Finance Lecture4

MBAM 614 Finance NPV And Investment Decisions • MBAM614 Class 4 - 1 Summary of Last Class 1. 2. 3. 4. 5. Bond Value = PV of Coupons + PV of Face Value YTM is the discount rate that satisfies Bond Value = C * PVIFA(YTM,t) + F * PVIF(YTM,t) Bond Value drops as YTM rises Bond Value increases as YTM decreases All else equal: - longer term means greater interest rate risk - lower coupon means greater interest rate risk Spot rates and forward rates are linked (1 + r1)(1 + f1,2) = (1 + r2)2 6. • MBAM614 Class 4 - 2 1 Summary of Last Class 1. P0 = D1/(1 + r) + D2/(1 + r)2 + … + Dt /(1 + r)t + … 2. if g = 0, 3. if g < r, P0 = D/r P0 = D1/(r - g) Pt = Dt+1/(r - g) 4. r = D1/P0 + g = (Dividend Yield) + (Capital Gains) 5. g ≈ Retention Ratio * ROE • MBAM614 Class 4 - 3 Agenda 1. Project Investment Decisions 2. Net Present Value 3. Payback Rule 4. Discounted Payback 5. Average Accounting Return 6. Internal Rate of Return 7. NPV Profiles 8. Profitability Index • MBAM614 Class 4 - 4 2 Investment Decisions How does a firm decide which investments to make (projects to adopt)? That is, how is the Capital Budgeting Decision made? Simple rule is: “Accept any project that increases share value” The difference between the market value of a project’s benefits (cash flows) and its costs is called its Net Present Value (NPV) NPV > 0 ⇔ (value of benefits) > costs so project adds value Valuing a project by discounting its future cash flows is called Discounted Cash Flow (DCF) Analysis • MBAM614 Class 4 - 5 Finding the Net Present Value First, estimate all costs and benefits – costs are cash outflows or negative cash flows – benefits are cash inflows or positive cash flows Costs are generally easy to est., benefits usually are not Determine an appropriate discount rate (usually not simple, either) Find the present value of all signed cash flows. The sum is the project NPV • MBAM614 Class 4 - 6 3 Example: A Photo Maker You have been considering a new business opportunity. Topanga Mall has offered to pay you $30,000 per year at the end of each of the next 4 years to set up a photo finishing machine on their second floor. You can purchase a new photo machine for $90,000 and your required return for something like this would be 20%. What is the NPV of this business opportunity? t=0 - $90,000 + $25,000 + $20,833 + $17,361 + $14,468 - $12,338 • MBAM614 1 + $30,000 2 + $30,000 3 + $30,000 4 + $30,000 Negative because it is a cost Class 4 - 7 When Should We Accept A Project? Since NPV > 0 ⇔ (value of benefits) > costs, we should accept any project with NPV > 0 This is the Net Present Value Investment Rule Clearly, you should not go into the photo business at the Topanga Mall! (it would be like giving the Mall $12,338 today for no reason) • MBAM614 Class 4 - 8 4 Example: A New Mine Recently some CFA made a fabulous find of rust at Voisey Bay. Cleverly, he kept the rights to all the very valuable rust (to be used as a paint pigment) and sold the rights to all other mineral deposits to a bunch of yahoos from a no-name firm called Diamond Field Resources (of all things). The DFR suckers actually paid $15,000 for the other mineral rights which our wise friend plans to spend sinking a mine shaft. If all goes well, the first load of rust will be sold in one year for $12,000. To get to the “really rich” vein, an additional $25,000 must be spent on the mine in year 2 but then, the Rust-man will earn $10,000 per year for the next 10 years. If the required return for this mine is 15%, is he really our “wise” friend? • MBAM614 Class 4 - 9 Our, Uh, “Wise” Friend t=0 1 2 3 4 5 6 7 8 9 10 11 12 -15 +12 -25 +10 +10 +10 +10 +10 +10 +10 +10 +10 +10 +10.435 - 18.904 + 6.575 + 5.718 + 4.972 + 4.323 + 3.759 + 3.269 + 2.843 + 2.472 + 2.149 + 1.869 NPV = $14,480 so YES • MBAM614 Class 4 - 10 5 A Trick t=0 1 2 3 4 5 6 7 8 9 10 11 12 -15 +12 -25 +10 +10 +10 +10 +10 +10 +10 +10 +10 +10 Annuity +10 +10 +10 +10 +10 +10 +10 +10 +10 +10 +10 +10 + 2 - 35 