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Part 2 · Section B

Corporate Finance

Risk and return, valuing bonds and stock, the cost of capital, raising and returning capital, working capital, restructuring and international finance. This section is 20% of Part 2, and most questions are calculations built on the time value of money.

Begin topic 1 Finance calculators

About 20 of the 100 multiple-choice questions. Estimated study time: 34 hours.

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Your learning path

Six topics in the IMA outline order. Topics 2 and 4 carry the most calculations; the interest tables are on the formula sheet.

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Topic 1 of 6

Risk and return

How to measure the return you expect and the risk you bear, and why only market risk earns a premium.

Expected return and standard deviationMeasuring stand-alone risk
Expected return
$$E(R) = \sum p_i R_i$$
Standard deviation
$$\sigma = \sqrt{\sum p_i \left(R_i - E(R)\right)^2}$$

Coefficient of variation = σ ÷ E(R): risk per unit of return, for comparing investments of different size.

Diversification and betaSystematic vs unsystematic risk
  • Unsystematic (diversifiable, firm-specific) risk: strikes, lawsuits, a failed product. Diversification removes it, so the market does not reward it.
  • Systematic (market) risk: interest rates, recessions, inflation. It cannot be diversified away and is measured by beta.
  • Beta = 1: moves with the market. Beta > 1: amplifies market moves. A portfolio's beta is the weighted average of its stocks' betas.
  • Combining assets with correlation below +1 lowers portfolio σ below the weighted average of the individual σs.
Two-asset portfolio standard deviation
$$\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2}$$
Exam trapA stock with a high standard deviation can have a low beta. In a diversified portfolio, required return depends on beta, not on standard deviation.
CAPM and the security market lineThe required return for systematic risk
Capital asset pricing model
$$k_e = R_f + \beta\,(R_m - R_f)$$

(Rm − Rf) is the market risk premium. Plotting k against β gives the security market line (SML).

Exam trapWhen a question gives the market risk premium (e.g. 6%), do not subtract the risk-free rate again: k = Rf + β × premium.
Exam trapDiversification lowers portfolio risk only when correlation is below +1. With perfect positive correlation, portfolio standard deviation is simply the weighted average of the individual standard deviations.
Instructor noteA stock plotting above the SML offers more return than its beta requires (undervalued, buy); below the line it is overvalued. That single picture answers most CAPM interpretation questions.

Finished Risk and return?

Mark it complete when you can compute E(R), σ and a CAPM return, and explain why beta matters.

Topic 2 of 6

Long-term financial management

Pricing bonds and shares as present values, turning those prices into costs of capital, and combining them into WACC.

Bond valuationPresent value of coupons and face value
Bond price
$$P = C \times PVA_{k,n} + F \times PV_{k,n}$$

C = annual coupon, F = face value, k = market rate (YTM). Semiannual: halve the coupon and the rate, double n.

  • Market rate > coupon rate → bond sells at a discount; market rate < coupon → premium.
  • Bond prices move opposite to interest rates; longer maturity and lower coupons mean greater price sensitivity (interest-rate risk).
Exam trapUse the market rate (YTM) to discount, not the coupon rate. Discounting at the coupon rate always gives face value.
Stock valuationDividend discount and Gordon growth
Gordon (constant growth)
$$P_0 = \frac{D_1}{k_e - g} = \frac{D_0(1 + g)}{k_e - g}$$
Preferred stock (perpetuity)
$$P = \frac{D_p}{k_p}$$
Exam trapGordon uses next year's dividend. If the question gives the dividend "just paid", grow it by one year first.
Cost of capital and WACCComponent costs and market-value weights
Debt (after tax)
$$k_d(1 - t)$$

kd = yield to maturity on new debt, not the coupon rate.

Preferred stock
$$k_p = \frac{D_p}{P_{net}}$$

Pnet = price less flotation costs. No tax adjustment: dividends are not deductible.

Common equity
$$k_e = \frac{D_1}{P_0} + g \quad\text{or CAPM}$$
Weighted average cost of capital
$$WACC = w_d k_d(1 - t) + w_p k_p + w_e k_e$$

Weights from market values (or the target capital structure), not book values.

Exam trapOnly debt gets the tax adjustment. Retained earnings are not free: their cost is the shareholders' required return (ke without flotation costs).
Capital structure and leverageOperating, financial and total leverage
Degrees of leverage
$$DOL = \frac{CM}{EBIT} \qquad DFL = \frac{EBIT}{EBIT - I} \qquad DTL = DOL \times DFL$$

With preferred dividends: DFL = EBIT ÷ [EBIT − I − Dp ÷ (1 − t)].

  • Trade-off theory: debt adds value through the interest tax shield until expected financial-distress costs outweigh it, so an optimal structure minimizes WACC.
  • Pecking order: firms prefer internal funds, then debt, then new equity, because issuing equity signals that managers think shares are overvalued.
Exam trapThe cost of debt is the yield investors require on new debt today, not the coupon rate on bonds issued years ago. A 6% coupon bond yielding 9% has a pre-tax cost of 9%.
Exam trapThe (1 − t) adjustment applies to debt only. Preferred dividends are paid from after-tax income, so the cost of preferred stock is never reduced for taxes.
Instructor noteMost cost-of-capital errors are one of three: using the coupon rate instead of YTM, forgetting the tax shield on debt, or using book-value weights. Check all three before you pick an answer.

Finished Long-term financial management?

Mark it complete when you can price a bond from the tables, value a growing stock and build a WACC.

Topic 3 of 6

Raising capital

How companies raise long-term funds, how they return cash to shareholders, and when leasing beats buying.

Issuing securitiesIPOs, private placements and the role of investment banks
  • IPO: first public sale of shares, registered with the SEC. Underwriters either buy the whole issue (firm commitment, they bear the price risk) or sell what they can (best efforts). IPOs are often underpriced on the first day.
  • Private placement: sale to a few institutional investors without public registration; faster and cheaper to issue, but usually a higher required return and restrictions on resale.
  • Shelf registration (SEC Rule 415): register once and issue over time as market conditions allow.
  • Rights offering: existing shareholders may buy new shares in proportion to their holdings, protecting them from dilution.
Exam trapIn a best-efforts offering the investment bank does not guarantee the proceeds; under a firm commitment it does. A question about who bears the risk of unsold shares tests exactly this.
Dividend policy, splits and repurchasesReturning cash and changing share counts
  • Policies: residual (pay what is left after funding positive-NPV projects), stable dividend per share (most common; cuts send a bad signal), constant payout ratio.
  • Theories: dividend irrelevance (Modigliani–Miller, perfect markets), bird-in-the-hand (investors value certain dividends), tax preference (capital gains taxed later), signaling and clientele effects.
  • Dates: declaration (liability recorded) → ex-dividend (buyers on or after this date do not get the dividend; price drops about by the dividend) → record → payment.
  • Stock split / stock dividend: more shares, proportionally lower price, no change in total equity or each holder's share of the company. A small stock dividend moves retained earnings to paid-in capital at market value.
  • Repurchases return cash flexibly, signal undervaluation, offset option dilution and raise EPS if earnings fall less than the share count.
Exam trapSplits and stock dividends do not change total shareholders' equity or anyone's ownership percentage. Only cash dividends and repurchases send cash out of the company.
Lease vs buyComparing after-tax present-value costs

Treat a lease as a financing alternative to borrowing and buying. Discount both sets of after-tax cash flows at the after-tax cost of debt, because lease payments are as certain as loan payments. Choose the alternative with the lower present-value cost.

Lease vs buy (present-value cost)
$$PV_{lease} = L(1 - t) \times PVA_{k_d(1-t),\,n}$$ $$PV_{buy} = \text{Price} - \text{Dep}\cdot t \times PVA - \text{Salvage}_{after\text{-}tax} \times PV$$
Exam trapA buyback raises EPS only if the earnings yield on the shares retired (EPS ÷ price) exceeds the after-tax return the cash was earning. Paying a high price with cash that earned a good return can lower EPS.
Instructor noteDiscount lease-vs-buy flows at the after-tax cost of debt, not WACC. The decision to acquire the asset has already been made; the only question is how to finance it.

Finished Raising capital?

Mark it complete when you can explain the dividend dates and theories and compare lease and buy costs.

Topic 4 of 6

Working capital management

Managing cash, receivables, inventory and payables, and pricing the short-term credit that funds them.

Cash and marketable securitiesSpeeding collections, slowing payments
  • Motives: transactions, precautionary, speculative, compensating balances required by banks.
  • Accelerate collections: lockbox systems, electronic payments, concentration banking. Control disbursements: zero-balance accounts, paying on the due date (not earlier).
  • Marketable securities hold surplus cash safely and liquidly: Treasury bills, commercial paper, money-market funds. Safety and liquidity come before yield.
  • Value of a lockbox = days saved × average daily collections × interest rate − cost of the service.
Value of faster collection
$$\text{Annual benefit} = \text{Days saved} \times \text{Daily collections} \times r - \text{Cost}$$
Receivables and trade creditCredit terms and the cost of skipping a discount
Cost of not taking a trade discount
$$\frac{d}{1 - d} \times \frac{360}{\text{Net days} - \text{Discount days}}$$

Simple annual rate on a 360-day year (the CMA convention unless told otherwise).

Effective annual rate
$$EAR = \left(1 + \frac{d}{1 - d}\right)^{Y/(\text{Net} - \text{Disc})} - 1$$

Y = days in the year: use the same convention (360 or 365) as for the nominal rate.

Credit policy change
$$\Delta\text{Profit} = \Delta S \cdot CM\% - \Delta\text{Bad debts} - \Delta AR \times VC\% \times k$$

AR = sales ÷ 360 × DSO. The extra investment in receivables is measured at variable cost.

Exam trapThe cost of forgoing a discount uses the days between the discount date and the net date (here 20), not the full 30 days.
Inventory: EOQ, safety stock and reorder pointBalancing ordering and carrying costs
Economic order quantity
$$EOQ = \sqrt{\frac{2DS}{H}}$$

D annual demand, S cost per order, H annual carrying cost per unit. At EOQ, ordering cost = carrying cost.

Reorder point
$$ROP = \text{Daily usage} \times \text{Lead time} + \text{Safety stock}$$
Exam trapEOQ rises with the square root of demand: doubling demand raises EOQ by only about 41%, not 100%.
Short-term financingEffective rates on bank credit
Effective interest rate
$$\text{Effective rate} = \frac{\text{Interest} + \text{Fees}}{\text{Usable funds}}$$

Usable funds = principal − discount interest − compensating balance (if not otherwise held).

Exam trapKeep EOQ units consistent: if demand is given per month, either convert it to annual demand or use a monthly carrying cost. Mixing monthly demand with an annual carrying cost understates EOQ by a factor of √12.
Exam trapA compensating balance raises the effective rate only to the extent it exceeds the cash the company would hold anyway. If it already keeps that balance, usable funds are not reduced.
Instructor noteFor every short-term financing question, ask: how much interest (and fees) do I pay, and how much money can I actually use? The ratio is the effective rate.

Finished Working capital management?

Mark it complete when you can price a trade discount, an EOQ and a discount loan.

Topic 5 of 6

Corporate restructuring

Why companies combine and separate, how a target is valued, and how targets defend themselves.

Mergers and acquisitionsTypes, motives and valuation
  • Horizontal (competitors), vertical (supplier or customer), conglomerate (unrelated businesses).
  • Sound motives: synergies (cost savings, revenue gains), economies of scale, access to technology or markets, tax benefits. Weak motives: diversification for its own sake (shareholders can diversify cheaply themselves), managers' empire-building, EPS bootstrapping.
  • Valuation: discounted free cash flows (with a terminal value), comparable-company multiples (P/E, EV/EBITDA) and precedent transactions.
Value to the acquirer
$$NPV_{acq} = V_{target} + \text{Synergies} - \text{Price paid}$$

The target's shareholders capture the premium (price − stand-alone value); the acquirer gains only if synergies exceed the premium.

Exam trapA higher combined EPS after a share-for-share acquisition does not prove value was created: buying a lower-P/E company mechanically raises EPS (bootstrapping) without any synergy.
Divestitures and takeover defensesSeparating businesses and resisting bids
Forms of divestiture
Form What happens Cash to the parent?
Sale (divestiture) A unit is sold to another company Yes
Spin-off Shares of a new company are distributed pro rata to the parent's shareholders No
Equity carve-out A minority stake in a subsidiary is sold to the public in an IPO Yes
Split-off Parent shareholders exchange parent shares for subsidiary shares No
Leveraged / management buyout A unit or company is bought mostly with debt, often by its managers Yes (to sellers)
  • Defenses: poison pill (rights that dilute a hostile bidder), staggered board, supermajority voting, white knight (a friendlier buyer), crown-jewel sale, Pac-Man (counter-bid), golden parachutes, greenmail (buying back the raider's shares at a premium).
Exam trapA spin-off raises no cash for the parent; a carve-out does. Both create a separately traded company.
Exam trapDiscount the target's cash flows at a rate reflecting the target's risk, not the acquirer's WACC. Using a lower acquirer rate for a riskier target overstates its value and invites overpaying.
Instructor noteDefenses that entrench management (greenmail, golden parachutes) can harm shareholders. The exam likes to ask which defense pays a premium only to the raider (greenmail) or dilutes the bidder (poison pill).

