Corporate Finance: Valuation, Capital Structure, and M&A

Net Present Value and Cash Flows

The Net Present Value (NPV) formula is the sum of cash flows discounted by appropriate interest rates in future time periods. Free Cash Flows (FCF) are not simply profit, as non-cash assets exist, whilst FCF is equal to Cash From Operations (CFO) minus Capital Expenditure (CAPEX) minus the change in working capital (if included). Working capital is equal to current assets (e.g., accounts receivable) minus current liabilities (accounts payable). Investments in working capital are cash outflows, just like an investment in CAPEX. NPV only concerns cash because of the time value of money (cash can be reinvested to make more earnings, making a future £1 worth less than a present £1). Net income in year t is earnings in year t post-tax, which represents profit. Capital expenditure affects (free) cash flows but not profit; depreciation affects profit but not (free) cash flows. Cash flows are estimated on an incremental basis, meaning they do not factor in opportunity costs, other incidental effects, or sunk costs. Corporate taxes with tax rate t_c are taken from Revenues + Extraordinary gains - Depreciation - Expenses. Cash from operations is equal to net income + depreciation, so CFO = NI + D = (R - E - D + X)(1 - t_c) + D = t_cD + (1 - t_c)(R - E - X); t_cD represents the tax shield from depreciation.

Stock Valuation and Growth Opportunities

The price of a stock is determined by the sum to infinity of all dividends discounted by the discount rate (r) in future time periods, simplified to D / (r - g) assuming a constant required rate of return and growth rate. The former requires extremely accurate forecasting over long time periods, while the latter is often not true as firms grow faster in youth relative to maturity. Combined method: Accurate forecasting up to T years (former method) + terminal value discounted by (1 + r)^T. The methods using dividends are the discounted dividends formula, which can use the substitution D_t = E_t(1 - k). Terminal value can be calculated assuming constant dividend growth from T+1 onwards (TV_T = D_T+1 / (r - g)) or using the exit multiple method (EMM). EMM assumes you sell the business in year T, so you can use comparable companies analysis to determine the sale price. This can be done by forecasting a value driver in T or T+1 years and applying a multiple based on how peers are currently trading (using apples-to-apples comparisons). Examples include: Market/Book (preferred for capital-intensive firms), Price/Earnings (used for banks), and Aggregate Value (Market Equity + Net Interest [+ Minority Interest]) / EBITDA (earnings before interest, tax, depreciation, and amortization) or Sales (most firms will use this).

P/E ratio - Ratio of price to earnings per share. It is a commonly used indicator of stock value. P₀ = E₁ / r + PVGO. E/r is the PV of earnings of the existing business of the company, and PVGO is the Present Value of Growth Opportunities through potential new business (investment). Growth stocks have larger shares of PVGO relative to price. We can rewrite this to P₀ / E = 1 / r * (1 - PVGO / P₀). A high P/E ratio can be caused by a low cost of equity (which occurs if you have low systematic risk) or large growth potential. The relevant E is the sustainable long-run earnings under no growth.

Dividends = Earnings * (1 - plowback ratio). The plowback ratio (k) represents the share of earnings reinvested in the company, multiplied by the return on equity/rate of return/yield (y) to get growth. This growth is also the value of returns from capital gains. kE_t = I_t, where I is investment. Payout ratio = 1 - k. PVGO = (y - r)kE / r(r - yk) = (y - r) * I / r(r - g). PVGO > 0 if and only if (iff) y > r; PVGO is positive only if the return on projects exceeds the cost of capital, which may not occur even if growth is positive. Firms should not take projects with a PV less than 0, so PVGO will not be negative if the firm is behaving rationally. Also, note that dividend growth is tied to earnings growth if the plowback/payout ratio is fixed/constant.

