Principles of Finance Lecture 3 & 4 PDF

Introduction Shareholder Wealth Capital Budgeting Techniques Principles of Finance Lecture 3 & 4: Investment Decision: The Certainty case (CWS ch. 2) Rikke Seje...

Introduction Shareholder Wealth Capital Budgeting Techniques Principles of Finance Lecture 3 & 4: Investment Decision: The Certainty case (CWS ch. 2) Rikke Sejer Nielsen 1 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Investment decision Investment decision: ⇒ How much not to consume today to increase future consumption possibilities. Ex. for firms: Managers decide on how to distribute earnings 1 pay out earnings as dividends (possibility for shareholders to use for consumption today) 2 invest earnings in productive opportunities to increase future consumption possibilities for shareholders Optimal investment decision ⇒ Optimal if investment maximizes expected utility of consumption over a life time. ⇒ Invest when expected utility of future consumption provided by additional one-dollar investment is higher than the utility of using that extra dollar on consumption today. 3 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Investment decision with no uncertainties Setting: Capital markets are perfect and complete, The market interest rate is nonstochastic - known with certainty in all time periods (not necessarily constant!), All payoffs from current investment decisions are known with certainty. 4 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Investment decision with no uncertainties Recall from Lecture 2: From Fisher Separation Theorem, we know 1 Shareholders can delegate investment decisions to the manager of the firm in which they are owners, as the investment decision is independent of the shareholders’ time-preferences for consumption. ⇒ The manager of the firm will always undertake all projects that earn more than the market rate of return ⇒ Optimal investment decision, where MRT = −(1 + r ) ⇒ Maximizes wealth of the shareholders 2 Individuals take income from productive investments (P0 , P1 ) and borrow or lend to optimally plan their consumption, where MRS = −(1 + r ) 5 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Investment decision with no uncertainties Recall from Lecture 2: ⇒ W0∗ = P0 + P1 (1 + r )−1 = C0∗ + C1∗ (1 + r )−1 ⇒ Maximizing wealth of the shareholders = Maximizing life-time utility of consumption 6 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Investment decision with no uncertainties Two topics interesting for the investment decision 1 Defining wealth of the shareholders 2 Different techniques for project selection (Capital Budgeting Techniques) 7 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Shareholder Wealth Shareholders’ wealth determined by after-tax cash flows available for consumption: 1 Dividends (Divt ) paid to shareholders at time t 2 Capital gains in case of sale of stock(s) ⇒ Valuation of common stocks 9 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Setting: All future cash flows are known with certainty ks = Shareholders’ market-determined required rate of return on equity ▶ Assumed nonstochastic and constant over time ▶ Market-determined opportunity cost of capital for equivalent income streams, and thus determined by the slope of the capital market line. Personal taxes are ignored 10 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks The price of the common stock today Div1 + S1 S0 = 1 + ks Similarly, we must have at time 1 Div2 + S2 S1 = 1 + ks Combining these two equations gives Div1 Div2 + S2 S0 = + 1 + ks (1 + ks )2 11 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks For a stockholder with investment horizon H: Div1 Div2 DivH + SH S0 = + 2 +... + 1 + ks (1 + ks ) (1 + ks )H ⇒ Value of stock = PV of future dividends + PV of stock price at the end of investment. 12 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Dividend Discount Model  a stockholder withinvestment horizon H → ∞ For Div∞ +S∞ (1+ks )∞ → 0, Why ? : Div1 Div2 Div3 Div4 S0 = + + + +... 1 + ks (1 + ks )2 (1 + ks )3 (1 + ks )4 ∞ X Divt = (1 + ks )t t=1 ⇒ Value of stock = PV of future dividends. 13 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Example - Valuation of common stocks It is known that the firm ABC will pay dividends of $5, $5.25 and $6.50 over the next three years, respectively At the end of the third year you sell your stock at a market price of $100. What is the price of the stock, given a required rate of return on equity of 12%? S0 = 14 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Special case I - Constant growth in dividends forever If dividends grow forever at a constant rate, g: Divt = Div0 (1 + g)t ∀t = 1,..., ∞ Div0 (1 + g)3 Div0 (1 + g)2 Div0 (1 + g) Time 0 1 2 3 1 ··· 1 Then the stock price at time 0 is Div0 (1 + g) Div0 (1 + g)2 Div0 (1 + g)3 S0 = + 2 + +... 1 + ks (1 + ks ) (1 + ks )3 ∞ X Div0 (1 + g)t = (1 + ks )t t=1 15 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Special case I - Constant growth in dividends forever Value of stock at time 0 is ∞ X Div0 (1 + g)t S0 = (1 + ks )t t=1 ⇒ Growing perpetuity with Div1 = D0 (1 + g) as the first payment (Using Gordon’s growth formula) Div0 (1 + g) Div1 ⇔ S0 = = , ks − g ks − g and generally for time t Divt (1 + g) Divt+1 St = = , ks − g ks − g Note: Only true if g < ks. 16 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Special case II - Constant growth in dividends forever after time t If dividends grow forever at a constant rate, g, after time t : Divt (1 + g)2 Divt (1 + g) Div2 Divt Div3 Div1 Time 0 1 2 3 1 ··· 1 t t+1 t+2 1 ··· 1 Div1 Div2 Div3 Divt Divt (1 + g) S0 = + + +... + + +... 