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 NPV = APV - 15 + 1.739 - 26.465 NPV = 10*PVIFA(15%,12) - 15 + 1.739 - 26.465 = 54.206 - 15 + 1.739 - 26.465 = 14.480 • MBAM614 Class 4 - 11 Example: Replacing a Pump Georgia Pacific is considering two possible replacements for some of the pumps in their Columbia Falls mill. The first alternative costs $260,000 but will save $50,000 a year for the next 7 years. The second choice costs $250,000 and saves $75,000 per year for 4 years. Should GP choose either project if an appropriate discount rate is 12%? What if they must choose (only) one? Option 1: NPV = $50,000*PVIFA(12%,7) - $260,000 = $228,188 - $260,000 NPV = - $31,812 • MBAM614 Class 4 - 12 6 Example: Replacing a Pump Option 2: NPV = $75,000*PVIFA(12%,4) - $250,000 = $227,801 - $250,000 NPV = - $22,199 Neither has NPV > 0 so reject both If one MUST be selected, choose the one with greatest NPV (Option 2) • MBAM614 Class 4 - 13 The Payback Rule The length of time until the accumulated cash flows equal or exceed the original investment is called the “Payback Period” Payback Period Rule: accept a project if its payback period is less than or equal to some pre-specified period (usually number of years) • MBAM614 Class 4 - 14 7 Example: Payback Rule Consider a project that costs $1000 today but produces cash inflows of $200, $400, and $600 over the next three years. What would this project’s payback period be? Question is really “How long does it take to earn back our initial investment ($1000)?” $1000 is 2/3 between so Payback is 2 2/3 years Cash Year Flow 0 -$1000 1 200 2 400 3 600 Acc. Cash Flow 200 600 1200 Total Cash Flow -1000 -800 -400 200 or 0 is 2/3 between so Payback is 2 2/3 years • MBAM614 Class 4 - 15 Payback vs NPV Say we are considering two investments that cost $500 each. The first pays $200 in one year and $400 in two years. The second investment pays $150 for each of the next 5 years. What are the payback periods? If an acceptable payback period is 3 years, which investment(s) would the payback rule cause us to accept? If the required rate of return for these investments is 12%, what are their NPV’s? Which investments would the NPV rule accept? Investment 1 CF Acc CF Year PV 0 -$500 -$500 1 200 200 179 2 400 600 319 3 4 5 Payback/NPV 1 3/4 -$2 • MBAM614 Investment 2 CF Acc CF -$500 150 150 150 300 150 450 150 600 150 750 3 1/3 PV -$500 134 120 107 95 85 $41 Class 4 - 16 8 Payback Period Characteristics Does not use discounting Simple to use Ignores time value of money Ignores cash flows beyond the payback point Doesn’t account for differences in risk Can adjust by changing maximum payback period Just how do you determine the cutoff? Biased toward short-term projects Promotes liquidity Biased against long-term projects Seriously flawed and ad hoc • MBAM614 Class 4 - 17 Discounted Payback Address principal concern by looking at discounted cash flows The length of time until the accumulated discounted cash flows equal or exceed the initial investment is called the “Discounted Payback Period” Method is still arbitrary and requires all the work of NPV. Why bother? Note that if project pays back on discounted basis, NPV must be ≥ 0 • MBAM614 Class 4 - 18 9 Example: Discounted Payback You are considering a project that costs $3000 and produces cash flows of $1000 per year for 5 years. Your required return for this type of investment is 12%. What is the project’s payback period? What about its discounted payback period? Does this project have a positive NPV? Cash Flow Undisc Discounted -3000 -3000 1000 893 1000 797 1000 712 1000 636 1000 567 Accumulated CF Undisc Discounted 1000 normal 893 2000 payback 1690 3000 2402 4000 3038 5000 3605 discounted payback Year 0 1 2 3 4 5 NPV = $605 • MBAM614 Class 4 - 19 Average Accounting Return Generally: (some measure of average accounting profits) AAR = (some measure of average accounting value) (average net income) AAR = (average book value) Specifically: “Average Accounting Return Rule” is accept