Finished Corporate restructuring?

Mark it complete when you can value a target and match each divestiture and defense to its description.

Topic 6 of 6

International finance

Reading exchange rates, measuring currency exposure, hedging it, and getting paid safely in foreign trade.

Exchange rates and parityQuotes, cross rates and forward rates
  • Direct quote: home currency per unit of foreign ($1.10 per €). Indirect: foreign per unit of home (€0.909 per $).
  • If the $ per € rate rises, the euro has appreciated and the dollar depreciated: US exports become cheaper in Europe.
  • Interest rate parity: the currency with the higher interest rate trades at a forward discount. Purchasing power parity: higher inflation leads to currency depreciation.
Interest rate parity (direct quote)
$$F = S \times \frac{1 + r_{home}}{1 + r_{foreign}}$$
Cross rate
$$\frac{A}{B} = \frac{A/C}{B/C}$$
Exposure and hedgingForwards, futures, options and swaps
  • Transaction exposure: receivables and payables already contracted in a foreign currency. Translation: restating a foreign subsidiary's statements. Economic: long-run effect on cash flows and competitiveness.
Currency hedging tools
Tool Features Hedge a receivable / payable
Forward contract Customized, over the counter, settled at maturity; locks in a rate Sell / buy the currency forward
Futures contract Standardized, exchange-traded, marked to market daily, margin required Sell / buy futures
Option Right, not obligation; costs a premium; protects the downside and keeps the upside Buy a put / buy a call
Money-market hedge Borrow or lend in the two currencies to lock in the rate Borrow foreign now / invest foreign now
Swap Exchange of cash-flow streams (currencies or fixed vs floating interest) over time Long-term exposures, foreign-currency debt
Exam trapA company that will receive foreign currency hedges by selling it forward or buying a put. A company that must pay foreign currency buys it forward or buys a call.
Financing international tradeGetting paid across borders
  • Letter of credit: the importer's bank guarantees payment once the exporter presents the required documents: the safest method for the exporter short of cash in advance.
  • Documentary collection: banks exchange documents for payment (sight draft) or acceptance (time draft), with no bank guarantee.
  • Banker's acceptance: a time draft accepted by a bank, which the exporter can sell at a discount for cash now.
  • Forfaiting (selling medium-term receivables without recourse), factoring, countertrade (barter-type deals) and export-credit agencies also finance trade.
Exam trapUnder a letter of credit, the bank pays against documents, not against the condition of the goods. Discrepancies in the documents can delay or block payment.
Exam trapCheck the quote direction before computing. A rise in a direct quote ($ per €) means the euro appreciated; a rise in an indirect quote (€ per $) means the dollar appreciated. Invert (1 ÷ rate) to switch.
Instructor noteRanked from safest to riskiest for the exporter: cash in advance, letter of credit, documentary collection, open account. The importer's preference runs the other way.

Finished International finance?

Mark it complete when you can compute a forward rate and pick the right hedge for a receivable or payable.

Calculators

Interactive tools

Each tool is pre-filled with an example from the lessons. Change any input; the results show the method, your numbers and what they mean.

WACC builder

Component costs from market data (after-tax debt, preferred, and common equity by CAPM or dividend growth) weighted by market values.

Capital components

Bond price and yield to maturity

Price a bond from its yield, or find the yield from its price. For whole years with annual coupons, the table-factor price is shown next to the exact price.

Bond terms

EOQ and reorder point

Economic order quantity, annual ordering and carrying costs, and the reorder point with safety stock.

Inventory data

Cost of forgoing a trade discount

Simple annual cost (360- or 365-day year) and the compounded effective annual rate, compared with your borrowing rate.

Credit terms

CAPM and the security market line

Required returns from CAPM for up to five securities, plotted on the security market line with their expected returns.

Market and securities

Print-ready

Formula sheet

Every formula in Corporate Finance, followed by present- and future-value interest tables. Print it from here: the sidebar is hidden and the sheet prints black on white.

Spaced repetition

Flashcards

Recall first, then flip. Your grade schedules the next review (SM-2-lite).

Exam-style questions

Practice MCQs

Practice mode gives instant feedback; timed mode allows 1.8 minutes per question, like the exam. Filter by topic, difficulty, or questions you missed.

Essay section

Written-response practice

Write your answer first (aim for about 30 minutes per case), then compare it with the model answer and score yourself against the rubric. Show your calculations: the exam awards marks for method.

Key terms

Glossary

Search the section's vocabulary. Underlined terms in the lessons show these definitions on hover or keyboard focus.