Most formulas use the ex-dividend price, meaning the price immediately after a dividend is paid out. The cum-dividend price is the price before the dividend is paid out, so you add the dividend to the ex-dividend price. The PVGO method is not preferred over the standard discounting dividend model unless you are told to calculate PVGO explicitly, or you have no information on dividends. Remember your economics consumption possibility frontier (CPF) over two time periods models, as they may come up.

Investment and Decision Rules

Investment and decision rules should ideally consider the time value of money, all (and only) of a project's cash flows, and have a clear benchmark. Here are the primary rules:

1. NPV Rule: Accept any project with a positive NPV, and reject those with a negative NPV. Managers should always make investment decisions that have a positive NPV regardless of individual shareholder preferences, aiming to maximize shareholder wealth. You can borrow/lend across different time periods risk-free, so this is always optimal regardless of when cash flows occur or preferences for consumption in different time periods (outward CPF shift). This is the Fisher Separation Theorem, which means a firm's optimal choice of investments is separate from the attitudes of stakeholders/owners. This is what allows shareholders to be willing to own shares and delegate the running of the firm to managers. This theorem requires complete (markets for borrowing/lending and shares exist), efficient (market prices reflect all information, including private), and perfect (no distorting taxes that alter relative prices, and no frictions like transaction costs) markets.
2. Equivalent Annual Cash Flows (EACF): In the case of mutually exclusive or alternative investments, choose the one with the highest NPV if comparing investments with the same lifespan; otherwise, compute the EACF and choose the project with the highest EACF. EACF is the cash flow of an annuity giving an equivalent PV and the same lifespan; it is the rate you would pay for a lease in a competitive market.

   

   More informally, compute the NPV and then equate it to a cash flow C multiplied by an annuity factor for time T = [1/r] * (1 - 1/(1+r)^t). Note that if it is a cost, a lower EACF is better, and if it is revenue, a higher one is better.
3. Profitability Index (PI) Rule: If limited in resources (usually money), then choose the project with the largest "bang-for-your-buck," or Profitability Index (PI). This is equal to PI = NPV / -C₀. If you cannot choose "fractional" investments, you have to use linear programming. You should accept any project with a positive PI and reject any with a negative one. Note that the rule is equivalent to the NPV rule if the cost in the initial period is positive, and the rule is reversed for borrowing projects instead of lending ones (so accept only negative PI). It can be misleading for some projects requiring incremental cash flows to salvage, and it assumes only period 0 investment, meaning reinvestment is impossible. See the IRR rule below for more details.
4. Payback Period Rule: Consider the time taken to recover the initial investment and accept the project only if it is lower than some threshold. This method ignores the time value of money (though you can discount cash flows to fix this), ignores cash flows beyond the cut-off period, and gives no indication of what the threshold should be.
5. Accounting Rate of Return (ARR) Rule: Average net income of a project (profit after taxes) divided by the average book value of the investment: (beginning investment + final investment) / 2. This is then compared with some arbitrary yardstick, usually the book rate of return for the firm as a whole. This method ignores relevant cash flows to focus solely on accounting profits, leaving it affected by the chosen depreciation method. It also ignores risk and the time value of money, making it entirely arbitrary.
6. Internal Rate of Return (IRR) Rule: The constant discount rate y such that the NPV of the project is 0. A project should be accepted only if y exceeds the yield on financial securities (mainly bonds) with comparable maturity, cash flows, and risk (opportunity cost of capital). For flat term structures where r is constant, it implies we should accept only if y > r. You may have to draw a graph where the y-axis is NPV, the discount rate r is the x-axis, and the intercept of the x-axis is the IRR. This method struggles with non-flat term structures as the opportunity cost of capital is a "complicated average of interest rates... r₁, r₂, ... r_T" such that a project with a higher IRR can have a lower or even negative NPV. When comparing projects of different time periods, you should use different cut-offs and bonds with different durations and yields to avoid this, comparing the required price of a comparable bond and finding the yield required to make the value of a project equal to each bond. You would then reject projects with an IRR < y, but this merely leads back to the NPV rule. Also, note that y/IRR > r should not be accepted if the project is borrowing, only when lending. Use y/IRR < r as the rule if borrowing, but it can be difficult to determine borrowing or, in some cases, alternating cash flows. Projects can also have multiple IRRs if there are changes in the signs of cash flows, or even no IRRs, and this can be misleading in some edge cases of mutually exclusive projects. This can be salvaged by looking at the IRR of the difference between profits in some cases (incremental cash flows).

