Corporate Finance Lectures PDF

Corporate Finance Agenda 1. What is corporate finance? 2. The corporate business form 3. Key financial decisions Corporate Finance Corporate finance is the study of how firms or businesses make financial decisions. Firms generate cash flows (CFs) by investing in real assets, which they pay for...

Corporate Finance Agenda 1. What is corporate finance? 2. The corporate business form 3. Key financial decisions Corporate Finance Corporate finance is the study of how firms or businesses make financial decisions. Firms generate cash flows (CFs) by investing in real assets, which they pay for by issuing financial assets (eg, stocks and bonds). Our view of the firm: a stream of (uncertain) cash flows. Flow of Funds 1 1 Source: Brealey, Myers, and Allen Types of Firms (US) 2 2 Source: Berk and DeMarzo The Corporate Business Form A corporation is a legal entity (ie, a legal “person”) owned by, but legally distinct from its owners (“shareholders”). It is typically characterised by: • Separation of ownership and control • Limited liability for its owners • Owners and the business are taxed separately (leads to the “double taxation problem”) Goal of the corporation: maximise shareholder wealth. Organisational Chart of a Typical Corporation 3 3 Source: Berk and DeMarzo The Key Financial Decisions The role of the financial manager Valuation and investment decisions Cash flows correctly computed Return rate should be appropriate Dividend decisions How much? What form? Financing decisions Identify costs & benefits of financing instruments Choose the optimal mix Risk Management and Hedging Identify which risks should be hedged Find the appropriate instruments The End Capital Budgeting and the NPV Rule Capital Budgeting A key task of managers is to allocate capital between projects. • Stand-alone: Is Project A better than doing nothing? • Mutually exclusive: Is Project A better than Project B? The objective of capital budgeting is to select the optimal mix of physical (“real”) investments/projects. Our focus will be on the financial tools for valuation. These tools attach numerical values to projects to aid comparison and assist in the decision-making process. Opportunity Cost of Capital 1 Financial managers should always consider the opportunity cost of investing in a project. 1 Source: Brealey, Myers, and Allen Net Present Value (NPV) NPV0 = N X t=0 E (CFt ) (1 + r )t NPV converts a project’s future cash flows into comparable quantities that can simply be summed. A project’s NPV measures its dollar contribution to firm value in today’s money. NPV rule (stand-alone project): Accept the project if NPV > 0. NPV Advantages Precise; NPV accounts for: • Time value of money • Compensation for bearing risk Convenient: present values are additive • NPV(A + B) = NPV(A) + NPV(B) • Assuming Projects A and B are independent The End The Optimality of the NPV Rule Optimality of NPV • Two-period model: t = 0 and t = 1 • A firm has current endowment B0 , which can be used to support current and future consumption, C0 and C1 , respectively • Two ways to invest 1. Financial markets: • borrow/lend at interest rate r > 0 2. Real assets: • t = 0: I0 ⇐ investment outlay • t = 1: f (I0 ) ⇐ income from physical investment Optimality of NPV (cont.) • Budget constraints • Savings (t = 0): S0 = B0 − (C0 + I0 ) (1) C1 = f (I0 ) + S0 (1 + r ) (2) • Future consumption (t = 1): • Combining (1) and (2) gives the intertemporal budget constraint line y-intercept z }| slope { z }| { C1 = [(B0 − I0 ) (1 + r ) + f (I0 )] − (1 + r ) C0 (3) Graphically C1 (B0 − I0 ) (1 + r ) + f (I0 ) slope = −(1 + r ) C0 Investors prefer more consumption to less, so irrespective of how they feel about consuming today vs. tomorrow, the further away from the origin the