1 + ks (1 + ks )2 (1 + ks )3 (1 + ks )t (1 + ks )t+1 t X Divτ St = + , (1 + ks )τ (1 + ks )t τ =1 Divt+1 Divt (1+g) where St = ks −g = ks −g 17 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Valuation of common stocks Special case III - Several growth rates growth in dividends If dividends grow at a constant rate, g1 in t periods and forever at a constant g2 after time t: Divt Divt (1 + g2 )2 ⇑ Divt (1 + g2 ) Div0 (1 + g1 )t Div0 (1 + g1 )3 Div0 (1 + g1 )2 Div0 (1 + g1 ) Time 0 1 2 3 1 ··· 1 t t+1 t+2 1 ··· 1 Div0 (1 + g1 ) Div0 (1 + g1 )2 Div0 (1 + g1 )t Div0 (1 + g1 )t (1 + g2 )1 S0 = + 2 +... + t + +... 1 + ks (1 + ks ) (1 + ks ) (1 + ks )t+1  t ! Div1 1 + g1 St = 1− + , ks − g1 1 + ks (1 + ks )t Divt+1 Div0 (1+g1 )t (1+g2 ) where St = ks −g2 = ks −g2 18 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Exercise 1 - Valuing common stocks A firm pays a $5.00 dividend next year and then increase the dividend at a rate of 7% per year, indefinitely. The market-determined required rate of return on equity is 10%. What is the value of the firm’s stock? S0 = If the dividend grows with a annual rate of 2% instead, what is the same stock selling for in the stock market? S0 = 19 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Exercise 2 - Valuing common stocks A firm just paid out a dividend of $3. The next three years, the dividend will grow by 5% per year, whereafter it will grow with an annual rate of 2% forever. The market-determined required rate of return on equity is 12%. What is the value of the firm’s stock? S0 = 20 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Shareholder Wealth Recall shareholders wealth determined by cash flows available for consumption: 1 Dividends (Divt ) paid to shareholders at time t 2 Capital gains in case of sale of stock(s) ⇒ Captured in price per share For managers to maximize shareholders’ wealth ⇒ Maximize the price per share = maximize PV(cash flows) provided by investment projects Next: Investment decision rules 21 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Investment decision Investment decision Typically many different projects/investments to choose between, but insufficient resources. Which projects add value to the firm? If mutual exclusive investments, what project should we choose? How do we make an objective assessment of the different investments? ⇒ We will now look at different rules for acceptance or rejection of projects. 23 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Investment decision Note in our setting Perfect and complete capital markets No uncertainty So Cash flows provided by a project are known with certainty ⇒ Free Cash Flows in time period t (FCFt ) Required rate of return for projects (k) = The opportunity cost of capital provided to the firm, k = Risk-free rate (T-bill rate) for all projects 24 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Primary investment decision rules 1 Payback method 2 Net Present Value (NPV) 3 Internal Rate of Return (IRR) Note that we skip the Accounting Rate of Return (ARR). 25 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Assessment of the investment decision rules How well do the investment decision rule maximize shareholders’ wealth? Four assessment criteria need to be considered: 1 Are all cash flows considered? 2 Does the decision rule account for the time-value of money? 3 If mutually exclusive projects, is the decision rule useable for selecting in between projects? 4 Does the decision rule allow the manager to consider one project independently from all others (value-additivity principles)? ⇒ Spoiler alert: NPV decision rule is the only technique that is consistent with maximization of shareholders’ wealth. 26 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Payback method The payback period: The number of years it takes to recover the initial investment. Exact payback period using simple linear interpolation: | cum. FCF in period A | payback period = period A + FCF in the period after period A where period A is the last period with neg. cum. FCF The payback investment rule: Invest if payback period < arbitrary cutoff period 28 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Payback method - Example 1 Management has decided to only invest in projects, where the initial investment is recovered within 3 years. Cash flows of the project considered: Time 0 1 2 3 4 FCF -280,000 24,000 36,000 80,000 150,000 Cum. FCF -280,000 -256,000 -220,000 -140,000 10,000 Payback period = Exact Payback period = 29 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Payback method Disadvantages ▶ Cash flows beyond the payback period are not considered ▶ No discounting - do not account for the time value of money! ▶ Not good for selection between mutually exclusive projects - favors short-lived projects ▶ Violates value-additivity principle (see exercise 3) Advantages ▶ Simple ▶ Good if firm is capital constrained 30 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Net Present Value, NPV Net Present Value (NPV): N X NPV = FCFt (1 + k)−t − I0 t=1 k = Weighted average cost of capital N = Number of project periods The NPV investment rule: NPV > 0 ⇒ Accept project ⇒ Managers increase shareholders’ wealth by accepting all project that are worth more then they cost. 32 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Net Present Value, NPV - Example 