Cost of Capital and WACC

Discount rates are based solely on project risk, not company or existing asset risk, as you could just pay out cash and allow investors to invest in similar risk projects. The return on such a stock is the opportunity cost of investing in the project. Companies should not have a company-wide "hurdle" rate, and acquisitions should consider the target's cost of capital only. Project risk is systematic risk, not idiosyncratic risk. This is because investors are likely to be diversified. Projects with high idiosyncratic risk can have low systematic risk, leading to low discount rates. Idiosyncratic factors (e.g., the effectiveness of future carbon capture technology) only affect cash flows, not discount rates, betas, or returns.

The CAPM represents the return required by shareholders, but most firms are also (at least in part) debt-financed. The Weighted Average Cost of Capital (WACC) is r^* = r_D(D / (D + E)) + r_E(E / (D + E)). D is the market value of debt (net debt = short-term debt + long-term debt - cash and marketable securities), and r_D is the expected return on firm debt. For low-risk firms, the accounting value of debt is a fair approximation of D. FCFs in the numerator of NPV should assume all-equity financing. This is the unlevered free cash flow. The effect of leverage is captured by WACC (the denominator/discount rate for the firm/assets as a whole). Also, recall r_A = r_f + (r_m − r_f)β_A, where beta represents the firm's asset beta, which is its business risk (systematic risk of FCFs generated by assets). More cyclical firm businesses have a higher beta.

Note that this assumes no taxes. Asset betas are fixed as they measure the systematic risk of FCFs which accrue to the firm, while the equity beta measures the systematic risk of equity returns which accrue only to shareholders. This means it incorporates business risk like asset betas but also financial risk; returns can vary widely with the debt amount, as debt payoffs are generally more constant between good and bad states, passing volatility onto shareholder/equity returns. A calculated WACC for a firm should be used for new projects that share the same systematic risk as existing assets (asset betas will always be the same, but equity betas will normally not be). Otherwise, estimate using the asset beta from comparable companies when estimating CAPM/return on assets, as opposed to blindly plugging values in. If an asset consists of multiple assets with known betas, sum the product of the share of each asset with the asset's beta to get the overall beta. Company-wide discount rates are wrong to use in principle, but in the real world, with uncertainty around cash flows and growth rates, they can be good enough (fine-tuning estimates is expensive and requires too much effort). In the real world, CAPEX in non-core divisions can be higher than optimal/expected if it has a higher asset beta than the core division (CEOs do not discount properly). Conglomerates often target high WACC firms, and shareholders see slightly lower returns when using the acquirer's WACC.

Niche example: An export-focused firm in a country with capital controls; when lifted, the stock price will fall relative to domestic firms due to a higher global beta (sensitivity to global market returns), giving a higher required rate of return and pushing down the stock price.

Dividend Policy and Market Imperfections

Dividend policy is the decision of how much a firm should pay out as dividends versus retain. Dividend cuts can lead to severe declines in the stock price (if the reason is not properly explained or credible), leading to CEO/board changes from angry shareholders. However, maintaining a dividend policy at a high level can prevent the undertaking of profitable investments and become a political issue (e.g., worker layoffs). If a firm deviates from the perceived optimal dividend policy, the stock may be sold by traditional investors, while activist investors may buy larger stakes to force a policy change. Dividend policies can be sticky; cuts are very rare, and raises occur only if sustainable long-run earnings are achieved. Firms have long-run target dividend payout ratios, and managers focus on dividend changes more than absolute levels.

