Investment Banking

A bond is essentially an IOU - the issuer borrows money from investors and promises to pay it back with interest. Unlike equity (where returns are uncertain), a bond gives you a contractual claim on specific cash flows: periodic coupon payments and the return of the face value (par) at maturity. This predictability is what makes bonds the starting point for valuation - if you can price a bond, you can price anything.

Bonds are classified in several ways. By issuer: Government bonds are the benchmark for the risk-free rate - T-bills (<1 year, issued at a discount, no coupons), T-notes (1–10 years, semi-annual coupons), and T-bonds (>10 years). Corporate bonds carry default risk and therefore pay higher yields.

By feature: A bond can have a fixed or floating coupon. It can be secured (backed by collateral) or unsecured. A zero-coupon bond pays no coupons - the entire return comes from buying at a discount and receiving par at maturity. A callable bond lets the issuer redeem early (bad for investors if rates fall). A puttable bond lets the holder force early redemption (good for investors if rates rise). Convertible bonds can be exchanged for the issuer's equity.

The price of a bond is nothing more than the present value of all cash flows it will generate. You receive a coupon C at regular intervals, and the face value F at the end. Each cash flow is discounted at the market interest rate r, and the further away a cash flow is, the more it gets discounted.

The first term is the present value of all coupons (an annuity). The second term is the present value of getting the face value back at maturity (a lump sum).

Most bonds pay coupons semi-annually, not annually. When interest compounds more frequently, the same nominal rate produces a higher effective return because you earn "interest on interest" within the year. To compare securities with different compounding on a level playing field, we convert to the Effective Annual Rate.

This is the single most important relationship in fixed income: bond prices and yields move in opposite directions. If market rates rise to 8% but your bond only pays 5%, nobody will pay full price for it - the price must fall until the total return matches the market. Conversely, if rates fall to 3%, your 5% coupon looks generous, so investors bid the price up.

Critically, this relationship is convex (curved), not linear. The chart below shows this: the actual price curve bows outward from the duration estimate (the straight tangent line). This means when yields fall, real price gains exceed the duration prediction, and when yields rise, real losses are smaller. This asymmetry favours the bondholder.

Yield to Maturity (YTM) is the single discount rate that makes the present value of all a bond's future cash flows equal to its current market price. It is the internal rate of return (IRR) you would earn if you bought the bond today, held it to maturity, and reinvested every coupon at the same rate.

But be careful - YTM is not your guaranteed return. It assumes you reinvest every coupon at the YTM rate, which may not happen (reinvestment risk). Zero-coupon bonds eliminate reinvestment risk because there are no coupons to reinvest.

Bonds rarely trade on a coupon date. If you buy between coupon dates, the seller has held the bond for part of the current coupon period and is entitled to the interest earned so far. The buyer pays accrued interest on top of the quoted price.

Government bonds from stable countries are considered "risk-free" because the government can tax and print money to honour debts. Corporate bonds carry default risk - the chance the company cannot pay. To compensate, corporate bonds must offer a higher yield. The difference is the credit spread.

The critical dividing line is between investment grade (BBB−/Baa3 and above) and speculative grade / "junk" (BB+/Ba1 and below). Many institutions are prohibited from holding sub-investment-grade paper, so a downgrade across this line triggers forced selling and a liquidity cliff.

The yield curve plots YTM against maturity for bonds of similar credit quality (usually governments). Its shape encodes the market's collective expectations about future rates and the economy.

Three theories explain the shape: Expectations Hypothesis (long rates = average of expected short rates), Liquidity Preference (natural upward bias from a term premium), and Market Segmentation (supply and demand in each maturity bucket independently determine rates).

A forward rate is the future interest rate implied by today's spot yield curve. The logic comes from a no-arbitrage argument: an investor should be indifferent between investing for 2 years at the 2-year spot rate, or investing for 1 year and rolling into a second year. If these give different returns, there's an arbitrage - so the forward rate must make them equivalent.

Duration answers a practical question: "how long, on average, do I wait to receive my bond's cash flows?" It does not weight each cash flow equally - it weights them by their present value. A coupon in year 1 is worth more (in PV terms) than one in year 10, so it gets a heavier weight. The result is a single number, in years, capturing the bond's effective economic maturity.

