Cost of Capital: formula sheet

Key formulas

Explicit cost (IRR approach)

PV of cash inflows from the source = PV of cash outflows to the source, at rate k

The rate k that solves this is the explicit cost. Inflows are net funds received; outflows are interest, dividends and repayments.

Composite cost (WACC)

Ko = Σ (Wi × Ki), where ΣWi = 1

Wi is the weight of each source and Ki its specific cost. Detailed use is in the WACC topic.

Project acceptance rule

Accept if project return > cost of capital; reject if project return < cost of capital

At equal return and cost, NPV is zero and the project is just acceptable.

After-tax cost of a tax-deductible cost

After-tax cost = Pre-tax cost × (1 − tax rate)

Applies to interest on debt. Preference and equity dividends are not tax-deductible.

Net proceeds (NP)

NP = Issue price − Issue costs (add premium if issued at premium; subtract discount if issued at discount)

Use NP, not face value, whenever issue costs, discount or premium are given.

Irredeemable debt, before tax

Kd = I ÷ NP

I is the annual interest on face value (coupon rate × face value).

Irredeemable debt, after tax

Kd = I(1 − t) ÷ NP

t is the tax rate. Use this value in WACC.

Redeemable debt, before tax (approximation)

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

n is years to redemption. RV is the amount repaid, including any premium.

Redeemable debt, after tax (approximation)

Kd = [I(1 − t) + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]

This is the usual ICAI form. Tax is applied to interest only. If the question says to compute before-tax Kd and then adjust, follow its instruction.

YTM (exact method)

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

Try two rates, get NPVs of opposite sign, then interpolate to find k.

Term loan

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

If a processing fee is given, treat it as an issue cost and reduce the net amount received.

Irredeemable preference shares

Kp = PD ÷ NP

PD = annual preference dividend (rate × face value). NP = net proceeds = issue price − flotation cost per share.

Redeemable preference shares (approximate)

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

RV = redemption value (including any premium). n = years to redemption. NP = net proceeds. Use when the question does not ask for an exact rate.

Redeemable preference shares (exact, IRR method)

NP = Σ [PD ÷ (1 + Kp)^t] for t = 1 to n + RV ÷ (1 + Kp)^n

Find Kp by trial and interpolation between two discount rates. Use when the question asks for the exact or yield-based cost.

Net proceeds

NP = Issue price − discount (if any) − flotation cost

Flotation cost may be given as a percentage of issue price or face value. Read the wording.

Tax treatment

Kp is not adjusted for tax

Preference dividend is paid out of profit after tax. Where a question mentions a dividend distribution tax, follow the data given in the question.

Dividend price approach

Ke = D1 ÷ P0

D1 is the dividend expected at the end of year 1. P0 is the current market price. Use when dividends are constant.

Dividend growth model (Gordon)

Ke = D1 ÷ P0 + g

Where D1 = D0 × (1 + g). Do not use D0 directly when the question gives the dividend just paid.

Growth rate from retention

g = b × r

b is the retention ratio and r is the return on equity. Use when g is not given and retention and ROE are.

Earnings price approach

Ke = E1 ÷ P0

E1 is expected EPS. If only current EPS is given, use it as stated unless growth is also given.

Realized yield approach

Ke = IRR of the cash flows: purchase price, dividends received and final sale price

Solve for the rate that makes the present value of the actual dividends and sale price equal to the purchase price.

CAPM

Ke = Rf + β × (Rm − Rf)

Rm − Rf is the market risk premium. If the question gives only Rm and Rf, compute the premium yourself.

Cost of new equity (with flotation cost)

Ke = D1 ÷ (P0 − F) + g

F is the flotation cost per share. It applies to new issues, not retained earnings.

Basic cost of retained earnings

Kr = Ke

Use when the question gives no personal tax or brokerage. Find Ke by the dividend growth model, CAPM or earnings model.

Dividend growth model for Ke

Ke = (D1 ÷ P0) + g

D1 = expected dividend next year = D0 × (1 + g). P0 is the current market price. No floatation cost is deducted for retained earnings.

CAPM for Ke

Ke = Rf + β × (Rm − Rf)

Use when risk-free rate, beta and market return or premium are given.

Cost of retained earnings after personal tax and brokerage

Kr = Ke × (1 − Tp) × (1 − B)

Tp = shareholders' personal tax rate; B = brokerage rate, both as decimals. Apply only the adjustments the question mentions.

Adjustment for tax only or brokerage only

Kr = Ke × (1 − Tp) or Kr = Ke × (1 − B)

If only one item is given, apply only that factor.

WACC

WACC = Σ(W × K) ÷ ΣW = (E×Ke + R×Kr + P×Kp + D×Kd) ÷ (E + R + P + D)

E, R, P, D are the amounts of equity, retained earnings, preference and debt. Use the same basis (book or market) for all of them. If weights are proportions that add to 1, no division is needed.

Weight of a source

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

Value is book or market depending on the basis chosen.

After-tax cost of debt (irredeemable)

Kd = [I × (1 − t)] ÷ NP

I is annual interest, t is the tax rate, NP is net proceeds. For debt issued at par with no cost, NP equals face value. For redeemable debt, use the approximation or IRR method your question needs.

