CMA Intermediate · Financial Management and Business Data Analytics

Cost of Capital: formula sheet

Full chapter guide

Key formulas

Cost of capital as a decision rule: Accept a project if its return (IRR) > cost of capital; Equivalent to NPV > 0 when cash flows are discounted at the cost of capital.
Explicit cost (IRR of the source): Net funds received = Σ [Outflow in year t ÷ (1 + k)^t]; The rate k that solves this equation is the explicit cost of that source.
Overall cost of capital (WACC): WACC = Σ (Weight of each source × Specific cost of that source); Weights are proportions of each source in the total capital. Detailed use is in the WACC topic.
Implicit cost: Implicit cost = Return from the best alternative forgone; Opportunity cost idea. No formal cash outflow equation is used.
Net proceeds (NP): NP = Face value − Discount (or + Premium) − Issue costs; Issue costs on a percentage basis: check whether the percentage applies to face value or to issue price.
Irredeemable debt, before tax: Kd = I ÷ NP; I = annual interest on face value (coupon rate × face value).
Irredeemable debt, after tax: Kd (after tax) = I × (1 − t) ÷ NP = Kd (before tax) × (1 − t); t = tax rate. Both forms give the same answer here.
Redeemable debt, before tax (approximate): Kd = [I + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]; RV = redemption value, n = years to redemption. The denominator is the average of RV and NP.
Redeemable debt, after tax (approximate): Kd (after tax) = [I × (1 − t) + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]; This applies the tax shield to interest only. Some solutions multiply the whole before-tax rate by (1 − t). Follow the method the question states and show it clearly.
Redeemable debt, exact (yield) method: NP = Σ I ÷ (1 + r)^k + RV ÷ (1 + r)^n, for k = 1 to n; Find r by trial at two rates and interpolate. Using pre-tax interest I gives the before-tax yield. Using I × (1 − t) in place of I gives an approximate after-tax yield. The tax effect of amortising the discount or premium is ignored here unless the question requires it.
Term loan: Kd (after tax) ≈ [Interest rate × (1 − t)] ÷ (1 − fee %); The upfront fee reduces net proceeds. Dividing by (1 − fee %) is the same as dividing by net proceeds per ₹100 borrowed (NP = ₹100 × (1 − fee %)). With no fee, Kd = Interest rate × (1 − t).
Annual preference dividend: D = Dividend rate × Face value; Always on face value, never on issue price or net proceeds.
Net proceeds: NP = Issue price − Flotation costs; If flotation cost is given as a % of face value, apply it to face value. If given as a % of issue price, apply it to issue price. Either way, deduct the cost from the issue price to get NP.
Cost of irredeemable preference shares: Kp = D ÷ NP; If no flotation cost is given and shares are issued at par, Kp equals the dividend rate. If a current market price is used, Kp = D ÷ market price.
Cost of redeemable preference shares (approximate method): Kp = [D + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]; RV is the redemption value including any premium; n is the years to redemption. This is the usual exam formula.
Cost of redeemable preference shares (exact method): NP = Σ D ÷ (1 + Kp)^t for t = 1 to n + RV ÷ (1 + Kp)^n; Kp is the discount rate that equates present value of dividends and redemption value to net proceeds. Solve by trial and interpolation, as for IRR.
Tax treatment: Kp is not adjusted for tax; Preference dividend is not a tax-deductible expense, so there is no tax shield.
Dividend growth model (existing shares): Ke = D1 ÷ P0 + g, where D1 = D0 × (1 + g); D1 is next year's expected dividend. If the question gives D0 (dividend just paid), grow it by g first.
Cost of new equity issue: Ke = D1 ÷ (P0 − F) + g, or D1 ÷ NP + g; F is floatation cost per share; NP is net proceeds per share. Growth g is not adjusted for the cost.
Earnings yield: Ke = E1 ÷ P0 (new issue: E1 ÷ (P0 − F)); Use EPS, not DPS. Suitable when the question asks for the earnings price approach.
CAPM: Ke = Rf + β × (Rm − Rf); (Rm − Rf) is the market risk premium. If Rm is given, subtract Rf. If the premium is given directly, do not subtract again.
Realized yield: Yield for a year = (D + P1 − P0) ÷ P0; Ke = average of yearly yields; Use the average (arithmetic mean) of the yields unless the question asks for another method.
Bond yield plus risk premium: Ke = Yield on company's long-term bond + Risk premium; The risk premium is a judgemental figure given in the question.
Growth rate from retention: g = b × r, where b = retention ratio and r = return on equity; Use when g is not given but retention and ROE are.
Basic cost of retained earnings: Kr = Ke; Used when no tax or brokerage is given. Ke is found by the dividend growth model, CAPM or earnings yield.
Cost of equity, dividend growth model: Ke = D1 ÷ P0 + g; D1 is the expected dividend at the end of year 1, P0 is the current market price, g is the constant growth rate. If D0 is given, 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 equity beta.
Cost of retained earnings with tax and brokerage: Kr = Ke × (1 − t) × (1 − b); t is the shareholders' personal tax rate and b is the brokerage or commission rate, both as decimals. Use only when the question gives them.
WACC: WACC = Σ (Wi × Ki) = (E × Ke + P × Kp + D × Kd after tax) ÷ (E + P + D); Wi is the weight of each source and Ki its cost. The weights must add up to 1 (or 100%). Use the same method, book or market, for all sources.
Weight of a source: Weight = Value of that source ÷ Total value of all sources; Use book values or market values as the question directs. Do not mix the two in one calculation.
After-tax cost of debt: Kd (after tax) = Interest rate × (1 − tax rate); Interest is tax-deductible, so debt cost is taken after tax. Preference dividend and equity return are not tax-deductible.
Cost of equity (CAPM): Ke = Rf + β × (Rm − Rf); Use when the question gives a risk-free rate, beta and market return or premium.
Cost of equity (dividend growth): Ke = D1 ÷ P0 + g; D1 is next year's expected dividend, not the dividend just paid. If D0 is given, D1 = D0 × (1 + g).
Cost of irredeemable preference shares: Kp = Preference dividend ÷ Net proceeds (or market price); For redeemable shares, use the yield-to-maturity or approximation method that the question requires.
Break point: Break point = Amount of capital available from the source at the given cost ÷ Weight of that source in the target capital structure; Calculate one break point for each cost change of each source. Weights must be decimals or fractions that add to 1.
Marginal cost of capital in a range: MCC = Σ (Weight of source × Marginal cost of that source in the range); Recalculate in every range between break points using the costs applicable in that range.
After-tax cost of debt: Kd (after tax) = Interest rate × (1 − tax rate); Use the after-tax cost in MCC. Adjust for issue costs only if the question gives them.
Cost of new equity (growth model): Ke = D1 ÷ (P0 − F) + g; Without issue cost F, this becomes D1 ÷ P0 + g. Use it for cost of retained earnings (F = 0) and for new equity (with F).