Earnings + Cash Flows of New Shares = Dividends + Investment. All are in the same time period; assume Earnings and Investment are constant.

Stock repurchases are an alternative method of distributing cash to investors instead of dividends.

Miller and Modigliani (MM): Dividend policy is irrelevant in perfect capital markets (no taxes, transaction costs, or inefficiencies, as stated earlier). One can replicate dividends by selling shares, and if dividends are paid out, the payoff for shareholders is the same, such that levered value (V_L) equals unlevered value (V_U), with the return on capital r_A (expected returns of firm assets/company cost of capital) being independent of capital structure. V = X / r_A assuming a level perpetuity, where X is the unlevered free cash flow. This makes the following counterpoints fallacious (wrong):

• Dividends are needed by some shareholders to live on.
• Dividend irrelevance is inconsistent with the stock price being the PV of future dividends.
• The "bird in the hand" fallacy: Dividends are cash in hand while capital gains are risky, so dividends should make equity less risky and therefore more valuable. This is wrong because r_E is not constant; it increases with financial risk, so the increase in EPS is offset exactly by the increase in r_E, as shown using MM Proposition 1.

MM Proposition 1: V_L = V_U, making r^* constant at r_A. MM Proposition 2 is that an increase in the D/E ratio results in an increase in the expected return on equity, reflecting the effect of financial leverage on betas. This is r_E = r_A + (D/E)(r_A - r_D), which is also analogous to β_A = (D/V)β_D + (E/V)β_E or β_E = β_A + (D/E)(β_A - β_D).

Real arguments why dividends may matter:

• Signalling: Higher dividends are a favorable signal of future earnings from management to investors. The signal is credible because managers with unfavorable information will not raise dividends, as they will not have the cash to sustain them, which would result in lowering the dividend and causing the stock to plummet. The signal generally outweighs the negative signal about growth opportunities (PVGO) and has strong academic support.
• Dividend irrelevance assumes that dividend policy does not add value to shareholders, but market imperfections like taxes, issuance costs, and agency costs make this untrue in reality.
• Tax costs: Dividends of X reduce capital gains by X, so if the dividend tax is higher, you would prefer lower dividends and vice versa. This means you would prefer, in some cases, a lower pre-tax rate of return from shares offering capital gains instead of dividends. (Remember, the after-tax return demanded will be fixed as business and financial risk remain unchanged, so you will need to compute the after-tax return demanded in an exam question asking about this. Also, earnings/total payoff should not change in the next period, only the present price; it can make sense for the stock price to fall if dividends are tax-inefficient).
• Issuance costs occur because paying dividends increases the need to raise external funding, which is costly and should thus be minimized. Doing a regression with a modified CAPM (r_i = a₁ + a₂β_i + a₃d_i) offers weak real-world support for this.
• Agency costs are the loss in firm value caused by shareholders and managers having different interests (the principal-agent problem, where shareholders bear the cost of a manager's value-destroying decisions). Shareholders will anticipate this, paying less for shares and causing the stock price to fall. Dividends can force the payout of excess cash, preventing managers from wasting it in this way, which is amplified by the stickiness of dividends, making them hard to cut without a strong negative market reaction. If agency costs matter, dividends should be higher if there are high agency costs (measured by a high number of shareholders and a low percentage of the firm held by insiders). Low cash needs would also lead us to expect higher dividends since dividends are a use of cash, and this is measured by a low growth rate of revenues and low volatility (beta). Regression shows all four conditions mentioned predict 48% of observed variation in dividend payouts.

All these factors can make repurchases preferable to dividends if a company has excess cash, as they are flexible and do not create expectations of future payouts (no signaling effect).

Capital Structure and Leverage

Inefficiently high leverage can result in firm bankruptcy, whilst inefficiently low leverage can increase a firm's cost of capital. A suboptimal capital structure can also lead to takeovers and management being fired. This is because if a firm deviates from the perceived optimal capital structure policy, the stock may be sold by traditional investors, while activist investors may buy larger stakes to force a policy change, with a takeover on the extreme end (same as for dividend policy!). Remember, MM means that the level of debt determines only the split of total cash flows between bond and equity holders (total remains unchanged).

