper for practitioners

Why debt lowers the WACC, up to a point. Debt is cheaper than equity because it is safer for the lender and the interest saves tax. Adding it lowers the average. But more debt raises the risk to shareholders and so the cost of equity, and in time the cost of debt as well. The theories of the next chapter disagree on how far this goes.

A decision. A project returns 13% and the WACC is 12.7%, but the project is far riskier than the firm’s usual business. Should the firm accept it, and what rate would you use instead?

Try it

The chapter’s firm is filled in, at book values. Change the amounts or costs, add retained earnings, or try a project’s return.

SourceAmountCostWeightWeighted cost
Debt (after tax)₹2,00,00010%0.404%
Preference capital₹50,00012%0.101.2%
Equity₹2,50,00015%0.507.5%
Total₹5,00,0001.0012.7%
WACC12.7%The minimum average return investors require
The project14%Above the WACC: it adds value
Check yourself

1. The weight of equity in ₹2,00,000 debt, ₹50,000 preference and ₹2,50,000 equity is…

Not quite. The answer is “0.50”. ₹2,50,000 ÷ ₹5,00,000 = 0.50.

2. The weighted cost of the debt (₹2,00,000 at 10%) in a total of ₹5,00,000 is…

Not quite. The answer is “4.0%”. Weight 0.40 × 10% = 4.0%.

3. A project returns 14% and the firm’s WACC is 12.7%. The project…

Not quite. The answer is “Has the potential to add value”. A project earning more than the cost of capital adds value, if the cash flows are reliable and the risk is typical.

Reflect & discuss

“Why does the marginal cost of capital often rise as a firm raises more money?”

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One-page summary
Weighted average cost of capital
  • WACC = wdKd + wpKp + weKe + wrKr; weights sum to 1.
  • Debt is taken after tax.
  • Project return above WACC adds value; below it reduces value.
  • Marginal cost of capital is the cost of the next increment.
Remember

Weight each cost by its share, then add.

Test yourself

All 9 questions from this chapter, in a new order.

The ones you miss join your review, and come back until they stick.

Start the chapter test

How this chapter connects

Worked out from the glossary terms each chapter uses. A chapter is listed when two or more terms are shared.

Uses ideas from
Its ideas are used in
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