Quick revision

Cost of capital is the minimum required return that keeps the firm's value unchanged.
Post-tax cost of debt = Kd × (1 − t), where Kd is the pre-tax cost and t is the tax rate.
Debt has a tax shield; preference dividend and equity dividend do not.
Irredeemable preference cost = Preference dividend ÷ Net proceeds.
Redeemable approximation: [Annual payment + (Redemption value − Net proceeds) ÷ n] ÷ [(Redemption value + Net proceeds) ÷ 2].
Dividend growth model: Ke = D1 ÷ P0 + g, where D1 = D0 × (1 + g).
CAPM: Ke = Rf + β × (Rm − Rf).
Earnings yield method: Ke = EPS ÷ Market price, used when earnings are expected to be constant.
Cost of retained earnings is usually taken as equal to the cost of equity, adjusted for any tax or brokerage if the question asks.
WACC = Σ(weight × cost of each source), and the weights must add up to 100%.
Market value weights reflect current conditions; book value weights are easier to compute.
Marginal cost of capital is the weighted cost of the next lot of funds raised, using target proportions.

Common mistakes

Calling retained earnings a free source of funds with no cost. Fix: State that they carry an implicit (opportunity) cost, the return shareholders could earn by investing the money elsewhere.
Treating explicit cost as only the interest rate. Fix: Explicit cost is the IRR of the net cash received against the cash paid out. Flotation costs and premium change it.
Dividing interest by face value instead of net proceeds. Fix: Always compute NP first. Cost of debt equals coupon rate only when issue is at par with no issue costs.
Calculating interest on issue price or net proceeds. Fix: Interest is always coupon rate × face value. Only the denominator uses NP.
Calculating dividend on issue price or net proceeds instead of face value. Fix: Always compute D as dividend rate × face value. Use net proceeds only in the denominator.
Multiplying the cost of preference shares by (1 − tax rate). Fix: Remember that preference dividend is paid from profit after tax and is not deductible, so no tax adjustment is made.
Using D0 instead of D1 in the Gordon formula. Fix: Check the wording. 'Has just paid' or 'last dividend' means D0. Multiply by (1 + g) before dividing.
Subtracting Rf twice in CAPM. Fix: If the premium is given, use Ke = Rf + β × premium. Subtract only when Rm, the market return, is given.
Taking the cost of retained earnings as zero Fix: Remember the opportunity cost. Shareholders expect at least Ke on the funds retained.
Deducting floatation cost from the market price Fix: Use P0 as given. Floatation cost applies only to fresh issues.

Exam tips

Write the definition in one sentence first. It earns the first mark and frames the rest of the answer.
For 'distinguish between' questions, use two columns in your answer: meaning, basis, example, and use. Always give one example for each side.
In MCQs, match words to type: 'opportunity cost' means implicit, 'IRR of the source' means explicit, 'weighted' means overall.
Link every answer to decision use. Say that future and marginal costs are used for new projects.
There is no negative marking, so attempt every MCQ on this topic. Classification questions are usually answerable by elimination.
Always show NP, RV, I, and the amortisation figure on separate lines. Step marks are awarded even if the final percentage is slightly off.
Write which method you use (approximate or IRR) and whether tax is applied to interest only. This protects your marks if the examiner's method differs.
In MCQs, estimate first: issue at discount or with issue costs means cost above the coupon rate. Eliminate options that break this logic before calculating.