Why does this matter? Because Macaulay duration directly determines how sensitive the bond's price is to interest rate changes. The longer you wait for your money, the more exposed you are to rate moves.

Macaulay duration tells you the weighted average time, but what you really want is: "if yields move by 1%, how much does my price change?" Modified duration gives you exactly this.

Duration gives a linear approximation, but the actual price-yield curve is convex. For small yield changes (<50 bps) the linear estimate is close. For larger moves, the error grows. Convexity captures this curvature and corrects it. Think of it like this: duration is the speed, convexity is the acceleration.

Immunisation is a passive portfolio strategy used by pension funds and insurance companies. The core idea: set your portfolio's duration equal to your investment horizon. When this is done, the two effects of a rate change - price risk and reinvestment risk - exactly offset each other at the horizon date.

When rates rise, your portfolio loses value (price effect - bad), but coupon reinvestments earn more (reinvestment effect - good). When rates fall, the opposite happens. At the horizon date, these cancel out, locking in terminal wealth. The catch: duration changes over time, so the portfolio must be periodically rebalanced.

Cash flow matching is simpler: buy bonds whose coupon and principal payments exactly match the timing of your liabilities. This eliminates both price risk and reinvestment risk with no rebalancing required - but it is more expensive and inflexible.

Dedication extends cash flow matching to a stream of liabilities. Active strategies attempt to beat the market by exploiting rate forecasts or mispricing - substitution swaps, intermarket swaps, rate anticipation, and pure-yield-pickup strategies. These require a genuine information edge; most managers fail to outperform passive benchmarks after fees.

Before projecting future cash flows, it helps to know what the company's assets are worth on paper. There are three balance-sheet reference points:

Book value is accounting net worth (assets − liabilities − preferred equity). It reflects historical cost, not what assets could earn or sell for. Liquidation value is what selling all the assets and paying off all debt would net - a worst-case floor. Replacement cost is what it would cost to rebuild the entire asset base from scratch.

These are reference points only. The market price reflects expected future cash flows, not just what is on the balance sheet today.

The expected holding-period return over one year combines dividend income and capital gain:

A share's value is the PV of all future dividends. If dividends grow at a constant rate g forever (and g < k), this infinite sum collapses to a simple formula known as the Gordon Growth Model. It is the cornerstone of equity valuation.

Most firms grow fast initially, then settle into a stable long-run rate. A two-stage DDM discounts the high-growth dividends explicitly, then caps the stream with a Gordon terminal value at the transition point.

Growth does not appear from nowhere - it comes from reinvesting earnings at a return. The sustainable growth rate links profitability (ROE) and retention (plowback ratio b). The more you reinvest and the higher the return on that reinvestment, the faster you grow.

The P/E ratio is not just an arbitrary market number - it can be derived from the Gordon model, revealing what fundamentally drives it:

The Present Value of Growth Opportunities decomposes a stock's price into two parts: what the firm would be worth if it never grew (a no-growth perpetuity), and the value added by future reinvestment.

The cost of equity is not observable - you must estimate it. The Capital Asset Pricing Model compensates investors only for systematic (non-diversifiable) risk, measured by beta. Firm-specific risk can be diversified away and therefore earns no premium.

Preferred stock pays a fixed perpetual dividend, so it is essentially a perpetuity:

The cost of debt is the yield investors demand on the firm's bonds. If bonds trade publicly, use the YTM (not the coupon rate). If the firm is rated, approximate as R_f + default spread. Because interest is tax-deductible, the effective cost of debt is lower:

The Weighted Average Cost of Capital blends the costs of each capital source by their market-value weights. It is the minimum return the firm must earn on its investments to satisfy all capital providers - the discount rate used in every DCF.

When dividends are irregular or non-existent, you value the whole firm off its free cash flow - the cash available to all capital providers after operating expenses and reinvestment, but before any financing. This is the cash flow that DCF analysis (Session 8) will discount.

