CA Final · Integrated Business Solutions (Multidisciplinary Case Study with Strategic Management)

Advanced Financial Management: formula sheet

Full chapter guide

Key formulas

Net Present Value: NPV = Σ [Cash flow in year t ÷ (1 + k)^t] − Initial investment; k is the risk-adjusted cost of capital. Accept a project when NPV > 0, since it adds to shareholder wealth.
Economic Value Added: EVA = NOPAT − (WACC × Capital employed); NOPAT is net operating profit after tax. Positive EVA means the firm earns more than its cost of capital.
Market Value Added: MVA = Market value of the firm − Capital invested; Shows the wealth the firm has created for investors over the capital they put in. For equity, compare market capitalisation with equity capital invested.
Weighted Average Cost of Capital: WACC = (E ÷ V) × Ke + (D ÷ V) × Kd × (1 − t); V = E + D. Use market values of equity and debt where given. Kd is the pre-tax cost of debt.
Shareholder return: Total shareholder return = (Closing price − Opening price + Dividend) ÷ Opening price; Combines capital gain and dividend for one period.
Long call payoff at expiry: Profit = max(S − X, 0) − Premium; S is spot price at expiry and X is strike. Maximum loss is the premium.
Long put payoff at expiry: Profit = max(X − S, 0) − Premium; Used to protect against a fall in price.
Short option payoff: Writer's profit = − (buyer's profit); The writer's maximum gain is the premium received.
Put-call parity (European, no dividends): C + X ÷ (1 + r)^t = P + S₀; Use continuous form C + X × e^(−rt) = P + S₀ if the rate is continuously compounded. C and P are call and put premiums.
Cost of carry futures price: F = S₀ × (1 + r)^t; Adjust for income such as dividends: subtract the present value or amount of the income. Add storage costs if given.
Futures gain or loss: Long: (Closing price − Entry price) × Lot size; Short: the reverse; Settled daily through margin.
Hedge ratio for index futures: Number of contracts = (Target β − Current β) × Portfolio value ÷ (Index level × Lot size); The result is negative whenever target β is below current β, which means sell futures. It is positive when target β is above current β, which means buy futures. A full hedge is the special case where target β = 0, so the result is negative and the number of contracts to sell is β × Portfolio value ÷ (Index level × Lot size). For a partial hedge, use the same formula and sell the magnitude of the negative result.
Interest rate swap net payment: Net = (Fixed rate − Floating rate) × Notional × Period fraction; The fixed payer pays this if positive and receives if negative.
Swap saving from comparative advantage: Total gain = |Difference in fixed-rate spreads − Difference in floating-rate spreads|; A swap pays only if the two differentials differ. If they are equal, there is no gain. Share the gain as agreed between the parties, usually equally unless told otherwise.
Bid and ask rule: Bank buys base currency at bid; bank sells base currency at ask; Always take the customer's side as the opposite. An importer buys the foreign currency, so use the ask.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × (12 ÷ n) × 100, where n = months; Forward above spot is a premium on the base currency. Forward below spot is a discount.
Interest rate parity: Forward = Spot × (1 + i quote × t) ÷ (1 + i base × t); t is the period in years. For one year or longer, use compounding: (1 + i)^t. Use the rates of the quote and base currencies, not just 'India' and 'US'.
Purchasing power parity (relative): Expected spot = Spot × (1 + inflation quote) ÷ (1 + inflation base); This is an expectation, not a certainty. The higher-inflation currency is expected to depreciate.
Fisher equation: (1 + nominal rate) = (1 + real rate) × (1 + inflation rate); Use it to convert between nominal rates and inflation across countries.
Money market hedge for a foreign payable: Foreign PV = Payable ÷ (1 + i foreign deposit × t); buy this at spot ask; add rupee borrowing cost (1 + i rupee × t); Compare the rupee outflow at the payment date with the forward cost.