a project if its AAR exceeds a specified rate • MBAM614 Class 4 - 20 10 Example: Cider Press AAR A new cider press will last for 3 years and costs $240,000. Find the AAR given the following projected income statements: (all #’s in 1,000’s) Sales Costs Gross Profit Depreciation Earnings Before Tax Tax (@ 25%) Net Income Year 1 $ 440 220 220 80 140 35 105 Year 2 $ 240 120 120 80 40 10 30 Year 3 $ 160 80 80 80 0 0 0 Average net income = ($105,000 + $30,000 + $0) / 3 = $45,000 Average book value = (240,000 + 160,000 + 80,000 + 0) / 4 = $120,000 Average Accounting Return = $45,000 / $120,000 = 37.5% • MBAM614 Class 4 - 21 AAR vs NPV AAR involves accounting figures, not cash flows therefore it’s not comparable to capital market returns No discounting: money in all periods has same value No objective way to determine a cut-off Seriously flawed • MBAM614 Class 4 - 22 11 Internal Rate of Return The discount rate that makes the present value of all future project cash flows equal to the initial cash outflow is called the “Internal Rate of Return (IRR)” Alternatively, the IRR is the discount rate for which the NPV of all project cash flows is equal to 0 The IRR Rule: accept if required rate of return < IRR. Otherwise, investment should be rejected. The required rate of return is often called the project Hurdle Rate • MBAM614 Class 4 - 23 Example: Internal Rate of Return What is the internal rate of return (IRR) for a project that costs $200 and produces the following cash flows? Year 1 2 3 Cash Flow 50 100 150 Find IRR such that NPV = 0, that is: 0 = -200 + 50 100 150 + + 1 2 (1+IRR) (1+IRR) (1+IRR)3 • MBAM614 Class 4 - 24 12 Example: Internal Rate of Return Make a guess at IRR and solve for NPV If NPV is not 0, make another guess and try again Hints: – If early CF’s are negative followed by positive CF’s, then increasing IRR will usually decrease NPV and decreasing IRR will usually increase NPV – If early CF’s are positive followed by negative CF’s, then increasing IRR will usually increase NPV and decreasing IRR will usually decrease NPV – Reason is that higher IRR makes later CF’s “less important” or less valuable (in present value terms) • MBAM614 Class 4 - 25 Example: Internal Rate of Return Guess 50% 10% 25% 15% 20% 19.44% -200 + [50/(1.50)] + [100/(1.50)2] + [150/(1.50)3] (later CF’s undervalued so estimate too high) -200 + [50/(1.10)] + [100/(1.10)2] + [150/(1.10)3] (later CF’s overvalued so estimate too low) -200 + [50/(1.25)] + [100/(1.25)2] + [150/(1.25)3] (later CF’s undervalued so estimate too high) -200 + [50/(1.15)] + [100/(1.15)2] + [150/(1.15)3] (later CF’s overvalued so estimate too low) -200 + [50/(1.20)] + [100/(1.20)2] + [150/(1.20)3] (later CF’s undervalued so estimate too high) NPV -$77.78 $40.80 -$19.20 $17.72 -$ 2.08 $ 0 IRR = 19.44% • MBAM614 Class 4 - 26 13 NPV Profile A plot of an investment’s NPV at various discount rates is called its Net Present Value Profile May use the NPV Profile of a project to find its IRR – Plot various (NPV, discount rate) pairs – Make sure you have at least one NPV > 0 and one NPV < 0 – Point (discount rate) where NPV Profile crosses the NPV = 0 axis is the IRR • MBAM614 Class 4 - 27 Plotting NPVs Can use NPV Profile to solve for IRR graphically: $40 $20 NPV $ 0 -$20 -$40 -$60 -$80 • MBAM614 Class 4 - 28 DR 10% 15% 20% 25% 50% 19.44% NPV 40.80 17.72 - 2.08 -19.20 -77.78 Discount Rate 10% 30% 40% 50% 14 Multiple IRRs t=0 -252 1073 1145 -1942 -1707 1459 1202 -410 -316 NPV = 0 × 1 1431 1/1.3333 1/1.25001 2 -3035 × 1/1.25002 1/1.3333 3 2850 4 -1000 DR NPV 25.00% 0 33.33% 0 42.86% 0 66.67% 0 × 1/1.25003 1/1.3333 × 1/1.25004 1/1.3333 What’s going on here? What is the IRR? • MBAM614 Class 4 - 29 NPV Profile With Multiple IRRs NPV Profile 0.06 0.04 0.02 IRR = 25.00% IRR = 42.86% NPV (in $) 0 -0.02 -0.04 -0.06 -0.08 -0.1 20% IRR = 33.33% IRR = 66.67% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% Discount Rate • MBAM614 Class 4 - 30 15 Project Selection With Multiple IRRs Multiple IRRs