When you issue debt to buy back stock, use the current stock price. MM leads to the graph on the left, but in reality, r_D will rise owing to a greater risk of default, slowing the increase in r_E over time (r_A remains independent of capital structure). The MM proposition is important in spite of the lack of market perfection, as it suggests capital structure choice should only be driven by market imperfections. These violations can arise from:

1. Taxes

First, consider corporate taxes. Debt has a tax advantage over equity because interest payments are tax-deductible, while dividends and retained earnings are not. The interest payment on debt is I_t = D * r_D. The value of a year's tax shield is t_cr_DD, where t_c is the corporate tax rate. If debt is perpetual, discount by r_D to give t_cD as the value of the tax shield, making V_L = V_U + t_cD (this is the Adjusted Present Value, or APV). Put V_U and the present value of the tax shield on the asset side of the balance sheet, and debt and equity on the other. This makes WACC downward-sloping and r_E upward-sloping, not at a 45-degree line, but at (1 - t_c)(r_A - r_D). r_A in this model is not part of this course but is not fixed. MM Proposition 1 is now V_L = V_U + t_cD (APV), and also note V_L is always equal to D + E. MM Proposition 2 is now r_E = r_A + (D/E)(1 - t_c)(r_A - r_D) (or equivalently β_E = β_A + (D/E)(1 - t_c)(β_A - β_D)). WACC is now equal to (1 - t_c)r_D(D / (D + E)) + r_E(E / (D + E)), or just r_A(1 - t_c[D/V]). WACC was previously equal to r_A in all-equity firms, or without taxes regardless of leverage, but with taxes, it is reduced below it.

Note that if you drop the assumption that debt is fixed and tax shields are relatively safe, and instead assume firms rebalance for a constant D/V, D changes with V and thus economic conditions. This makes the tax shields risky and means they should be discounted by r_A. This makes it so the formula for r_A is the same, but MM Proposition 1 is now V_L = V_U + (t_c * r_D * D) / r_A = D + E. MM Proposition 2 remains the same as the case with no taxes, and WACC is still equal to (1 - t_c)r_D(D / (D + E)) + r_E(E / (D + E)), but not r_A(1 - t_c[D/V]).

Now consider personal taxes. If you are taxed t_D for interest and t_E for equity gains, each £1 in pre-tax earnings to shareholders is (1 - t_E)(1 - t_c), while bondholders will receive (1 - t_D) from each £1 from bondholders due to this being tax-deductible at the corporate level. The tax advantage of debt is t^* = 1 - (1 - t_E)(1 - t_c) / (1 - t_D). Usually, the tax on interest exceeds the tax on equity gains, as capital gains are taxed at a smaller rate than regular income, which is what interest (and dividend payments) are. Factoring in personal and corporate debts also results in MM1 now being V_L = V_U + t^*D_L, so the levered firm is more valuable only if t^* > 0; otherwise, equity is tax-advantaged. Previously, MM under a singular deviation from perfect markets of corporate taxes implied 100% debt financing was optimal. We return to the previous formula in the case where t_E = t_D and t^* = t_c.

r_D and r_E are before-personal-tax rates of return, and this implies that t^* > 0 leads to an increase in leverage, reducing WACC and increasing firm value, implying 100% debt financing is still optimal. However, in reality, firms cannot always use the tax shield, as tax losses can only be carried forward for a limited time, so the expected tax shield is less than the statutory rate t^*. More debt increases the risk of losses, reducing the expected tax shield.