2 A firm has the opportunity to buy a building for $440,000. The investment will generate $30,000 in FCFs (i.e. rent) during the first three years. At the end of year three, you will sell the building for $500,000. The weighted average cost of capital, k, is 10%. What is the NPV of this investment? Should you invest or not? 33 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Net Present Value, NPV Advantages ▶ All cash flows are considered ▶ Account for the time value of money ▶ Good for selection between mutually exclusive projects - select project with highest NPV. ▶ Value-additivity principle holds Disadvantages ▶ Not simple 34 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Net Present Value, NPV The Value-Additivity Principle holds! Based on NPV rule: Project 1 is preferable to 2 and 3, and Project 3 is preferable to 2. For value-additivity principle to hold: ⇒ Project 1 + 3 should be preferable to 2 + 3 (True!) 35 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Internal Rate of Return (IRR) Method Internal Rate of Return (IRR) IRR is defined as the discount rate that ensures a NPV of 0 It is the solution to: N X NPV = 0 = FCFt (1 + IRR)−t ) − I0 t=1 IRR can be considered as the rate of return on invested capital that the project is returning to the firm. The IRR investment rule: IRR > k ⇒ accept project (Invest!) where k is the weighted average cost of capital. 37 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method IRR - Example 2 cont. Same setup as in example 2 Free Cash flows of the project: Time 0 1 2 3 FCF -440,000 30,000 30,000 530,000 and the weighted average cost of capital, k, is 10%. What is the IRR on this project? Should you invest or not? 38 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Equivalence between IRR method and NPV method Generally, IRR- and NPV method are similar: 39 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Pitfalls with IRR rule Reinvestment rate assumption ▶ IRR method assumes reinvestment at the IRR for each project ▶ All project have the same risk as CFs are known with certainty ⇒ Should be discounted at the same rate ⇒ IRR method discount CFs at the wrong rate. ⇒ Choosing the project with highest IRR, not necessarily the project with highest NPV that maximizes shareholder wealth. ▶ Violates the Fisher separation theorem. The Value-Additivity Principle doesn’t hold! Several IRRs can appear when CFs shift sign more than once 40 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Pitfalls with IRR rule The Value-Additivity Principle doesn’t hold! Based on IRR rule: Project 3 is preferable to 1 and 2, and Project 1 is preferable to 2. For value-additivity principle to hold: ⇒ Project 1 + 3 should be preferable to 2 + 3 (Not true!) 41 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Pitfalls with IRR rule Several IRRs can appear when CFs shift sign more than once Consider a project with the following free cash flows, Time 0 1 2 3 FCF -90,000 132,000 100,000 -150,000 and opportunity cost of capital, k = 12%. 42 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Pitfalls with IRR rule Several IRRs can appear when CFs shift sign more than once 43 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method IRR vs. NPV method Generally equivalence between IRR method and NPV method, but, but, but IRR rule is bad when choosing between mutually exclusive projects. ▶ Project with highest IRR not necessarily the project with the highest NPV due to reinvestment rate assumption. ▶ Combining the two projects with the highest IRR, do not always have the highest IRR when combined (Value-Additivity Principle doesn’t hold!). ⇒ If combining several projects, all possible combinations of projects need to considered to find combination with highest IRR. Potentially more than one IRR - which of the IRRs should the investment decision be based on? ⇒ NPV is a safer criteria than IRR. 44 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Example from CWS 2 - Mutual exclusive projects Projects A-D have the following free cash flows: Project Time A B C D 0 -1000.00 -1000.00 -1000.00 -1000.00 1 100.00 0.00 100.00 200.00 2 900.00 0.00 200.00 300.00 3 100.00 300.00 300.00 500.00 4 -100.00 700.00 400.00 500.00 5 -400.00 1300.00 1250.00 600.00 NPV -406.83 510.70 530.95 519.47 IRR -200% 20.92% 22.79% 25.38% Payback 2 4 4 3 Assuming an opportunity costs of capital, r, of 10%. 45 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Exercise 3 Problem 10 in end-of chapter problems (CWS 2, page 39) The cash flows for projects A, B, and C are given below. 1 Calculate the payback period and net present value for each project (assume a 10% discount rate). 2 If A and B are mutually exclusive and C is independent, which project, or combination of projects, is preferred using (a) the payback method or (b) the net present value method? 3 What do the results tell you about the value-additivity properties of the payback method? 46 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method Exercise 4 - Mutual exclusive projects Projects A-D have the following free cash flows: Free Cash Flows from projects t A B C D 0 -200000 -55000 -300000 -30000 1 84000 12000 82000 15000 2 95000 12000 86000 9000 3 50000 12000 91000 4000 4 0 12000 96000 8000 5 0 12000 0 0 6 0 12000 0 0 NPV IRR Payback Note how the different methods rank investments differently. 47 / 48 Introduction Shareholder Wealth Capital Budgeting Techniques Payback method NPV method IRR method References CWS, ch. 2 48 / 48