Discount FCFF at WACC (which already captures the debt tax shield - do not double-count by adding it to FCFF). Then subtract net debt to get equity value:

The first and most important step is choosing which companies to compare the target against. This is where the "garbage in, garbage out" principle applies most - if you pick the wrong peers, the multiples you extract are meaningless. The challenge is that no two companies are identical, so peer selection is "as much art as science."

Start by studying the target's "story" - what does it do, who are its customers, where does it compete, what drives its economics? Then screen potential peers on two dimensions:

Pure-play comparables - companies that do exactly the same thing in the same markets - are rare. In practice, peers are often tiered: Tier 1 is the closest 2–3 direct competitors (these get the most weight); Tier 2 is a broader set of companies in the same industry; Tier 3 might be global players in adjacent segments.

Once you have your peer universe, you need standardised financial data for each company. This step is about gathering and organising - the actual calculations happen in Step III. The primary sources, in order of reliability:

Every multiple puts a value measure in the numerator over an operating metric in the denominator. But there are two different value measures, and they must be matched to the right denominator. Getting this wrong is a cardinal error in valuation.

The intuition is simple: if you buy the whole company, you pay for the equity (what you're buying) and you also assume the debt (which comes with the business). Cash on the balance sheet offsets this because it can immediately be used to repay debt. So EV = Equity + Total Debt − Cash = Equity + Net Debt.

Equity value must use fully diluted shares, not basic shares. Why? Because outstanding options, warrants, and convertible securities represent claims on the equity - if they are in the money (strike price below current share price), they will almost certainly be exercised, creating new shares and diluting existing shareholders.

The treasury-stock method (TSM) handles this correctly. It assumes that all in-the-money options are exercised and the proceeds from exercise are used to buy back shares at the current market price. The net new shares are what matter:

This is the most commonly violated rule in valuation, and violating it produces nonsensical results. The logic is about who has a claim on the cash flow being measured:

Raw reported numbers cannot be compared directly - they must be standardised. Three adjustments are essential:

LTM (Last Twelve Months). Annual filings are often stale by the time you use them. LTM combines the most recent annual data with the most recent quarterly data to get a trailing twelve-month figure that is as current as possible:

Calendarisation. Peers with different fiscal year-ends (e.g. Company A ends in December, Company B in March) cannot be compared on the same time period without adjustment. Calendarise by weighting the overlapping fiscal years to align them to a common calendar period.

Non-recurring adjustments. Strip out one-time items - restructuring charges, impairments, gains on asset sales, litigation settlements - so that multiples reflect sustainable, recurring earnings. If BP takes a $5bn impairment, leaving that in EBITDA distorts the multiple against peers.

Once you have clean, standardised multiples for each peer, the analytical work begins. Compute the mean, median, high and low of the relevant multiple across the universe. Drop statistical outliers - but only after investigating why they are outliers (a structural reason like a different business mix is valid; a one-time data error is not). Give the 2–3 closest peers the most weight.

Then derive the target's implied value by applying the multiple range to the target's own financial metric:

For equity-based multiples, the route is different: Implied Equity = Target NI × (P/E range), then add net debt for implied EV. Results from both routes are displayed on a football field alongside the other methods (DCF, precedents, LBO).

Under normal market conditions, PTA produces a higher multiple range than CCA. This is not random - it reflects two distinct economic forces:

First, the control premium. Trading comps reflect the price of a passive minority stake - owning a few shares gives you a pro-rata claim on dividends but no ability to change how the company is run. An acquirer buying 100% gains control: the ability to set strategy, cut costs, replace management, sell assets, or merge operations. This control is valuable, so acquirers pay more for it.

Second, synergies. Strategic acquirers can realise cost savings (redundant headcount, facility consolidation, purchasing power) and revenue opportunities (cross-selling, new markets) that neither company could capture independently. Part of this value is shared with the target's shareholders as a premium to get the deal done.

Cast a wide net initially, then filter ruthlessly. The goal is to identify past M&A deals where the target is sufficiently similar to the company being valued - similar industry, size, growth profile, and market conditions. The key difference from trading comps: the multiple you extract is only interpretable in context. A deal done during a credit boom may not be relevant during a recession.