You can use the formulas on the right to find discount rates if you have perpetual cash flows and the total value of those cash flows, as the result in the 4th column is equal to that of the 2nd/3rd. Remember, X is pre-tax earnings, and the leverage ratio means D/V = D / (D + E). Same business risk means the same r_A assuming no taxes. r_E, r_D, and WACC_L are not comparable across different companies in the same industry; r_A is. r_A and WACC_L are both used to discount unlevered cash flows, but the former results in V_U while the latter results in V_L. r_A depends on business risk only; the others also depend on financial risk.

2. Bankruptcy Costs

Leverage increases the probability of bankruptcy, which is costly due to direct bankruptcy costs (difficulties in recovering collateral, costs of legal fees, etc.) and indirect bankruptcy costs (assets being sold for less in fire sales, intangible assets being worth less after bankruptcy, customers/employees fleeing even before bankruptcy occurs). MM1 changes to V = V_U + PV(tax shield) - PV(bankruptcy costs).

3. Agency Costs

When a firm has too much equity financing, it imposes little discipline on managers, who may waste cash on inefficient investments. Debt forces managers to pay out free cash rather than wasting it (see the dividend discussion earlier) and gives managers a greater proportion of the firm's equity, which creates greater incentives to create value (as managers do not have their shares bought back). This is how debt-equity buybacks create value. However, agency costs of debt can also arise if too much debt financing occurs. Managers of highly levered firms may take excessive risks, as if total firm value is unchanged, greater risk reduces debt value and increases equity value (e.g., increasing the risk of firm assets by undertaking risky investments with zero/negative NPV, reducing assets serving as collateral for debt like paying out high dividends to shareholders, or issuing additional debt). Debt contracts mitigate this by including covenants to limit investment, forcing firms to forgo good investments in some cases. MM1 is now V = V_U + PV(tax shield) - PV(bankruptcy costs) - PV(agency costs). The joint effects of these three lead to a trade-off theory of capital structure between the tax advantage of debt and agency costs of equity versus bankruptcy costs and agency costs of debt.

The trade-off theory of capital structure suggests you should borrow more if the firm is: profitable (instead of unprofitable), holds tangible assets (instead of intangible or valuable growth opportunities), is safer (as opposed to risky), is based in a country with higher taxes/lower bankruptcy costs, and when corporate taxes rise. Evidence supports propositions on intangible assets and risky firms, but not profitable companies.

4. Asymmetric Information

Not discussed.

Now let's assume that project NPV must include the value contributed by financing decisions. This can be done by calculating an adjusted NPV (APV), which is the sum of the project NPV and the NPV of the change in financing decisions. This is done by finding the NPV of the project to an all-equity firm, then adding on the financing decisions' value. You do not consider interest payments, as efficient capital markets make the NPV of a loan 0, but if a loan is subsidized, this results in smaller tax shields, but the NPV of the loan becomes positive. You can instead discount cash flows using an adjusted cost of capital taking into account risk and financing tax effects, focusing on the tax impact alone in a simpler procedure.

Two formulas are often used: the weighted-average cost of capital formula ("debt-rebalanced") and Modigliani and Miller's formula ("debt fixed"). The WACC formula ((1 - t_c)r_D(D / (D + E)) + r_E(E / (D + E))) assumes the project supports permanent additional debt ΔD issued at r_D, allowing it to work for a rebalanced debt structure. The MM formula is the expression r^* = r_A(1 - t_cL), representing the project's contribution to a firm's debt capacity as a proportion of the project's market value, where L = ΔD / PV(project). This is MM's formula, analogous to WACC = r_A(1 - t_c[D/V]) but for an entire firm. You typically assume this rather than assuming a specific ΔD. Again, the MM formula only works if using a level perpetual cash flow and constant debt forever. Errors are only 2-6% if this does not hold, and we can use r^* in this course, using CAPM to compute r_A from beta A, then setting r^* = r_A(1 - t_cL) to reflect tax shields and discounting cash flows to get APV.

