WACC: 6.4% (Same as our project!) Cash Flows: Year 0: -690,000 Year 1: 105,000 Year 2: 125,000 Year 3: 210,000 Year 4: 109,000 Yera 5: 255,000 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 (000) Balance -690 -690 105 -585 125 -460 210 -250 109 -141 255 WACC does not matter for the payback method. But we would use it in the discounted payback method. Years Create this balance column in Excel As each cash flow is earned, deduct that CF from the previous balance forward Note how many periods in which your CF is less than the balance forward record those years in the last column to the right Once your CF is greater than the absolute value of the balance forward - stop We have 4 full years plus some percentage of a year left. We calculate that percentage year by taking the balance forward and dividing by the remaining cash flow. In this case 141/255 or .55 of one year. This means that the payback on this project is 4 years and .55/100 of a year. 0 1 2 3 4 -0.55294 4.55 -5000 2000 2000 2000 9.70% 9.70% Cash flow Year 0 Cash Flow Year 1 Cash Flow Year 2 Cash Flow Year 3 IRR MIRR =MIRR(A1:A4,0.097,0.097) Note: no change in IRR to MIRR when finance rate and reinvest rate are the same as IRR. Notice what happens when we change the finance rate to 12% 9.70% Nothing =MIRR(A1:A4,0.12,0.097) Notice what happens when we change the reinvest rate to 6% 8.39% The reinvest rate is what we invest the proceed cash flows if different from the cost of capital. cost of capital. If you have an initial cash out flow of $1000 pays back $400 the first year, $300 the second year and $390 the third year, $500 CF0 CF1 CF2 CF3 CF4 i/y NPV CF -1000 400 300 390 500 PV -1000.000 363.6364 247.9339 293.0128 341.5067 Forumla =B9 =B3/(1+$B$8) =B4/((1+$B$8)^2) =B5/((1+$B$8)^3) =B6/((1+$B$8)^4) 10% 246.09 =NPV(B8,B3:B6)+B9 246.090 =SUM(D5:D9) Decision for NPV is: If NPV is greater than zero then accept. IRR is equal to the rate of return where NPV = 0; therefore we know IRR rate will be more than 10% Excel is the best way. For this the cash flows must be in order beginning with CF0 CF0 CF1 CF2 CF3 CF4 IRR -1000 400 300 390 500 20.43% =IRR(B23:B27) Decision is: If IRR is greater than the Cost of Capital (hurdle rate, internal expected rate, or we year and $390 the third year, $500 the fourth year you have a rate of return of 10%. The calculations are as followed: e as followed: Chapter 11 The Basics of Capital Budgeting Net Present Value (NPV) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR) Regular Payback Discounted Payback 11-1 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is capital budgeting? • • • Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures. Very important to firm’s future. 11-2 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Steps to Capital Budgeting 1. Estimate CFs (inflows & outflows). 2. Assess riskiness of CFs. 3. Determine the appropriate cost of capital. 4. Find NPV and/or IRR. 5. Accept if NPV > 0 and/or IRR > WACC. 11-3 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is the difference between independent and mutually exclusive projects? • • Independent projects: if the cash flows of one are unaffected by the acceptance of the other. Mutually exclusive projects: if the cash flows of one can be adversely impacted by the acceptance of the other. 11-4 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is the difference between normal and nonnormal cash flow streams? • • Normal cash flow stream: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal cash flow stream: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Examples include nuclear power plant, strip mine, etc. 11-5 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Net Present Value (NPV) • Sum of the PVs of all cash inflows and outflows of a project: N CFt NPV =  t ( 1 + r ) t =0 11-6 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Example Projects we’ll examine: Year 0 1 2 3 Cash Flow L S -100 -100 10 70 60 50 80 20 CF 0 -60 10 60 CF is the difference between CFL and CFS. We’ll use CF later. 11-7 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is Project L’s NPV? WACC = 10% Year 0 1 2 3 CFt -100 10 60 80 PV of CFt -$100.00 9.09 49.59 60.11 NPVL = $ 18.79 Excel: =NPV(rate,CF1:CFn) + CF0 Here, CF0 is negative. 11-8 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is Project S’ NPV? WACC = 10% Year 0 1 2 3 CFt -100 70 50 20 PV of CFt -$100.00 63.64 41.32 15.02 NPVS = $ 19.98 Excel: =NPV(rate,CF1:CFn) + CF0 Here, CF0 is negative. 11-9 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Solving for NPV: Financial Calculator Solution Enter CFs into the calculator’s CFLO register. CF0 = -100 CF1 = 10 CF2 = 60 CF3 = 80 Enter I/YR = 10, press NPV button to get NPVL = $18.78. 11-10 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Rationale for the NPV Method • • • NPV = PV of inflows – Cost = Net gain in wealth If projects are independent, accept if the project NPV > 0. If projects are mutually exclusive, accept projects with the highest positive NPV, those that add the most value. In this example, accept S if mutually exclusive (NPVS > NPVL), and accept both if independent. 