Week 2: Corporate Governance and Discounted Cash Flow Valuation (Ch. 2, 5)

Week 2 covers two chapters. Chapter 2 (corporate governance) asks whether managers and large shareholders actually pursue the goal of maximising shareholder value, and which mechanisms and institutions help. Chapter 5 (discounted cash flow valuation) extends the time value of money from single payments to multiple cash flows: perpetuities, annuities (ordinary, due, delayed and growing), compounding more than once a year (EAR, APR) and the most common loan types.

Corporate governance

Corporate governance is concerned with how firms manage themselves and how that performance is monitored. When shareholders hire professional managers, it must be ensured that decisions maximise shareholder wealth and not the personal wealth of managers. Corporate governance sits between four groups: managers, controlling shareholders, minority shareholders and other stakeholders. The lecture uses the takeover of Twitter by Elon Musk (shareholders approved his $44 billion bid in September 2022 while Musk tried to back out of the deal) as a business example.

(Book, 2.1) The three legal forms of business are the sole proprietorship (one owner, unlimited liability, income taxed as personal income, life limited to the owner, capital limited to the owner's wealth), the partnership (general partners with unlimited liability; in a limited partnership limited partners are liable only for what they contributed) and the corporation, a legal person separate from its owners. The corporation offers limited liability, easy transfer of ownership and unlimited life, which makes it superior for raising cash; its main disadvantage is double taxation (profits taxed at the corporate level and dividends again at the shareholder level). In the Netherlands the NV is the publicly listed form and the BV the private limited form.

Agency theory: two types of relationship

An agency relationship exists whenever a principal hires an agent to represent his or her interests. There is always a possible conflict of interest between the two (for example, an agent who sells your car for a flat fee wants a quick sale, not the best price; a commission aligns interests better).

Type I: conflicting goals and agency costs

Left alone, managers may maximise the resources under their control (overemphasis on size and growth, overpaying for acquisitions), overemphasise organisational survival to protect their jobs, and dislike outside interference. The costs of this conflict are agency costs:

CEO pay. The CEO-to-worker compensation ratio in large US companies rose from about 20 in 1965 to over 350 around 2000 and was about 271 in 2016. Executive pay in the US and UK consists largely of long-term incentives (shares and options); in continental Europe (for example Italy) base salary is a larger part.

Aligning managers' interests with shareholders' interests. Whether managers act for shareholders depends on how well their goals are aligned (compensation) and whether they can be replaced (control). Four mechanisms:

• Managerial compensation: performance-based pay such as shares and options, so managers gain when the share price rises. Better performers also get promoted and are in higher demand on the labour market.
• Control of the firm: the power of shareholders to control the firm through the board structure and voting rights. Shareholders elect the board, which hires and fires managers (Steve Jobs was once removed from Apple by the board).
• Shareholder rights: the facility for shareholders to call managers to account, laid down for example in the bylaws. Other rights: to share proportionally in dividends and in liquidation proceeds, to vote on major matters such as mergers, and sometimes a pre-emptive right to buy new shares first.
• Proxy voting: a proxy is a grant of authority by a shareholder allowing another person to vote his or her shares. Management tries to collect as many proxies as possible; dissatisfied shareholders can start a proxy fight to replace management.

(Book) Some firms have classes of shares with unequal voting rights: Alphabet's founders own Class B shares with 10 votes each, giving them 57% of the votes with 5.7% of the shares. Dividends are paid at the discretion of the board, are not a liability until declared, are not tax deductible and are taxed at the shareholder level; paying out cash can discipline managers who might otherwise waste it.

Unitary versus dual board structures

Type II: conflicting goals and agency costs

When an investor owns a large stake, he or she can install or remove the board and thus steer the firm towards personal objectives, which may differ from those of minority shareholders. Examples of type II agency costs:

• A majority shareholder makes one of her firms trade on attractive terms with another of her firms: a related party transaction.
• A majority shareholder forces the company to declare a large (extraordinary) dividend because she needs the cash, for example for an investment in another company.

Stakeholders (employees, customers, suppliers, government) also have claims on the firm's cash flows and may try to exert control.

Board voting systems: cumulative versus straight voting

Example (Sole SpA): 10,000 shares outstanding, cumulative voting, 3 directors up for election. You need 10,000/(3 + 1) + 1 = 2,501 shares. With 2,500 shares against 7,500 a tie is possible (the majority can give 2,500 votes to each of three candidates); with 2,501 the remaining 7,499 votes can never give all three rivals more than 2,501 votes. At a share price of €20 the seat costs 2,501 x €20 = €50,020.

Tutorial: 20,000 shares at €25 and 4 directors up for election: 20,000/5 + 1 = 4,001 shares, costing 4,001 x 25 = €100,025. Book example: Smith has 20 shares, Jones 80, four seats: Smith casts 80 votes on himself and Jones cannot give four candidates more than 80 each, so Smith wins a seat; under straight voting Jones takes all seats.

Staggered elections (only part of the board is elected at a time) reduce the effect of cumulative voting: with 2 seats up it takes 1/3 of the shares plus one. Staggering also makes takeovers harder, but provides continuity ('institutional memory').

International corporate governance

A third type is religious law (for example sharia, which forbids interest). Besides the legal system, enforcement and corruption matter (Transparency International's Corruption Perceptions Index).

A common measure is domestic bank deposits divided by stock market capitalisation: a high ratio means bank-based. Examples: US 0.91 and UK 1.03 (market-based), Netherlands 1.63, Germany 5.01 and Austria 10.24 (bank-based). Ownership structure differs too: 100% of the 20 largest UK firms are widely held, whereas family or state ownership dominates in countries such as Greece, Belgium or Austria. Widely held firms face mostly type I problems; closely held firms mostly type II problems. Family firms tend to take a longer-term view; state-owned firms also pursue political objectives.

Underlying assumption for the rest of the course: corporate executives act in the interest of the shareholders. There is no self-dealing or investment in projects that maximise managers' own wealth, and no financing decisions that minimise the risk for the firm (or managers) but not for shareholders. Transparency and timely disclosure are essential; most countries have a corporate governance code (the Netherlands: the Dutch Corporate Governance Code).

Multiple cash flows

Week 1 dealt with a single payment (what is a payment now worth later, or a future payment worth today). Now we look at multiple cash flows, especially cash flows that occur periodically and are always of the same amount. The present value of several cash flows is the sum of their individual present values; the future value is the sum of their individual future values.

PV example: €1,000 at the end of each of the next five years at 6%: 1,000/1.06 + 1,000/1.06^2 + ... + 1,000/1.06^5 = 943.40 + 890.00 + 839.62 + 792.09 + 747.26 = €4,212.37.

FV example: €2,000 invested at the end of each of the next five years at 10%: 2,000 x 1.1^4 + 2,000 x 1.1^3 + 2,000 x 1.1^2 + 2,000 x 1.1 + 2,000 = 2,928.20 + 2,662.00 + 2,420.00 + 2,200.00 + 2,000.00 = €12,210.20. The last payment earns no interest because it is made at the end of year 5.

Perpetuities

V0 = C/(1 + r) + C/(1 + r)^2 + C/(1 + r)^3 + ... The slides derive the formula in two ways. (1) Divide the series by (1 + r) and subtract it from the original: V0 - V0/(1 + r) = C/(1 + r), because the term C/(1 + r)^(infinity) goes to zero. Then V0 x r/(1 + r) = C/(1 + r), so V0 = C/r. (2) With the geometric series 1 + q + q^2 + ... = 1/(1 - q) for |q| < 1 and q = 1/(1 + r): V0 = C/(1 + r) x 1/(1 - 1/(1 + r)) = C/(1 + r) x (1 + r)/r = C/r.

Example (apartment building): cash flows to the landlord of €100,000 next year, growing 5% per year forever, discount rate 11%: PV = 100,000/(0.11 - 0.05) = €1,666,667. Tutorial: an oil source produces €100m next year, growing 2% forever, at 10%: PV = 100/(0.10 - 0.02) = €1,250m.

Annuities

Derivation with the finite geometric series 1 + q + ... + q^(n - 1) = (1 - q^n)/(1 - q), or intuitively: annuity = perpetuity minus delayed perpetuity. A perpetuity starting now is worth C/r; a perpetuity whose payments start after date T is worth (C/r)/(1 + r)^T; their difference is exactly the payments from 1 to T.

Solving for the payment: C = PV / A(r, T). Mortgage example (slides): a Dutch bank's calculator says that with a gross income of €100,000 you can borrow €320,367 with an annuity mortgage at 3.61% fixed for 30 years (360 months). Monthly payment: C = 320,367 / [1/(0.0361/12) - 1/((0.0361/12)(1 + 0.0361/12)^360)] = €1,458.33. In an annuity mortgage (annuïteitenhypotheek) the total monthly payment is constant: at the start mostly interest, at the end mostly repayment. In a linear mortgage (lineaire hypotheek) the repayment is constant, so the total payment starts high and falls as the interest decreases.

Finding the number of payments: you borrow €1,000 on a credit card at 1.5% per month and pay €20 per month. 1,000 = 20 x [1/0.015 - 1/(0.015 x 1.015^T)] gives 1.015^T = 4, so T = ln 4/ln 1.015 = 93.11 months (almost 8 years).

Annuity due

Example: you win £50,000 per year for 20 years, paid at the start of each year starting immediately; discount rate 8%. Value = 50,000 + 50,000 x [1/0.08 - 1/(0.08 x 1.08^19)] = 50,000 + 480,180 = £530,180: the payment at t = 0 plus a 19-year ordinary annuity.

Delayed annuity

If the first payment is not at t = 1, value the annuity at one period before its first payment and then discount that single amount back to t = 0.

Example (Danielle Caravello): a 4-year annuity of €500 per year with the first payment at date 6, at 10%. Step 1: value in year 5: V5 = 500 x [1/0.1 - 1/(0.1 x 1.1^4)] = €1,584.93. Step 2: discount to year 0: V0 = 1,584.93/1.1^5 = €984.12.

Exercise: a 5-year annuity of €600 with the first payment in year 5, at 5%. Value in year 4 = 600 x A(5%, 5) = 2,597.69; PV0 = 2,597.69/1.05^4 = €2,137. Common mistake: discounting 5 years instead of 4.

Growing annuity

Example (lottery): 20 payments, first 200,000, then growing 5% per year, discount rate 11%: PV = 200,000 x [1 - (1.05/1.11)^20]/(0.11 - 0.05) = 2,236,337. Tutorial: a project paying €10,000 in year 1, growing 4% per year for 8 years, at 8%: PV = 10,000 x [1 - (1.04/1.08)^8]/0.04 = €65,151.18, the maximum you should pay.

Future value of an annuity

Tutorial examples: £400 per month at 7% compounded monthly for 40 years (480 deposits): FV = 400 x [(1 + 0.07/12)^480 - 1]/(0.07/12) = £1,049,925. €500 per month at 9% compounded monthly, but with the first deposit two months from now and the horizon 30 years: there are 359 deposits, FV = 500 x [(1.0075)^359 - 1]/0.0075 = €908,061 (with 360 deposits it would be €915,372).

Compounding more than once per year: EAR

Interest can be paid semi-annually (2 times a year), quarterly (4), monthly (12), weekly (52), daily (365) or continuously.

• Quoted (stated, nominal) interest rate: the rate expressed in terms of the interest payment made each period, quoted per year without compounding.
• Effective annual rate (EAR): the rate expressed as if it were compounded once per year.

Tutorial: a car loan at 0.75% per month has EAR = 1.0075^12 - 1 = 9.38%. If the EAR is 13%, the effective weekly rate is 1.13^(1/52) - 1 = 0.2353%. A quoted 4% gives an EAR of 4.00% (annual), 4.04% (semi-annual) and 4.08% (weekly). APR and EAR are identical when the interest rate is 0% or compounding is annual.

Multi-year compounding: Harry DeAngelo invests €5,000 at a quoted 12% compounded quarterly for five years. Either use the EAR, 5,000 x (1 + EAR)^5, or directly the quarterly rate: 5,000 x (1 + 0.12/4)^(4 x 5) = 5,000 x 1.03^20 = €9,031. Tutorial: £58,000 in seven years at 10% compounded daily: PV = 58,000/(1 + 0.10/365)^(365 x 7) = £28,804.71. €5,100 for 20 years at 10% compounded semi-annually: FV = 5,100 x 1.05^40 = €35,903.94.

The annual percentage rate (APR)

Many loans have front-end or back-end fees (management, administration). In the EU, since 2010 all consumer loans below €75,000 (in the Netherlands also mortgages) must state the effective interest rate including all costs, not just the interest payments. This is the Annual Percentage Rate (APR). Often APR = EAR, if there are no extra fees or costs not already included in the EAR. Beware: in the US the APR means the stated (simple) interest rate, which is lower than the EAR.

Example (homework, car loan): price £30,000, 'simple annual interest of 12% on the original amount over three years, payable in 36 monthly instalments', plus an administration fee of £250. The lender charges 12% on £30,000 every year: £3,600 per year, £10,800 in total. Monthly payment = 30,000/36 + 30,000 x 0.12/12 = 833.33 + 300.00 = £1,133.33. The effective APR is the rate that makes the PV of 36 payments of £1,133.33 equal to the net amount received (30,000 - 250 = 29,750): about 1.818% per month, so APR = 1.01818^12 - 1 = 24.13% (found numerically, for example with Excel). By law the lender must also state the total amount payable (£250 + 36 x £1,133.33 = £41,050) and the total charge for credit (£41,050 - £30,000 = £11,050). The quoted 12% hides the fact that interest is charged on the full original amount although the debt is repaid gradually.

Loan types and amortisation

Pure discount loan (T-bill): a T-bill promises £10,000 in 12 months; the market rate is 7%. Price = 10,000/1.07 = £9,346. The loan amount is £9,346 and the 'interest' is £654.

Amortised loan (mortgage): a €100,000 commercial mortgage at 1% effective per month with 20-year (240-month) amortisation is an ordinary annuity: 100,000 = C x [1/0.01 - 1/(0.01 x 1.01^240)], so C = €1,101.09 per month.

Partially amortised loan (balloon): the same mortgage with a five-year (60-month) balloon. After 60 payments the remaining loan is a 180-month annuity; the balloon equals the PV of those remaining payments: 1,101.09 x [1/0.01 - 1/(0.01 x 1.01^180)] = €91,744 at t = 60.

Tutorial (mortgages): a 32-year mortgage with quarterly payments of €4,000 at 2.14% per year compounded quarterly: loan = 4,000 x [1 - 1/(1 + 0.0214/4)^128]/(0.0214/4) = €370,009.50; with an extra deposit of 20% of the loan the purchase price is 1.2 x 370,009.50 = €444,011. A 25-year mortgage with monthly payments of €717 at 6.14% compounded monthly: loan = €109,820; purchase price = 1.2 x 109,820 = €131,784.

Tutorial (comparing annuities): investment X pays €6,500 per year for 9 years, Y €8,000 per year for 6 years, at 15%: PV(X) = €31,015 and PV(Y) = €30,276, so X is worth more. If X pays £5,000 per year for 9 years at a stated 5% (PV = £35,539.11) and Y pays semi-annually for 6 years at 2.5% per half year, the equal-value semi-annual payment is 35,539.11/A(2.5%, 12) = £3,464.61.

Tutorial (retirement): you deposit £500 a month in a share account (EAR 7%) and £500 a month in a bond account (EAR 4%) for 30 years. Monthly rates: 1.07^(1/12) - 1 = 0.5654% and 1.04^(1/12) - 1 = 0.3274%. FV = £584,726 + £342,635 = £927,361. You then withdraw monthly for 25 years from an account earning 6% EAR (0.4868% per month): C = 927,361/A(0.4868%, 300) = about £5,885 per month. Note that an EAR must be converted to an effective monthly rate with the root, not divided by 12.

Overview of DCF formulas