Mergers and Acquisitions

Mergers occur when two firms join together to form a single firm; acquisitions/takeovers occur when a firm purchases another firm that becomes a subsidiary of the acquirer. Horizontal mergers occur in the same industry and same production stage; vertical mergers occur in the same industry but differing production stages; and conglomerate mergers occur between different industries.

Mergers create value if there are operational synergies. These include revenue synergies through: economies of scope/scale (cross-selling, R&D spillovers) and combining complementary assets. This can be achieved through contracts, so mergers should be chosen if contracts are incomplete, as this leads to the hold-up problem if there is high relationship specificity. This also includes cost synergies: economies of scale and consolidation of excess capital in declining industries. Financial synergies can generate value if internal capital markets are created, allowing firms to redeploy capital from divisions with high cash and low investment opportunities to those with low cash and high investment opportunities. This is less applicable in developed economies with efficient external capital markets, as excess cash is paid out in dividends. Mergers can also lower financial costs, but this is not necessarily a good motive for a merger, as the merger cannot reduce the actual expected cost of debt, only the promised return. It can still be worthwhile to do so if diversified merged firms have lower bankruptcy risk, thereby lowering expected bankruptcy costs. This allows the firm to take on more debt and enjoy a larger tax shield. Large debt issues are also more liquid than two smaller debt issues, which investors are willing to pay a premium for. This is a common justification for conglomerate mergers with weak synergies.

Takeovers can also be an expensive last resort in order to replace management that is underperforming. For mergers that only redistribute value: tax inversion/unused tax shields redistribute from the government, market power redistributes from customers/suppliers, and market inefficiency acts to redistribute from target shareholders. Redistribution can justify a merger if the acquirer gains from it, even if there is no increase in the value of the firms post-merger.

Mergers can destroy value when undertaken to: increase size for non-economy-of-scale reasons, secure private benefits (buying attractive sectors/people), overconfidence about synergies/ability to manage target firms, use surplus funds when investment opportunities are declining (should just pay out as dividends), diversify idiosyncratic risk (customers can diversify themselves if paid out dividends), or if the justification is solely the accretion of EPS (increasing EPS after the merger). Note that it is dilutive if EPS goes down. EPS can rise if P/E rises, but the value of PVGO may be low or earnings may be risky, meaning no value is generated, offsetting EPS accretion perfectly. Example that may come up: Selling £1 of stock means giving up a claim of £1/x earnings; buying £1 worth of stock means gaining a claim of £1/y. If a stock-for-stock acquisition occurs, it is accretive if x < y and dilutive if x > y, as you will be changing your earnings by 1/y - 1/x. If an acquirer's P/E is higher, it has a relatively higher value stock, allowing it to buy the target's earnings relatively cheaply, which will increase the firm's value. Note that accretive acquisitions must have a P/E of the target < P of what is being used to buy it, which is 1/r for debt-financed acquisitions, the P/E of cash if cash-financed (interest rate), or the P/E of the acquirer if stock-financed. The acquisition is earnings-neutral if y = 1/r. You can use earnings or P/E in an exam to solve this, except r would be the interest rate earned on cash in a cash-financed equation.

We can represent merger gains as ΔV_AT = V_AT − (V_A + V_T), with V_AT being the value of the merged firm's equity (PV of total FCF - debt, not the market value of equity, as the value of M&A can be partially reflected in the market value of equity of the target if anticipated). You want this to be positive, meaning the existence of economic gains from some kind of synergy that leads to the overall creation of value. If the acquirer pays a premium in cash, subtract that from the overall increase in NPV (merger gains) to get the acquirer's NPV, which is also equal to

where P is the price paid in cash. The target's NPV is simply the size of the premium, and their sum is equal to ΔV_AT. If the acquisition is done with a stock acquisition, the acquirer's NPV is equal to

