Cost of Capital

Why this chapter is the hinge of the whole paper

The method chapter already flagged this: cost of capital sits at the centre of the FM dependency chain. It is computed from the sources of finance introduced two chapters ago, it depends on the capital structure the firm has chosen, and it becomes the discount rate for every capital budgeting decision that follows. An error here is not contained to this chapter's own marks — it propagates. That is reason enough to treat this as the chapter that deserves the most careful, repeated practice in the whole paper.

Cost of capital is the minimum rate of return a firm must earn on its investments to satisfy the expectations of those who have supplied its capital — equity shareholders, preference shareholders, and lenders — and to keep the market value of the firm at least unchanged. Each source of finance has its own specific cost, called the specific cost of capital, and these specific costs are combined, weighted by how much of each source the firm actually uses, into a single blended figure, the weighted average cost of capital, or WACC.

Cost of debt

Debt is the most straightforward source to cost, because its return, the interest rate, is contractually fixed and stated upfront.

The before-tax cost of debt for a fresh issue is simply the effective interest rate the firm pays, adjusted for any difference between the issue price and face value if the debentures are issued at a discount or premium, and for flotation costs — the costs of issuing the debt, such as underwriting fees — if the question requires their inclusion.

The critical adjustment is tax. Because interest is a tax-deductible expense, the after-tax cost of debt is:

Kd = Interest rate × (1 − Tax rate)

This single formula is the most-tested individual line in the entire cost of capital chapter, precisely because it is also the most commonly misapplied — either by forgetting the tax adjustment altogether, or by mistakenly applying it to a source other than debt.

Where debt is issued at a discount or redeemed at a premium, or where flotation costs are involved, the more precise approach uses the net proceeds actually received by the firm, rather than the face value, as the base for computing the effective cost, since the firm's genuine cost of borrowing depends on what it actually received in hand, not on the face value stated on the instrument.

Cost of preference capital

Preference dividend is not tax-deductible, so no tax adjustment is applied here, unlike debt. The cost of preference capital, for a simple case with no redemption, is the fixed preference dividend rate expressed as a percentage of the net proceeds from issue:

Kp = Preference dividend ÷ Net proceeds

Where preference shares are redeemable, the cost must reflect both the periodic dividend and the return of capital at redemption, computed properly using time value of money techniques rather than a simple ratio, since redemption represents a cash outflow to the firm at a specific future date that a simple annual-dividend-to-proceeds ratio does not capture.

Cost of equity capital

Equity is conceptually the hardest source to cost, because unlike debt or preference, equity carries no contractually fixed rate — a firm makes no legal promise to pay any specific dividend to equity shareholders. Three approaches are used, each resting on a different underlying logic.

The dividend discount approach

If shareholders value a share based on the stream of future dividends they expect to receive, discounted to present value, then the cost of equity is the discount rate that equates the present value of expected future dividends to the current market price. For a firm expected to pay a constant dividend indefinitely, with no growth, this simplifies to:

Ke = D ÷ P₀

where D is the expected dividend and P₀ is the current market price. For a firm whose dividend is expected to grow at a constant rate g indefinitely — the Gordon growth model, also called the dividend growth model — the formula becomes:

Ke = (D₁ ÷ P₀) + g

where D₁ is the dividend expected next year, computed as this year's dividend grown by one year at rate g. This formula has two components worth naming separately in any answer: the dividend yield, D₁ ÷ P₀, and the expected growth rate, g, and together they represent the total return — income plus growth — shareholders require to be willing to hold the share at its current price.

The earnings-based approach

An alternative view treats the cost of equity as the rate that equates the present value of expected future earnings, rather than dividends specifically, to the current market price, on the reasoning that dividends are only one form in which shareholder value is realised, and earnings retained for reinvestment also belong to shareholders and should count towards the return they require.

The capital asset pricing model, CAPM

CAPM approaches the cost of equity from a risk-and-return perspective rather than a valuation-model perspective, and is examined regularly in its own right:

Ke = Rf + β(Rm − Rf)

where Rf is the risk-free rate, Rm is the expected return on the market portfolio, and β, beta, measures the share's systematic risk relative to the market — a beta of 1 means the share moves in line with the market on average, a beta above 1 means it is more volatile than the market, and a beta below 1 means it is less volatile. The term (Rm − Rf) is the market risk premium, the extra return the market as a whole is expected to offer over the risk-free rate to compensate for bearing market risk, and multiplying it by β scales that premium to the specific share's own sensitivity to market movements.

CAPM's logic is distinct from the dividend discount approach: it does not require any assumption about future dividend growth at all, relying instead entirely on the share's risk relative to the market, which makes it especially useful for valuing equity in firms that pay no dividend or have an unpredictable dividend history, where the Gordon growth model simply cannot be applied.

Cost of retained earnings

Retained earnings, as the previous chapter established, are not a genuinely free source of capital, because they represent shareholders' funds retained rather than distributed, carrying an opportunity cost equal to what shareholders could have earned had the funds been distributed and reinvested elsewhere at comparable risk. The cost of retained earnings is therefore generally taken to be approximately the same as the cost of equity, sometimes adjusted slightly downward to reflect that a shareholder receiving a dividend would have incurred personal tax and brokerage costs on reinvesting it, costs the firm avoids by retaining the funds directly, though this refinement is a secondary point rather than the core logic examiners test.

Weighted average cost of capital

Once each source's specific cost is computed, WACC combines them:

WACC = Σ (Weight of source × Specific cost of that source)

The weights should, by convention, be market value weights unless a question specifies book value weights — this convention was flagged in the method chapter and is worth restating here because it is precisely in this chapter's numerical questions that the choice is most consequential. Market value weights are conceptually correct because they reflect what investors have actually committed at current value, and because market value based weights are what genuinely determine the firm's actual, current blended cost of raising fresh capital, which is the purpose WACC serves as a discount rate for new investment decisions.

Marginal cost of capital

A distinct and increasingly examined idea is the marginal cost of capital — the cost of the next rupee of capital raised, as opposed to the average cost of capital already raised. As a firm raises progressively larger amounts of fresh capital, the cost of raising each additional source can rise — a firm exhausting cheaper retained earnings must turn to more expensive fresh equity issuance beyond a certain point, or a firm's cost of debt itself may rise once lenders perceive the firm's rising leverage as increasing their risk. The marginal cost of capital, not the historical or average cost, is the theoretically correct discount rate for a genuinely new investment decision, since a new project is financed by the next increment of capital raised, not by the capital already sitting on the firm's balance sheet.

Why this chapter demands unusual care

Two disciplines separate a reliable cost of capital answer from an unreliable one, beyond the four general FM habits from the method chapter.

First, match the cost formula to the source correctly — the tax adjustment belongs to debt only; the dividend-based formulas belong to equity; preference capital gets neither the tax adjustment nor a growth term unless the question specifies a growth in preference dividend, which is unusual. Second, be deliberate about which weighting base the question intends, and state that choice explicitly, since this single decision changes every subsequent figure in a WACC computation, and a wrong but clearly stated assumption is far more markable than an unstated one that simply produces a different final number from the model answer.

Every later FM chapter treats the WACC or the specific cost of equity computed here as a known, given input. Getting this chapter genuinely solid is the highest-leverage single investment of study time in the entire Financial Management half.