Cost of Capital: formula sheet

Key formulas

Cost of capital as required return

Cost of capital = Return required by the investors on the funds supplied

Used as the cut-off rate: accept a project only if its expected return is at least this rate.

Decision rule in capital budgeting

Accept if IRR ≥ cost of capital; accept if NPV (discounted at cost of capital) ≥ 0

A project with IRR equal to cost of capital has NPV of zero.

Overall (weighted average) cost

Ko = Σ (Weight of each source × Cost of that source)

Weights are proportions of each source in total capital. Weights must add up to 1.

After-tax cost of debt (simple form)

Kd (after tax) = Interest rate × (1 − tax rate)

Applies to perpetual debt issued at par. Details are in the Cost of Debt topic.

Irredeemable debt (before tax)

Kd = I ÷ NP

I = annual interest on face value. NP = net proceeds (issue price less issue costs).

Irredeemable debt (after tax)

Kd (after tax) = [I ÷ NP] × (1 − t)

t = tax rate as a decimal. Use this form for WACC.

Redeemable debt (approximate yield, before tax)

Kd = [I + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]

RV = redemption value, n = years to maturity. If redeemed at a premium, RV is higher than face value.

Redeemable debt (after tax)

Kd (after tax) = Kd (before tax) × (1 − t)

Tax adjustment applies to the final rate when using the approximate formula with I as pre-tax interest.

Net proceeds

NP = Face value × issue price % − issue costs

Issue at discount lowers NP. Issue at premium raises NP.

Exact method

NP = Σ [I(1 − t) ÷ (1 + Kd)^n] + RV ÷ (1 + Kd)^N

Kd is the IRR found by trial and interpolation. Use it when the question asks for the exact or yield-to-maturity cost.

Cost of irredeemable preference shares

Kp = D ÷ NP

D = annual preference dividend (rate × face value). NP = net proceeds per share after premium, discount and issue costs.

Net proceeds per share

NP = Issue price − Issue costs (add premium, deduct discount)

Use the amount actually received. Issue costs are the flotation costs such as underwriting commission and brokerage.

Cost of redeemable preference shares (approximate)

Kp = [D + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]

RV = redemption value, n = years to redemption. The denominator is the average of RV and NP.

Cost of redeemable preference shares (exact)

NP = Σ D ÷ (1 + Kp)^t + RV ÷ (1 + Kp)^n

Solve by trial and error or interpolation. It is the IRR of the cash flows.

Tax treatment

Kp is not adjusted for tax

Preference dividend is an appropriation of profit, so no (1 − t) factor.

Dividend yield method

Ke = D1 ÷ P0

Assumes constant dividend with no growth, so D0 = D1 and you use the given dividend directly. P0 is the current market price. If the question gives the dividend just paid along with a growth rate, move to the growth model.

Dividend growth (Gordon) model

Ke = (D1 ÷ P0) + g, where D1 = D0 × (1 + g)

g is the constant annual growth rate of dividends. If D0 is the dividend just paid, first compute D1.

Earnings yield method

Ke = EPS ÷ P0

Used when the market price reflects earnings rather than dividends. It treats the whole EPS as the shareholders' return and assumes no growth in earnings. If the question gives the EPS expected for next year, use that figure with the price; otherwise use the EPS given.

CAPM

Ke = Rf + β × (Rm − Rf)

Rf is the risk-free return, Rm the expected market return, (Rm − Rf) the market risk premium. If the premium is given directly, use it as it is.

Net proceeds on new issue

Net price = Issue price − Floatation cost

For new equity shares, replace P0 with net proceeds: Ke = D1 ÷ NP + g.

Growth from retention

g = b × r

b is the retention ratio (1 − payout ratio) of earnings, and r is the rate of return on retained earnings. r equals the return on equity (ROE) only if the return on new investment equals the return on existing equity. The formula assumes a constant retention ratio and a constant return on retained earnings. Use it when g is not given directly.

Cost of retained earnings (basic)

Kr = Ke = D1 ÷ P0 + g

D1 is the expected dividend next year, P0 is the current market price, g is the constant growth rate. Use when no tax or brokerage is given.

Adjusted for personal tax and brokerage

Kr = Ke × (1 − t) × (1 − b)

t is the shareholder's personal tax rate and b is the brokerage rate on reinvestment. Apply only the adjustments the question gives.

Cost of equity by dividend growth

Ke = (D0 × (1 + g)) ÷ P0 + g

Use when the last dividend D0 is given, not D1. Find D1 first.

Cost of equity by CAPM

Ke = Rf + β × (Rm − Rf)

Use when the question gives risk-free rate, beta and market return.

Earnings approach

Ke = E1 ÷ P0

Used when growth is nil and all earnings are assumed distributed.

WACC

WACC = Σ (Wi × Ki) = (E × Ke + P × Kp + D × Kd(1 − t) + R × Kr) ÷ Total capital

Wi is the weight of each source and Ki its cost. Weights must add up to 1 or 100%.

Weight of a source

Weight = Value of the source ÷ Total value of all sources

Use book values or market values consistently for all sources.

After-tax cost of debt

Kd (after tax) = Interest rate × (1 − tax rate)

For irredeemable debt, Kd = I ÷ NP × (1 − t), where NP is net proceeds.

Cost of equity (dividend growth approach)

Ke = D1 ÷ P0 + g

D1 is the expected dividend next year. Use the figure the question gives you.

Cost of preference shares

Kp = Preference dividend ÷ Net proceeds (irredeemable)

No tax adjustment is made.

Cost of retained earnings

Kr = Ke (when no flotation cost or personal tax adjustment is given)

Treat retained earnings at the same cost as equity unless told otherwise.

Marginal cost of capital

MCC = Σ (Wᵢ × Kᵢ)

Wᵢ is the target weight of each source in the new capital. Kᵢ is the cost of that source for the new funds.

Break point

Break point = Amount of cheaper source available ÷ Weight of that source in the capital structure

It is the total new capital that can be raised before that source's cost increases. For example, retained earnings of ₹30,00,000 at a weight of 60% give a break point of ₹50,00,000.

Cost of debt (after tax)

Kd = I × (1 − t) ÷ NP, or Kd = r × (1 − t) for debt issued at par with no costs

Use the after-tax cost because interest is tax-deductible. t is the tax rate.

Cost of equity (dividend growth)

Ke = D₁ ÷ P₀ + g, or D₁ ÷ NP + g for new shares after flotation cost

D₁ is next year's expected dividend. For new equity, use net proceeds in place of the market price.

Cost of retained earnings

Kr = D₁ ÷ P₀ + g

Use the market price with no flotation cost, unless the question says to adjust for personal tax or brokerage.

Investment decision rule

Accept a project if IRR > MCC

The optimal capital budget is the amount of projects that clear this test.

Quick revision

• Cost of capital is the minimum return needed to satisfy investors and acts as the hurdle rate.
• Debt carries a tax shield: after-tax Kd = Kd × (1 − tax rate).
• Preference share dividend is not tax deductible, so Kp has no tax adjustment.
• Use the net proceeds (after issue costs) when the question gives flotation costs.
• For redeemable securities, the cost uses the annual payment plus the amortised gain or loss on redemption, divided by the average of proceeds and redemption value.
• Dividend growth model: Ke = D1 ÷ P0 + g, where D1 is the expected next-year dividend.
• CAPM: Ke = Rf + β × (Rm − Rf).
• Cost of retained earnings is an opportunity cost, usually taken equal to Ke, with adjustments only if the question gives them.
• WACC = Σ (weight × cost of each source), and the weights must add up to 1.
• Marginal cost of capital is the weighted cost of raising additional funds, using the proportions of the new financing.
• Always state whether you use book or market value weights.

Common mistakes

• Defining cost of capital only as the interest rate paid on loans. Fix: Say it covers all long-term sources. Equity has a cost too, even when no fixed payment is made.
• Saying retained earnings are free or have no cost. Fix: Explain the opportunity cost: shareholders could have invested the dividend elsewhere and earned a return.
• Calculating interest on issue price or net proceeds instead of face value Fix: Interest is always coupon × face value. Only the denominator uses net proceeds.
• Forgetting to deduct issue costs from proceeds Fix: Always write NP = issue price − costs before doing anything else.
• Using face value instead of net proceeds in the denominator. Fix: Always compute NP first. The dividend uses face value, the denominator uses what the company receives.
• Adjusting the cost for tax as if it were debt. Fix: Remember that preference dividend is paid from after-tax profit. No (1 − t) factor.
• Using D0 directly in the Gordon model instead of D1. Fix: If the dividend is paid already, multiply by (1 + g) first. Use the dividend as it is only when it is stated as expected next year.
• Using the market price for a new share issue and ignoring floatation cost. Fix: For a fresh issue, use net proceeds (issue price less floatation cost) in the denominator.
• Writing the cost of retained earnings as zero. Fix: Always explain the opportunity cost. Kr is at least the return shareholders expect on equity.
• Using D0 in place of D1 in D1 ÷ P0 + g. Fix: Check the wording. If the dividend is already paid, multiply by (1 + g) first.

Exam tips

• Start every theory answer with a crisp definition that includes minimum required return and hurdle rate. Examiners look for these words.
• Keep significance points to capital budgeting, capital structure, financing choice and performance. Put capital budgeting first.
• If asked for factors affecting cost of capital, group them into those the firm controls and those it does not.
• In short numericals, always state the comparison with cost of capital and then the accept or reject conclusion in a full sentence.
• Use the remaining time for the calculation topics that follow, such as cost of debt, equity and WACC, because they carry most numerical marks.
• Write net proceeds as a separate line. Examiners give step marks for it even if the final rate is off.
• State which formula you are using, such as the approximate yield method, unless the question asks for exact IRR.
• Show both before-tax and after-tax rates when the question is unclear. It protects your marks.