are possible when cash flows change sign more than once t=0 -252 1 1431 2 -3035 3 2850 4 -1000 Cash Flow Sign Change 1 + Change 2 Change 3 + Change 4 - Must use NPV Rule in these cases • MBAM614 Class 4 - 31 Example: Bayman Oil Your oil company, Bayman Oil, has two possible well sites. One is shallow but doesn’t contain as much oil as the other. Projected costs and cash flows from developing each well are as follows: Project Well A Well B Yr 0 -$350 -$250 Yr 1 50 125 Yr 2 100 100 Yr 3 150 75 Yr 4 200 50 Plot the NPV Profiles for both projects. What are their IRRs? If an acceptable rate of return is 16%, should you develop either well? What if 12% is acceptable? If you can only afford to develop one well, which one is best? Which well has the highest NPV if the required return (discount rate) is 11%? If it’s 6%? Which well will you choose? • MBAM614 Class 4 - 32 16 Example: Bayman Oil NPVs Discount Rate 6% 7% 10% 11% 12% 15% 16% 20% IRR NPV A 75.5 59.1 27.4 17.6 8.2 -17.9 -26.0 -55.6 12.9% NPV B 59.5 53.5 36.8 31.5 26.5 12.2 7.7 -8.9 17.8% • MBAM614 Class 4 - 33 Example: Bayman Oil NPV Profiles 150 Well A 100 NPV (in $MM) NPVA = 75.5 59.5 NPVB = 31.5 NPVA = 17.6 Crossover Point ≈ 8.0% Acceptable Return = 16% 50 0 -50 Well B IRRA = 12.9% -100 2% 4% 6% IRRB = 17.8% 8% 10% 12% 14% 16% 18% 20% 22% 24% Discount Rate • MBAM614 Class 4 - 34 17 Crossover Rate The point at which the NPV profiles of two projects intersect (if they do) is called their Crossover Rate Two ways to find the crossover rate: – Plot NPV profiles – Take “differential” cash flows and solve for their IRR Project Well A Well B A-B Yr 0 Yr 1 Yr 2 -$350 50 100 -$250 125 100 -$100 -75 0 IRR of (A - B) = 8.06% IRR of (B - A) = 8.06% Yr 3 150 75 75 Yr 4 200 50 150 • MBAM614 Class 4 - 35 Mutually Exclusive Projects If selecting one project means another may not be taken, then the projects are Mutually Exclusive If projects are mutually exclusive, the project with the highest IRR may not have the highest NPV IRR Rule does not take account of project size (we want the project that adds greatest value) Use NPV Rule when projects are mutually exclusive • MBAM614 Class 4 - 36 18 IRR vs NPV For conventional (outflows early, inflows over project life), nonmutually exclusive projects, NPV and IRR Rules give identical results People often prefer talking about “rates of return” Doesn’t require a market discount rate to accept (if IRR is high enough) or reject (if IRR is too low). Still need to set “hurdle” rate Loan type (inflows early, then pay back) then IRR is borrowing rate and lower is better Cash flows alternate in sign ⇒ must use NPV Rule Mutually exclusive projects ⇒ must use NPV Rule Confusing, prone to misuse and often have to use NPV anyway • MBAM614 Class 4 - 37 Profitability Index The Profitability Index (PI) of a project is the present value of the future cash flows divided by the initial investment If a project has NPV > 0, then PI > 1 PI Rule is to accept projects with PI > 1 As with IRR, PI does not recognize project size for mutually exclusive projects Not looking for greatest return per $ but the project that adds greatest value • MBAM614 Class 4 - 38 19 Capital Budgeting in Practice Common practice is to use several methods – Some sort of DCF (NPV, IRR, DP, PI) – AAR or Payback Period In theory, this is to reduce uncertainty in estimating cash flows and discount rates In practice, probably also related to reward systems – Usually based on accounting figures – Incentive to select projects that make these #s look good • MBAM614 Class 4 - 39 Key Points 1. Payback Period is the time it takes to recover the original investment 2. AAR = (average net income) (average book value) 3. The IRR is the discount rate for which the NPV of all project cash flows is equal to 0 4. When projects are mutually exclusive or have cash flows of alternating sign, use NPV 5. PI = PV(all future cash flows) (initial investment) 6. ALWAYS USE NPV: ACCEPT WHEN NPV>0 • MBAM614 Class 4 - 40 20