11-11 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Internal Rate of Return (IRR) • IRR is the discount rate that forces PV of inflows equal to cost, and the NPV = 0: N CFt 0= t (1 + IRR) t =0 • • Solving for IRR with a financial calculator: – – Enter CFs in CFLO register. Press IRR; IRRL = 18.13% and IRRS = 23.56%. Solving for IRR with Excel: =IRR(CF0:CFn,guess for rate) 11-12 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. How is a project’s IRR similar to a bond’s YTM? • • • They are the same thing. Think of a bond as a project. The YTM on the bond would be the IRR of the “bond” project. EXAMPLE: Suppose a 10-year bond with a 9% annual coupon and $1,000 par value sells for $1,134.20. – Solve for IRR = YTM = 7.08%, the annual return for this project/bond. 11-13 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Rationale for the IRR Method • If IRR > WACC, the project’s return exceeds its costs and there is some return left over to boost stockholders’ returns. If IRR > WACC, accept project. • • If IRR < WACC, reject project. If projects are independent, accept both projects, as both IRR > WACC = 10%. If projects are mutually exclusive, accept S, because IRRs > IRRL. 11-14 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. NPV Profiles • A graphical representation of project NPVs at various different costs of capital. WACC 0 5 10 15 20 NPVL $50 33 19 7 (4) NPVS $40 29 20 12 5 11-15 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Independent Projects NPV and IRR always lead to the same accept/reject decision for any given independent project. NPV ($) IRR > r and NPV > 0 Accept. r > IRR and NPV < 0. Reject. r = 18.1% IRRL = 18.1% r (%) 11-16 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Mutually Exclusive Projects If r < 8.7%: NPVL > NPVS IRRS > IRRL CONFLICT NPV L If r > 8.7%: NPVS > NPVL , IRRS > IRRL NO CONFLICT S r 8.7 % r IRRL IRRs 11-17 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Finding the Crossover Rate • • • Find cash flow differences between the projects. See Slide 11-7. Enter the CFs in CFj register, then press ◼ IRR. Crossover rate = 8.68%, rounded to 8.7%. If profiles don’t cross, one project dominates the other. 11-18 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Reasons Why NPV Profiles Cross • • Size (scale) differences: the smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so a high WACC favors small projects. Timing differences: the project with faster payback provides more CF in early years for reinvestment. If WACC is high, early CF especially good, NPVS > NPVL. 11-19 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Reinvestment Rate Assumptions • • • • NPV method assumes CFs are reinvested at the WACC. IRR method assumes CFs are reinvested at IRR. Assuming CFs are reinvested at the opportunity cost of capital is more realistic, so NPV method is the best. NPV method should be used to choose between mutually exclusive projects. Perhaps a hybrid of the IRR that assumes cost of capital reinvestment is needed. 11-20 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Since managers prefer the IRR to the NPV method, is there a better IRR measure? • • Yes, MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. MIRR assumes cash flows are reinvested at the WACC. 11-21 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Calculating MIRR 0 10% -100.0 1 2 3 10.0 60.0 80.0 10% 10% -100.0 PV outflows MIRR = 16.5% $158.1 $100 = (1 + MIRRL)3 MIRRL = 16.5% 66.0 12.1 158.1 TV inflows Excel: =MIRR(CF0:CFn,Finance_rate,Reinvest_rate) We assume that both rates = WACC. 11-22 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Why use MIRR versus IRR? • • MIRR assumes reinvestment at the opportunity cost = WACC. MIRR also avoids the multiple IRR problem. Managers like rate of return comparisons, and MIRR is better for this than IRR. 11-23 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. What is the payback period? • • The number of years required to recover a project’s cost, or “How long does it take to get our money back?” Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for the project turns positive. 11-24 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Calculating Payback Project L’s Payback Calculation 0 1 2 3 CFt -100 10 60 80 Cumulative -100 -90 -30 50 PaybackL = 2 + 30 / 80 = 2.375 years PaybackS = 1.600 years 11-25 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Strengths and Weaknesses of Payback • Strengths • Weaknesses – Provides an indication of a project’s risk and liquidity. – Easy to calculate and understand. – Ignores the time value of money. – Ignores CFs occurring after the payback period. 11-26 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Discounted Payback Period Uses discounted cash flows rather than raw CFs. 0 10% 1 2 3 10 60 80 CFt -100 PV of CFt -100 9.09 49.59 60.11 Cumulative -100 -90.91 -41.32 18.79 Disc PaybackL = 2 + 41.32 / 60.11 = 2.7 years 11-27 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Find Project P’s NPV and IRR Project P has cash flows (in 000s): CF0 = -$800, CF1 = $5,000, and CF2 = -$5,000. 0 WACC = 10% -800 • • • • 1 2 5,000 -5,000 Enter CFs into calculator CFLO register. Enter I/YR = 10. NPV = -$386.78. IRR = ERROR Why? 11-28 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Multiple IRRs NPV IRR2 = 400% 450 0 -800 100 400 WACC IRR1 = 25% 11-29 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. Why are there multiple IRRs? • • • • At very low discount rates, the PV of CF2 is large and negative, so NPV < 0. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. In between, the discount rate hits CF2 harder than CF1, so NPV > 0. Result: 2 IRRs. 11-30 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. When to use the MIRR instead of the IRR? Accept Project P? • • When there are nonnormal CFs and more than one IRR, use MIRR. – PV of outflows @ 10% = -$4,932.2314. – TV of inflows @ 10% = $5,500. – MIRR = 5.6%. Do not accept Project P. – NPV = -$386.78 < 0. – MIRR = 5.6% < WACC = 10%. 11-31 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
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