Cost of preference shares (irredeemable)

Kp = Preference dividend ÷ Net proceeds

No tax adjustment, because preference dividend is not tax deductible.

Cost of equity (dividend growth model)

Ke = D1 ÷ P0 + g

D1 is the expected dividend next year. D1 = D0 × (1 + g).

Cost of equity (CAPM)

Ke = Rf + β × (Rm − Rf)

Rf is the risk-free rate, Rm the market return, β the beta of the share.

Cost of retained earnings

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

Use the cost of equity unless the question gives an adjustment.

Marginal cost of capital

MCC = Σ (wᵢ × kᵢ)

wᵢ is the target proportion of source i in the new capital. kᵢ is the current after-tax cost of raising that source. Weights must add up to 100%.

Break point

Break point = Amount of a source available at a given cost ÷ Weight of that source in the capital structure

It is the total new capital at which that source's cost changes. Compute it for every cost change, then sort the break points in order.

After-tax cost of debt (irredeemable)

kd = Interest rate × (1 − t)

Use the new borrowing rate, not the old coupon. t is the tax rate. For redeemable debt or flotation costs, use the method from the Cost of Debt topic.

Cost of equity (dividend growth model)

ke = D₁ ÷ P₀ + g

D₁ is the expected dividend next year. P₀ is the current market price (net of flotation cost for new issue). g is the constant growth rate.

Decision rule

Accept a project if IRR > MCC at that level of funds

Where a project spans two MCC ranges, compare its IRR with the MCC of the range that its funds fall in. Use the higher MCC to be safe.

Quick revision

• Cost of capital is the minimum required return that keeps investors satisfied.
• After-tax cost of debt = Interest × (1 − t) ÷ Net proceeds, in the simple perpetual case.
• Interest on debt is tax deductible. Preference dividend is not, so there is no tax shield on Kp.
• Use net proceeds (after issue cost) for the cost of new debt, preference and new equity.
• Kp for irredeemable preference = Preference dividend ÷ Net proceeds.
• Dividend growth model: Ke = D1 ÷ P0 + g, where D1 = D0 × (1 + g).
• CAPM: Ke = Rf + β × (Rm − Rf).
• Earnings model: Ke = E ÷ P, used when earnings are expected to stay constant.
• Retained earnings have no floatation cost, so their cost equals Ke on existing shares.
• WACC = Σ (weight × cost) ÷ Σ weights, using after-tax costs.
• Prefer market value weights for decisions and state clearly which weights you used.
• Marginal cost of capital is the weighted cost of the next rupee raised, using target weights.

Common mistakes

• Treating retained earnings as free capital. Fix: Say it has an implicit (opportunity) cost: the return shareholders could have earned if the profit had been distributed.
• Confusing explicit cost with implicit cost. Fix: Explicit means actual cash flows are involved, like interest. Implicit means a forgone opportunity, with no cash payment.
• Using face value instead of net proceeds in the denominator. Fix: Always compute NP first. Circle every item that changes cash received: discount, premium, floatation cost, underwriting fee.
• Calculating interest on issue price or net proceeds. Fix: Interest is coupon rate × face value. Only the denominator uses NP.
• Applying the dividend rate to issue price instead of face value. Fix: Dividend = rate × face value, always. Issue price only affects the denominator.
• Multiplying Kp by (1 − tax rate). Fix: Preference dividend is not tax deductible, so there is no tax shield. Leave Kp unadjusted.
• Using D0 in place of D1 in the growth model. Fix: Look for words like 'has just paid' or 'last dividend'. Then multiply by (1 + g) to get D1. Use 'expected dividend' as D1 as given.
• Using the market return Rm as the premium in CAPM. Fix: The formula needs (Rm − Rf). If the question says 'market return is 12%', subtract Rf first. If it says 'market risk premium is 6%', use 6% directly.
• Treating retained earnings as free capital with zero cost. Fix: Remember the opportunity cost: shareholders could have reinvested the money. Cost is at least the adjusted Ke.
• Deducting floatation cost from the price while computing Kr. Fix: Retained earnings involve no issue, so no floatation cost. Use P0 as it is.

Exam tips

• For a 'meaning and significance' question, structure the answer as definition, components, types, then uses. Four short blocks fetch the full marks.
• Give a one-line example against every term you define, such as interest for explicit cost and retained earnings for implicit cost.
• In MCQs, read carefully whether the cost is for one source or all sources together. That separates specific from composite.
• If a numerical question mentions tax, check whether the cost you are computing is for debt, and use the after-tax figure.
• Link every statement of cost of capital to a decision in the last line. Examiners look for the connection to NPV, IRR and capital structure.
• Look for the words 'redeemable', 'at premium', 'floatation cost' and 'discount'. Each one changes NP or RV, and the examiner builds the question around them.
• If the question asks for YTM or IRR of the debenture, do not use the average formula. Set up the NPV equation, try two rates, and interpolate. Show the NPV at each rate.
• In MCQs, quickly check direction: discount or issue costs push Kd above the coupon, and tax pushes it below. Eliminate options that break this.