The same target, with the same EBITDA, can sell for very different multiples depending on who is buying, why, and how the process is structured. You cannot interpret a transaction multiple without understanding these dynamics:

Strategic vs financial buyer. A strategic acquirer (operating company buying a competitor or adjacent business) can pay more because it can realise synergies - cost savings, revenue opportunities - that a financial sponsor (PE fund) cannot. The sponsor is constrained by return hurdles (20%+ IRR) and the amount of debt it can raise. This is why LBO valuations typically sit below strategic-buyer valuations.

Auction vs negotiated sale. An auction process with multiple bidders creates competitive tension that drives the price up. A negotiated sale with a single buyer lacks this dynamic. The seller must judge whether the certainty and speed of a negotiated deal outweigh the potentially higher price from an auction.

Friendly vs hostile. A hostile bid typically requires a higher premium to overcome board resistance. The acquirer may need to go directly to shareholders via a tender offer, which demands a price attractive enough to bypass the board's recommendation.

How the buyer pays - cash, stock, or a mix - affects who bears the risk that asset values change between the signing date and the closing date (typically 3–6 months for regulatory approvals and shareholder votes).

In precedent transactions, equity value uses the announced offer price per share - not the pre-announcement market price. This is a crucial distinction from trading comps, where you use the current market price. The offer price reflects what the acquirer actually agreed to pay, including the control premium.

Transaction multiples mirror trading multiples - EV/EBITDA and P/E - but there are two critical differences. First, they are computed on actual LTM figures at announcement date, not forward projections (which are often confidential in private deals). Second, they run higher because of the control premium and synergies baked into the offer price.

The premium paid measures how much above the target's pre-deal share price the acquirer offered. But which pre-deal price? Rumours, leaks, and market speculation can inflate the share price before the official announcement. So the premium is typically calculated against the unaffected share price - the price before any deal speculation began, usually measured at 1 day, 7 days, and 30 days before announcement.

The headline transaction multiple (EV/EBITDA) can look expensive. But if the buyer expects to generate cost synergies from the combination, the effective multiple is lower - because the combined entity will produce higher EBITDA than the target alone. The synergy-adjusted multiple shows how much of the premium the synergies justify.

DCF uses unlevered free cash flow - the cash flow available to all capital providers (debt holders, preferred shareholders, and equity holders) after operating expenses and reinvestment, but before any financing payments. Why "unlevered"? Because we want to value the operating business independent of how it is financed. The financing decision is captured separately in the WACC discount rate.

This is a critical design choice: the interest tax shield is not added to FCF because it is already embedded in WACC (the after-tax cost of debt). Adding it to both would double-count the benefit of debt.

A DCF is only as good as its projections. Each line item is driven by a specific assumption:

Revenue: Use analyst consensus estimates for the first 2–3 years (these are well-researched and market-tested), then step down to sector or historical growth rates for the outer years. The terminal year must reflect a normalised, steady-state business - not an abnormally high or low growth period.

Costs and margins: Hold COGS and SG&A roughly constant as a percentage of sales in the outer years (unless there is a specific reason to expect margin expansion or compression). EBITDA and EBIT margins should stabilise by year 5.

Working capital is driven by efficiency ratios. These translate balance-sheet items into operational metrics that can be projected as a percentage of revenue or COGS:

WACC (covered conceptually in Session 4) takes on a specific operational role in DCF: it is the rate at which you discount unlevered FCF. Because UFCF belongs to all capital providers, the discount rate must reflect the blended cost of all capital - equity, debt, and preferred - weighted by their proportion in the capital structure.

Two practical decisions are required. First, which capital structure to use: the target's current structure, the industry average, or a target optimal structure. Banks typically use the target or peer-average structure because DCF values the ongoing business, not its current (potentially sub-optimal) financing. Second, how to estimate beta when the target is private or being recapitalised.

For a private target (or any company whose beta you cannot directly observe), you estimate beta from public peers. But each peer has its own capital structure, which inflates its observed beta. You need to strip out the leverage effect (unlever), average the "pure" business risk betas, then re-inject the target's specific leverage (relever).

Debt is cheaper than equity (it has a prior claim on cash flows and gets a tax shield), so adding debt initially lowers WACC. But beyond a point, the risk of financial distress (bankruptcy costs, loss of customers, employee flight) begins to raise the cost of both debt and equity faster than the tax shield saves. The result is a U-shaped curve with an optimal leverage ratio where WACC is minimised.