=

where X is the share of the merged firm given to the target firm. Targets generally get most of the value, while acquirers have a near-zero payoff, as acquirers often undertake bad mergers and there is competition between would-be acquirers. Friendly mergers occur when an agreement with management is made and approved by over 50% of shareholders, with management from both firms included. Tender offers aimed at shareholders are used in hostile takeovers where target management does not recommend the deal to shareholders. Takeover resistance can be done to drive up the price to increase shareholder value, or to avoid a takeover for management's personal goals. A staggered board of directors, supermajority approval, and poison pills (where shareholders have the right to buy bonds or preferred stock that can be converted into stock of the acquiring firm) can be used to resist pre-offer. Antitrust or similar litigation, public relations campaigns (arguing the firm is undervalued or shareholders will be harmed), inviting a friendly firm to take over instead, asset restructuring (selling off desired assets that the acquirer wants or buying assets the acquirer does not want), or implementing proposed changes by the would-be acquirer are possible resistance methods post-offer.

The Role of Financial Markets

Financial markets can have real positive benefits:

• Risk sharing: e.g., investment in two risky technologies negatively correlated with one another, reducing risk and benefiting society.
• Consumption smoothing: borrowing against future earnings or saving for the future.
• Capital allocation: perfect capital markets allow for all NPV-positive projects to be taken by borrowing against future cash flows (some financial constraints exist in the real world due to a lack of perfection).
• The informational role of prices.
• Liquidity provision: illiquid assets have to sell at a discount from fundamental value; liquid security markets mean a low price impact from the sale of a security.

This is all because financial markets allow for efficient money transfers over time amongst people and firms in different states of the world.

Responsible Business and ESG Investing

Friedman assumes governments are in the best position to deal with externalities, but lobbying and hard-to-police/track activities can make it so firms should act when the government won't or can't. Company decision-making is hard in these cases, as projects can have a negative NPV and may never generate profit. Firms should use the principles of responsible business to generate more value than the opportunity cost of resources:

1. Principle of Multiplication: Does £1 of spending on a stakeholder generate more than £1 of value to that stakeholder (social benefit vs. private cost)? If no, value is destroyed and the NPV is negative (both from a social standpoint). Alone, this is too weak, as it does not suggest a limit to spending on charities and the like (it is not hard to assume these cause more than £1 of benefit per £1 spent).
2. Principle of Comparative Advantage: Does my company deliver more value through this activity than other companies? If not, then there is someone else in a better position to do the activity/spending, so no value is generated (social benefit vs. social cost). Firms would have no comparative advantage in giving money to charities over other firms (ignoring tax rates/breaks and other factors). Firms may have a comparative advantage in giving surplus cafeteria food to the homeless, worldwide distribution of life-saving drugs, etc.
3. Principle of Materiality: Are the stakeholders who benefit from the activity material to the company? If no benefit is being created at the expense of important stakeholders (including investors), reject it (consider both business materiality for shareholders and intrinsic materiality for employees). Firms are for-profit enterprises. This includes not only shareholders but also employees, so employee programs can satisfy this plus principles 1 and 2 (e.g., an employee gym at the workplace), as employees are material stakeholders. Not only are employees made better off, but it can also help attract and retain talent, potentially putting a firm in a position to make a profit (though this is not guaranteed).

Responsible/ESG/Sustainable Investing is "a strategy and practice to incorporate environmental, social, and governance factors in investment decisions and active ownership":

• Financial goals: increase returns and/or reduce risk (normal stuff).
• Social goals: change the externalities a company produces.
• Values and tastes of investors are also relevant.

One common method is to exclude/divest stocks that do not tick a box ("sin" industries like war/drugs, high CEO-to-worker pay ratios, carbon footprint, board diversity, treatment of workers). Investors consider only stocks that do tick the box and then select primarily based on financial factors. This method is easy (cheap and easily scalable) and transparent. However, it can conflict with financial goals (values conflated with valuation) or social goals (no issues are black and white, divesting does not deprive a firm of capital, and the exclusion of certain industries prevents the ability to change them). A better approach is the net benefit test: "Does the company provide a net benefit to society?" Responsible Stewardship also considers incentives for stewards.