Money market hedge for a foreign receivable: Borrow Receivable ÷ (1 + i foreign borrowing × t); sell at spot bid; invest rupees at (1 + i rupee × t); Compare the rupee amount at the receipt date with the forward proceeds.
Cross rate: A/C = A/B × B/C; For bid and ask, combine so that the bank's margin is preserved: bid with bid, ask with ask when multiplying in the same direction.
International project NPV: NPV = Σ (Foreign cash flow × forecast rate in year t) ÷ (1 + home discount rate)^t − initial outlay in home currency; Match the currency of the cash flows with the currency of the discount rate.
Net Present Value: NPV = Σ [CFt ÷ (1 + k)^t] − Initial outlay; Use incremental after-tax cash flows. Include working capital and its recovery, and salvage value. Accept if NPV > 0.
Internal Rate of Return: IRR: Σ [CFt ÷ (1 + IRR)^t] = Initial outlay; Find by interpolation between two rates where NPV changes sign. Accept if IRR > cost of capital, but use NPV for mutually exclusive choices.
Profitability Index: PI = PV of inflows ÷ Initial outlay = 1 + NPV ÷ Outlay; Accept if PI > 1. Under capital rationing with divisible projects, rank on NPV ÷ Outlay (PI − 1).
Certainty equivalent coefficient: α = Certain cash flow ÷ Risky expected cash flow; α lies between 0 and 1. A lower α means higher risk or less tolerance for risk in that year.
Certainty equivalent NPV: NPV = Σ [αt × CFt ÷ (1 + Rf)^t] − Outlay; Discount at the risk-free rate only. Do not use the risk-adjusted rate here, or you count risk twice.
Risk-adjusted discount rate: RADR = Risk-free rate + Risk premium for the project; Use RADR on the unadjusted expected cash flows.
Standard deviation of project NPV (independent yearly flows): σNPV = √ Σ [σt² ÷ (1 + Rf)^(2t)]; Valid only if cash flows of different years are independent. If perfectly correlated, add the discounted SDs instead.
Expanded NPV with real options: Expanded NPV = Static NPV + Value of option(s); Option value is usually given or found from a decision tree or Black-Scholes in the question.
Equivalent Annual Cost/Benefit: EAC = NPV (or PV of costs) ÷ Annuity factor for project life; Use to compare mutually exclusive projects with unequal lives.
Bond value: V = Σ [C ÷ (1 + kd)^t] + F ÷ (1 + kd)^n; C is coupon, F is redemption value, kd is the required yield. Use the annuity factor for coupons and the single-sum factor for redemption.
Approximate YTM: YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]; A shortcut estimate. Where exact YTM is asked, use trial and interpolation at two discount rates.
Constant growth (Gordon) model: P0 = D1 ÷ (ke − g); Valid only when ke > g and growth is constant forever. D1 = D0 × (1 + g).
Multi-stage dividend valuation: P0 = PV of dividends in the high-growth years + PV of [D(n+1) ÷ (ke − g)] at year n; Value the terminal price at the end of the high-growth period, then discount it back.
CAPM: ke = Rf + β × (Rm − Rf); (Rm − Rf) is the market risk premium. If only Rm is given, subtract Rf first.
Beta: β = Cov(i, m) ÷ σm² = ρim × σi ÷ σm; Portfolio beta is the weighted average of the betas of its securities.
Two-asset portfolio risk: σp² = wA²σA² + wB²σB² + 2·wA·wB·ρAB·σA·σB; Take the square root for σp. With covariance given, the last term is 2·wA·wB·Cov(A, B).
Total risk: Total risk = Systematic risk + Unsystematic risk; In variance terms, σi² = β²σm² + variance of the residual (specific) risk.
Sharpe ratio: (Rp − Rf) ÷ σp; Uses total risk. Best for comparing portfolios that are not fully diversified.
Treynor ratio: (Rp − Rf) ÷ βp; Uses systematic risk. Suited to well-diversified portfolios.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive alpha means the manager beat the CAPM return for that beta.
Macaulay duration: D = Σ [t × PV of cash flow at t] ÷ Bond price; Stated in years. Modified duration = D ÷ (1 + y), with y the periodic yield.
Price change using duration and convexity: ΔP ÷ P ≈ − Modified duration × Δy + ½ × Convexity × (Δy)²; Duration alone gives a straight-line estimate. The convexity term adds the curvature.
Swap ratio on EPS: Swap ratio = EPS of target ÷ EPS of acquirer; Number of acquirer shares per target share. It keeps earnings per share neutral for the target at the old EPS. It ignores market prices.
Swap ratio on market price: Swap ratio = Market price per share of target ÷ Market price per share of acquirer; Use when the question says the exchange is at current market prices.
Swap ratio on book value: Swap ratio = Book value per share of target ÷ Book value per share of acquirer; Book value per share = Net worth ÷ number of equity shares.
Weighted swap ratio: Final ratio = Σ (ratio under each basis × weight assigned); Use when the question gives weights for book value, EPS and market price. Weights should add to 1 or 100%.
New shares issued: New shares = Target shares × Swap ratio; Acquirer's total shares after the deal = existing shares + new shares.
Post-merger EPS: EPS = (Earnings of A + Earnings of B + after-tax synergy) ÷ (Shares of A + new shares issued); Compare with A's old EPS to see accretion or dilution. Compare with the target's old EPS after multiplying by the swap ratio.
Post-merger market price: Market price = Post-merger EPS × expected P/E; The P/E must come from the question. It is often assumed to stay at the acquirer's P/E.
Synergy: Synergy = V(AB) − [V(A) + V(B)]; V(AB) is the value of the combined firm. A, B are standalone values.
Premium paid: Premium = Price paid for target − Standalone value of target; This is also the target shareholders' gain.
Net gain to acquirer: Net gain to acquirer = Synergy − Premium; For a cash deal. Same as V(AB) − V(A) − price paid.
Capitalisation of earnings: Value = Maintainable after-tax earnings ÷ Capitalisation rate; Capitalisation rate is the reciprocal of the P/E when P/E is used.
Terminal value (growing perpetuity): TV at year n = FCF(n+1) ÷ (r − g) = FCF(n) × (1 + g) ÷ (r − g); Valid only if r > g. Discount TV by the year-n factor.
Equity value from enterprise value: Equity value = Enterprise value − Debt + Cash and surplus assets; Use when the cash flows are free cash flows to the firm, discounted at WACC.
Debt-equity ratio: Debt-equity ratio = Total debt ÷ Shareholders' equity; Use the same basis (book or market) for before and after comparisons.
Interest coverage ratio: ICR = EBIT ÷ Interest; Tests whether an LBO's debt can be serviced. A low ICR signals risk.
Weighted average cost of capital: WACC = Σ (weight of each source × its cost); Cost of debt is used after tax: Kd × (1 − t).
Gain from divestiture: Gain or loss = Sale proceeds − Book value of net assets sold; Compare tax effects separately if the question gives them.
Share entitlement in a demerger: New shares received = Old shares held × Share exchange ratio; Total value held by a shareholder is expected to be split between the two companies, not created by the split alone.
Value creation test: Value created = Value of parts after restructuring − Value before restructuring; Positive only if focus, synergy or cheaper funding raises the combined value.
Net Asset Value per unit: NAV = (Market value of investments + Other assets − Liabilities and accrued expenses) ÷ Units outstanding; Use market value on the valuation date, not cost. Include accrued income and deduct accrued expenses.
Absolute return on a fund: Return % = [(Closing NAV − Opening NAV) + Distributions per unit] ÷ Opening NAV × 100; Adjust for entry load if you bought above NAV, and exit load if you sold below NAV.
Effective purchase price and sale price: Purchase price = NAV × (1 + entry load %); Redemption price = NAV × (1 − exit load %); Load is charged on NAV. Use these prices for the investor's actual return.
Annualised return: Annualised return = (Ending value ÷ Beginning value)^(1 ÷ years) − 1; Use this when the holding period is more than one year.
NAV after dividend: Ex-dividend NAV = Cum-dividend NAV − Dividend per unit; Assumes no other change in the portfolio value.
Factoring advance and cost: Advance = Receivables × advance % − factor's reserve and commission; Effective cost % = (Commission + Interest) ÷ Net funds advanced × (365 ÷ credit days); Commission is on invoice value. Interest is charged on the amount advanced. Adjust for savings in collection and bad-debt costs.
Securitisation flow: Originator → sells receivables to SPV → SPV issues rated securities to investors → collections pay investors; Know the three parties: originator, SPV, investors.

Quick revision

NPV = Σ cash flows ÷ (1 + r)^t − initial outlay; accept if NPV > 0.
Use incremental, after-tax cash flows and ignore sunk costs.
CAPM: Expected return = Rf + β × (Rm − Rf).
Cost of capital for valuation must match the cash flows being discounted.
Covered interest parity links spot, forward and interest rate differences between two currencies.
Hedging fixes or limits the outcome; compare the hedged result with the unhedged result before choosing.
An option buyer's loss is limited to the premium paid.
Swap ratio in a merger comes from the values or earnings per share of the two companies.
Check the effect of a merger on EPS and on the value of both sets of shareholders.
A mutual fund's NAV = (market value of assets − liabilities) ÷ units outstanding.
Always state assumptions when the case is silent.
End each answer with a clear recommendation.

Common mistakes

Treating profit maximisation and wealth maximisation as the same thing. Fix: Remember the three gaps: profit ignores time value, risk and cash flow. Name at least two in your answer.
Writing only textbook definitions without using case facts. Fix: Quote numbers and events from the case in every paragraph of your answer.
Ignoring the premium when computing option profit Fix: Always write Profit = exercise value − premium for the buyer, and the reverse for the writer.
Treating options as an obligation for the buyer Fix: Buyer exercises only if it pays. If not, the loss is the premium, so the payoff never goes below −premium.
Using the wrong side of the bank's quote, such as bid for an import payment. Fix: Ask: what does the customer do with the foreign currency? If buying, use ask. If selling, use bid.
Applying IRP with the interest rates swapped. Fix: Put the quote currency's rate on top and the base currency's rate below. Sense check: higher interest in the quote currency means a higher forward.
Discounting certainty equivalent cash flows at the risk-adjusted rate. Fix: CE already removes risk from the cash flows. Discount at the risk-free rate only.
Trusting IRR to choose between mutually exclusive projects. Fix: Rank by NPV. IRR can conflict with NPV because of scale, timing or unequal lives. Mention the reinvestment assumption in the answer.
Using D0 instead of D1 in the Gordon model. Fix: Check the wording. If the dividend has just been paid, compute D1 = D0 × (1 + g) before dividing by (ke − g).
Using the market return as the risk premium in CAPM. Fix: Always write ke = Rf + β × (Rm − Rf). Underline whether the question gives Rm or the premium.

Exam tips

In integrated cases, link financial policy to strategy language such as growth, turnaround or diversification, then back it with a figure.
Use the structure provision, facts, conclusion even for management questions: concept, case fact, verdict.
Do not state weightage guesses. Practise one case each from investment, financing and dividend areas.
For MCQs, wealth maximisation options usually mention cash flow, risk and long term. Prefer them over profit-only options.
Show calculations for EVA or WACC in steps so you earn method marks even if a number slips.
In case-scenario MCQs, find the exposure first. The right instrument usually follows directly from it.
For written answers, show the payoff at each expiry level in a small table so the examiner can award step marks.
Always state break-even, maximum loss and maximum gain when a strategy is asked.