You project FCF for 5 years, but the company does not stop operating in year 5. Terminal value captures all cash flow from year 6 to infinity and is typically 60–80% of total enterprise value. This dominance makes the terminal value assumptions - the exit multiple or the perpetuity growth rate - the single most sensitive inputs in the model.

Two methods exist, and you should cross-check one against the other:

Standard discounting assumes cash flows arrive at the end of each year. But in reality, cash flows are generated throughout the year. The mid-year convention assumes cash flows arrive at the midpoint of each year (0.5, 1.5, 2.5, ...) rather than at the end (1, 2, 3, ...). This gives a slightly higher value because each cash flow is discounted for less time.

After summing the PV of all FCFs and the PV of terminal value, you arrive at Enterprise Value. Then:

Because the DCF answer is so sensitive to WACC and terminal value assumptions, it is never presented as a single number. Instead, bankers show a sensitivity table (or "data table") varying the two most impactful inputs - typically WACC vs exit multiple, or WACC vs perpetuity growth rate:

The football field is the standard graphic for presenting valuation ranges from all four methods simultaneously. It shows where the methods converge (high confidence) and diverge (investigate assumptions). The typical ordering, from lowest to highest:

Five key participants make an LBO possible:

Financial sponsors (PE firms) raise capital as limited partnerships - the firm is the General Partner (GP, earns ~2% management fee + ~20% carried interest), investors are Limited Partners (LPs). Investment banks play a dual role: M&A advisor and financing provider (commit the debt, then syndicate it to investors). Bank & institutional lenders provide revolvers and term loans, demanding maintenance covenants and collateral. Bond investors buy the high-yield notes via a roadshow. Target management runs the business, rolls/co-invests equity (often 2–5%) and earns option packages; when management originates the deal, it is a management buyout (MBO).

LBO returns come from three distinct engines, and the value-creation bridge decomposes exit equity into its sources:

1. EBITDA growth - organic revenue growth + margin expansion raises EBITDA, directly increasing EV at exit. This is the most sustainable return lever. 2. Debt paydown (deleveraging) - FCF repays debt during the hold, so equity = EV − net debt rises mechanically even if EV stays flat. 3. Multiple expansion - exiting at a higher multiple than entry creates bonus value. Sponsors conservatively assume exit ≤ entry to avoid depending on this.

Debt is layered by security, seniority, maturity, coupon, and covenants. The higher a tranche sits in the stack, the lower its risk and cost; junior capital is more expensive but more flexible. In a default, claims are paid top-down; equity is the residual - first to absorb losses.

Structural vs contractual subordination: Contractual subordination ranks creditors at the same entity via the credit agreement. Structural subordination arises across entities: debt at the operating company (OpCo, where assets sit) is senior to debt at the holding company (HoldCo), unless HoldCo debt is guaranteed by OpCo.

This is a conceptual point students frequently miss. The target will be recapitalised - its old capital structure (old debt, old interest expense, old net income) is irrelevant. Operating performance (Revenue → COGS → Gross Profit → SG&A → EBITDA → D&A → EBIT) is independent of how the business is financed, so it is built first. Interest expense and net income are only layered on after the new debt structure is set in Step IV.

When you pay more than the book value of the target's net assets, the excess is recorded as goodwill on the pro-forma balance sheet:

The debt schedule is the mechanical core of the LBO model. It converts free cash flow into debt repayment and computes interest expense. The process works in waterfall order:

Step 1 - Cash available for debt repayment = cash flow from operations + investing activities (i.e., free cash flow after all operating needs). Step 2 - Mandatory amortisation (~1%/yr on term loans) is paid first. Step 3 - Excess cash sweep: all remaining cash is applied to optional prepayment in waterfall order (revolver → TLA → TLB), subject to a minimum cash balance. Step 4 - Interest is calculated on average debt balances and fed back into the income statement.

The debt schedule creates a circular reference that trips up every modeller the first time. The logic chain is:

Interest expense depends on debt balances (you need to know how much debt is outstanding to calculate interest). But debt balances depend on cash available for repayment (how much debt gets paid down depends on how much cash is left). And cash flow depends on interest expense (interest is a cash outflow that reduces available cash). The circle is complete.