intertemporal budget constraint line is, the better. Therefore, managers seeking to maximise shareholder utility should adopt a physical investment policy that pushes the line out as far out as possible. Optimality of NPV This goal is equivalent to maximising the x-intercept (or y-intercept) of the budget constraint line. • x-intercept occurs when C1 = 0. That is, when NPV z }| f (I0 ) − I0 C0 = B0 + (1 + r ) { • Maximise x-intercept ⇐⇒ maximise NPV of physical investments • The x-intercept also represents investors’ current wealth; therefore, maximising NPV is equivalent to maximising wealth The End Competitors to NPV Agenda 1. Book rate of return 2. Payback period 3. Internal rate of return (IRR) Book Rate of Return The book/accounting rate of return is average income divided by average book value over a project’s life. Book rate of return = Book income Book assets Decision rule: Accept if book rate of return is ‘high enough’. It is rarely used to make decisions; many problems: • The components reflect tax and accounting figures and are not market values or cash flows. • Time value of money is ignored. • It only considers averages, and risk is ignored. Payback Period The payback period is the the number of years it takes before the cumulative forecasted cash flows of a project equals the initial outlay. Decision rule: Accept projects that “pay back” within a desired time frame. This method is flawed: • It ignores all cash flows after the payback period. • It ignores time value of money and risk, although this can be remedied by discounting cash flows before calculating the payback period (called “discounted payback”). • The decision rule cut-off is arbitrary. Payback Period: Example Examine the following three projects and note the mistake we would make if we insisted on only taking projects with a payback period of two years or less. Project C0 C1 C2 C3 Payback NPV @ 10% A −2,000 500 500 5,000 2.2 +2,624 B −2,000 500 1,800 0 1.8 −58 C −2,000 1,800 500 0 1.4 +50 PaybackA = 2 + 2000−1000 5000 = 2 + 0.2 Internal Rate of Return (IRR) • An equivalent way of stating the NPV criterion: accept if the expected return on investment is higher than the opportunity cost of capital • The opportunity cost of capital is also called the project’s hurdle rate • When cost of capital = expected return on investment, NPV = 0 • The IRR is the discount rate that makes NPV = 0 NPV0 = N X t=0 E (CFt ) =0 (1 + IRR)t • Easily calculated in a spreadsheet or with a financial calculator IRR: Example • Upfront investment: $4,000 • The investment will generate $2,000 and $4,000 in cash flows in the next two years respectively • What is the IRR of the investment? 4000 2000 + =0 1 + IRR (1 + IRR)2 √ −b ± b2 − 4ac and use quadratic formula: x = 2a NPV = −4000 + • Set x = 1 1 + IRR • IRR = 28.08% IRR and the NPV Profile 2,000 NPV ($) 1,000 IRR Discount rate (%) 0 20 28 40 60 80 100 −1,000 −2,000 Decision rule: Accept investment opportunities offering an IRR in excess of their opportunity cost of capital. Pitfalls of IRR Blindly applying the IRR rule can lead to incorrect decisions, ie, accepting negative NPV projects. We need to be wary of: • Lending vs borrowing • Multiple IRRs • No IRR • Mutually exclusive projects Lending vs Borrowing • Two streams of cash flows, both same in magnitude but opposite in sign, will have the same IRR. • Take the following two projects as an example. Which project do you prefer? Project C0 C1 IRR A −1,000 +1,500 50% B +1,000 −1,500 50% NPV @ 10% +364 −364 You should be able to verify: NPVA = −NPVB → IRRA,B = (1500/1000) − 1 = 50% Lending vs Borrowing, (cont.) 500 400 300 NPV ($) 200 100 0 −100 10 20 30 40 50 60 70 Discount rate (%) 80 −200 −300 −400 Project A Project B −500 For financing projects, the IRR rule needs to be reversed: only accept if IRR < cost of capital. Multiple IRRs • Certain cash flow streams can generate NPV = 0 at two (or more) different discount rates. • This can happen when future cash flows change sign more than once. • Example: The following cash flow stream has an IRR at both 3.17% and 13.86%. C0 C1 −50 15 ... ... ... ... C9 15 C10 −90 Multiple IRRs, (cont.) 2 IRR2 = 13.86% NPV ($) 0 5 IRR1 = 3.17% −2 −4 −6 10 15 Discount rate (%) 20 No IRR • It is possible to have no IRR and a positive NPV, or no IRR and a negative NPV. • These are projects that should always be accepted or rejected, respectively. • For example: Project C0 C1 C2 C +1,000 −3,000 +2,500 D −1,500 4,000 −2,800 IRR NPV @ 10% None +339 None −178 No IRR, (cont.) 500 Project C Project D 400 300 NPV ($) 200 100 0 10 −100 −200 −300 20 30 40 50 60 70 80 90 Discount rate (%) 100 IRR and Mutually Exclusive Projects • Decision rule: Pick the project with the highest IRR. • Do not compare “apples to oranges”: the projects being compared should be in the same risk-class (ie, same cost of capital). • The IRR rule works well if the NPV profiles look like this: NPV ($) Project X Project Y 10 20 30 40 Discount rate (%) 50 IRR Pitfalls: Mutually Exclusive Projects, Part I But, the IRR rule can sometimes result in incorrect decisions when projects differ in their scale and/or the timing of their cash flows. Differences in scale • The following two projects illustrate the problem. IRR picks E, but F is better at the cost of capital. Project C0 E −10,000 F −20,000 C1 +20,000 +35,000 IRR NPV @ 10% 100% +8,182 75% +11,818 IRR Pitfalls: Mutually Exclusive Projects, Part II 15,000 Project E Project F NPV ($) 10,000 5,000 IRRE = 100% 0 10 20 30 40 50 60 70 80 Cross-over @ 50% IRRF = 75% 90 Discount rate (%) 100 110 120 IRR Pitfalls: Mutually Exclusive Projects, Part III Differences in the timing of CFs • Project G, where cash flows arrive relatively earlier, is favoured by IRR, but H is better at the cost of capital. Project C0 G −10,000 H −10,000 C1 +18,000 +5,000 C2 +500 +20,000 IRR NPV @ 10% 82.7% +6,777 68.6% +11,074 IRR Pitfalls: Mutually Exclusive Projects, Part IV 15,000 Project G Project H NPV ($) 10,000 5,000 IRRG = 83% 0 10 20 30 40 Cross-over @ 50% 50 60 70 IRRH = 69% 80 90 Discount rate (%) 100 110 120 IRR: A Quick Question Consider projects Alpha and Beta below. • You can undertake only one of the two projects. The opportunity cost of capital is 8%. Use the IRR rule to make the choice. Project C0 Alpha −400,000 Beta −200,000 C1 +241,000 +131,000 C2 +293,000 +172,000 IRR 21% 31% Hint: Calculating the IRR of the incremental cash flows that would result from taking one project instead of the other provides a potential remedy when comparing mutually exclusive projects. Answer • The incremental CFs from investing in Alpha rather than Beta are: Project C0 Alpha – Beta −200,000 C1 +110,000 C2 +121,000 • The IRR of the incremental CFs is 10%: 110, 000 121, 000 −200, 000 + + =0 1.10 1.102 • The IRR on Beta exceeds the cost of capital and so does the IRR of the incremental investment in Alpha. • Choose Alpha • Note: NPV at 8% gives the same choice. Answer Alpha Cross-over @ 10% Beta 1 · 105 NPV ($) 50,000 IRRBeta = 31% Discount rate (%) 0 8 10 20 −50,000 IRRAlpha = 21% 30 40 In Practice Survey data on CFO use of investment evaluation tools 1 1 Source: Brealey, Myers, and Allen The End Free Cash Flows Agenda 1. Free cash flow (FCF) 2. FCF components 3. Inflation NPV: What Do You Discount? NPV0 = N X E (FCFt ) t=0 (1 + r )t To calculate NPV, we need to forecast a project’s expected after-tax free cash flow (FCF). FCFs are the cash flows that would be ‘left over’ to distribute to investors after all operating and investment expenditures have been made, assuming the project is all-equity financed. Rules: • Only cash flows are relevant. • Estimate cash flows on an incremental basis. • Include opportunity costs. • Ignore sunk costs. • Include all externalities. • Treat inflation consistently. Free Cash Flow Approach: Start with incremental accounting earnings and then adjust to get to free cash flows. FCF = EBIT(1 − τc ) + Depreciation − Change in NWC − CAPEX + Salvage where: • EBIT: earnings before interest and taxes • NWC (net working capital): current assets − current liabilities • CAPEX: capital expenditures • Salvage: after-tax recovery value of used productive capital • τc : marginal corporate tax rate Note: We ignore any interest expense in the FCF calculation. • Rationale: keep investment and financing decisions separate Free Cash Flow and Depreciation Since EBIT = EBITDA − Depreciation, FCF = (EBITDA − Depreciation)(1−τc ) + Depreciation − Change in NWC − CAPEX + Salvage. Why subtract and then add back depreciation? • Because depreciation is a non-cash expense that reduces a firm’s tax bill (a cash expense). Simplifying the equation above, we get an equivalent expression for FCF: FCF = EBITDA(1 − τc ) + Depreciation×τc − Change in NWC − CAPEX + Salvage The term Depreciation × τc in the equation above is the tax benefit provided by depreciation, and is called the depreciation tax shield. Example: Depreciation Tax Shield XYZ has EBITDA = $100, τc = 30%, Change in NWC = CAPEX = Salvage = 0. • Suppose Depreciation = 0. What is its FCF? FCF = 100 × (1 − 30%) = $70 • What if Depreciation = 20? FCF = (100 − 20) × (1 − 30%) + 20 = 56 + 20 = $76 • With depreciation, FCF is higher by $6. This difference is equal to the tax savings that result from the ability to shield $20 of pre-tax income from tax by deducting depreciation. Depreciation tax shield = 20 × 30% = $6 Free Cash Flow: CAPEX and Salvage Values CAPEX Since investments in Plant, Property & Equipment (eg, machinery) generally cannot be claimed as an expense for accounting purposes, they do not appear on the income statement directly. • But investments cost money! • This expenditure will lower available FCFs, hence we subtract capital expenditures/investments in the FCF calculation. Salvage Value Used equipment can sometimes be sold. If the sale price of the asset exceeds its book value, then we need to pay tax on the gain. The after-tax proceeds of this sale (the “salvage value”) is a cash inflow that will increase FCF. • Salvage value = Sale price − (Gain on sale ×τc ) • Gain on sale = Sale price − Book value • Book value = Initial investment − Accumulated depreciation Free Cash Flows: Net Working Capital Net working capital (NWC) • NWC = Current assets − Current liabilities • Main Current assets (CA): Inventory, Accounts receivable, (Cash?) • Main Current liabilities (CL): Accounts payable • NWC captures how much liquidity is tied up in the operation • Accounts receivables (payables) are earnings (expenses) for which you are yet to receive (pay) cash. • Purchases of inventory require cash but won’t be recognised as an expense until the goods are sold. • A growth in NWC means a net investment in current assets, tying up more cash and thereby decreasing free cash flow; therefore, we subtract the change in NWC Change in NWCt = NWCt − NWCt−1 = Change in CAt − Change in CLt Inflation Recall the relationship between the nominal interest rate (rnom ), the real interest rate (ireal ), and the (expected) inflation rate (π): 1 + ireal = 1 + rnom 1+π Be consistent in how you handle inflation! • Use nominal interest rates to discount nominal cash flows. • Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures. Inflation: Example You invest in a project that will produce real cash flows of −$100 in year 0 and then $35, $50, and $30 in the following three years. If the nominal discount rate is 15% and the forecasted inflation rate is 10%, what is the NPV of the project? ireal = 1 + rnom 1.15 −1= − 1 ≈ 4.55% 1+π 1.10 Inflation: Example Nominal figures Year Cash flow PV @ 15% 0 −100 −100 1 35 × 1.10 = 38.5 38.5 1.15 = 33.48 2 50 × 1.102 = 60.5 60.5 1.152 = 45.75 3 30 × 1.103 ≈ 39.9 39.9 1.153 = 26.25 NPV = $5.48 Inflation: Example Real figures Year Cash flow PV @ 4.55% 0 −100 1 35 35 1.0455 = 33.48 2 50 50 1.04552 = 45.75 3 30 30 1.04553 = 26.25 −100 NPV = $5.48 The End Modelling 1: NPV Calculation VAS Project: Calculating FCFs, Part I Depreciation: Under straight-line depreciation, the annual depreciation expense is a constant proportion of the difference between the initial investment and the accounting salvage value (ie, book value): Depreciable amount = Initial investment − Book valueT = (250K + 50K) − 100K = £200, 000 1 × Depreciable amount T 1 = × 200K 4 = £50, 000 Annual depreciation = VAS Project: Calculating FCFs, Part II Salvage value: Since we have the required data, we can also calculate the tax due on the market salvage value: Taxable profit on salvage = 100K − 100K = 0 Tax due = 0 × τc = 0 After-tax market salvage value = 100K − 0 = £100, 000 VAS Project: Calculating FCFs, Part III 0 (1) (2) (3) (4) (5) (6) (7) Saved rent Heating Move-in/out costs Depreciation EBIT (1 − 2 − 3 − 4) Tax at 30% Profit after tax (5 − 6) (8) (9) (10) Operating cash flow (7 + 4) Change in NWC CF from investment activities (11) Free cash flow (8 − 9 + 10) 1 2 3 4 150 40 150 40 150 40 (25) (7.5) (17.5) 50 60 18 42 50 60 18 42 50 60 18 42 150 40 25 50 35 10.5 24.5 (17.5) 92 92 92 74.5 92 92 174.5 25 (300) (317.5) 100 92 First, calculate unlevered Net Profit = EBIT(1 − τc ) = (Revenues − Costs − Depreciation)(1 − τc ). For FCFs, we: • Add back depreciation (Operating Cash Flow = After-tax profit + Depreciation) • No NWC needs in this case • Determine cash-flows from CAPEX and Salvage VAS Project: NPV NPV using nominal cash flows and discount rate = 10%: NPV = −317.5K + 92K 92K 174.5K 92K + + + = 30.476K 1.10 (1.10)2 (1.10)3 (1.10)4 NPV = +£30,476 The End NPV Applications Agenda 1. Profitability index 2. Equivalent annual cash flow (EAC) Profitability Index When the total amount of funds available for investment are limited (called “capital rationing”), the profitability index (PI) provides a tool for selecting among various project combinations and alternatives. Profitability index = NPV Investment Decision rule: Choose the combination of projects with the highest weighted-average PI. Profitability Index: Example We only have $300,000 to invest. Which do we select? Project A B C D NPV 230,000 141,250 194,250 162,000 Investment 200,000 125,000 175,000 150,000 PI 1.15 1.13 1.11 1.08 Select projects with the highest weighted-average PI: • WAPI(BD) = (125/300) × 1.13 + (150/300) × 1.08 + (25/300) × 0 = 1.01 • WAPI(BC) = 1.12 (Choose this combination) • WAPI(A) = 0.77 Note that any unused cash has a PI = 0. Equivalent Annual Cash Flows Sometimes it is useful to transform the present value of an investment into a stream of equal future cash flows (eg, when choosing between projects with different lengths). The equivalent annual cash flow (EAC) of a project is the equal cash flow per period with the same present value as the actual cash flows of the project. When the cash flows are costs, this quantity is called the equivalent annual cost. EAC = PV(cash flows) annuity factor where Annuity factor = 1 − (1 + r )−n r ! EAC Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using the equivalent annual cost method. Machine A B 0 15 10 1 5 6 2 5 6 3 5 PV @ 6% 28.37 21.00 EAC 10.61 11.45 • EAC of machine A:  EACA ×  1 − (1.06)−3 = 28.37 → EACA ≈ 10.61 0.06 • EAC of machine B:  1 − (1.06)−2 EACB × = 21.00 → EACB ≈ 11.45 0.06  The End