Exit: conservatively assume an exit multiple at or below entry, so returns are driven by EBITDA growth and deleveraging rather than multiple expansion. Exit EV = exit multiple × exit-year EBITDA; exit equity = EV − net debt at exit.

IRR is sensitised - most commonly on entry vs exit multiple and exit year:

The LBO model serves a dual purpose in valuation. The forward mode asks: "given a purchase price, what IRR does the sponsor earn?" The backward mode - the course's signature framing - inverts the question: "given a target IRR (say 20%), what is the maximum price the sponsor can afford to pay?"

This backward-solved maximum entry price defines the LBO valuation floor. It sits below the DCF and comps valuations because the sponsor cannot capture synergies - it is constrained by leverage and return hurdles. A strategic buyer can pay more because synergies offset the premium. This is why the football field typically shows: LBO (lowest) → DCF → Comps → Precedents (highest).

Financial synergies include a lower blended cost of capital (larger firm → better credit rating → cheaper debt) and use of the target's net operating losses (NOLs) to shelter combined income from tax.

Financing hierarchy: Cash on hand and debt are both cheaper than equity. Cash is the cheapest (no issuance cost, no dilution - just foregone interest income). Debt is next (interest is tax-deductible, no dilution). Equity is most expensive (dilutes EPS, signals the acquirer thinks its stock is overvalued). Acquirers favour stock when their own shares are richly valued - issuing overvalued stock is a form of "currency arbitrage."

The deal structure drives after-tax outcomes for both buyer and seller. The key tension: buyers want tax-deductible asset write-ups (asset sale); sellers want simple, low-tax treatment (stock sale). The 338(h)(10) election is the compromise.

When the purchase price exceeds the fair value of the target's net identifiable assets, the excess is allocated first to asset write-ups (stepping up assets to fair market value), which creates a deferred tax liability (DTL). The residual after write-ups and DTL is goodwill.

The full accretion/dilution analysis combines the income statements, adjusts for deal-specific items, and derives pro-forma EPS:

Accretion is maximised by: a low purchase price, cheap financing (debt over equity), the optimal structure, and large achievable synergies. But always check credit statistics (Debt/EBITDA, EBITDA/Interest) - the most accretive structure (all debt) may not be acceptable for the acquirer's credit profile.

An auction markets the target to multiple bidders to create competitive tension and validate value. The sell-side advisor chooses the format based on the seller's priorities:

A negotiated sale is the third option - dealing directly with a single buyer. Compelling when there is a natural strategic acquirer with clear synergies willing to pay a premium. Faster and more confidential, but forgoes market validation.

The teaser is a 1–2 page, identity-masked synopsis sent to generate interest. It provides enough information to assess strategic fit without revealing the target's name. Interested buyers then sign a confidentiality agreement (CA) before receiving the full materials.

Key CA provisions: use restrictions (information only for evaluating the deal), term (2–3 years), non-solicit/no-hire (don't poach employees), standstill (for public targets - don't make unsolicited offers), and anti-clubbing (prevents buyers from colluding to suppress the price).

The Confidential Information Memorandum (CIM) is the 50+ page primary marketing document - business overview, industry analysis, financial information (3–5 years historical + 5 years projected), growth opportunities, and management team bios. It is the basis for buyer valuation and modelling. The sell-side advisor "normalises" financials - removes one-time items and presents EBITDA in the most favourable defensible light.

The sell-side advisor often keeps two parties in play during final negotiations to preserve leverage. The definitive agreement is the binding contract that sets all terms:

After board approval (and fairness opinion), the parties sign and announce. But the deal is not done - closing requires regulatory approval and shareholder approval.

HSR Act (Hart-Scott-Rodino): In the US, most M&A above a size threshold requires an antitrust filing with the FTC and DOJ, triggering a 30-day waiting period. If the agencies have concerns, they issue a "second request" for additional information, extending the review by months. Large cross-border deals may also need EU Commission and other foreign competition authority approvals.

Shareholder approval can be structured two ways: