FIN 3303.004 October 30, 2008 Payback Period Evaluate projects according to different techniques Choose the best projects to invest the firm’s capital Example: CF0= -100,000 CF1= 50,000 CF2= 30,000 CF3=40,000 CF4=20,000 Payback Period payback period = 2.5 years Accept or reject? Corporation set a max payback period of 2 yrs = REJECT Corporation set a max payback period of 3 yrs = ACCEPT Payback Period Discounted Payback Period Acceptance Criteria: Accept a project if payback period is less than or equal to max. payback period allowed Net Present Value (NPV) Sum of all PVs of CFs for a project (like the profit for a project) NPV= CF0 + (CF1/(1+r)1) + (CF2/(1+r)2) + (CFn/(1+r)n) r = discount rate; required rate of return for that project Example 2: r= 10% NPV= -100,000 + (50,000/1.11) + (30,000/1.12) + (40,000/1.13) + (20,000/1.14) NPV = $13, 961 ACCEPT (positive) If r=20%, NPV= -4,707 REJECT (negative) NPV Acceptance Criteria: accept a project if (given a certain required rate of return) NPV > 0 Internal Rate of Return (IRR) Required rate of return that makes NPV=0 NPV= CF0 + (CF1/(1+r)1) + (CF2/(1+r)2) + (CFn/(1+r)n) 0 = CF0 + (CF1/(1+r)1) + (CF2/(1+r)2) + (CFn/(1+r)n) Required rate of return is given 0 = -Price + (CF1/(1+r)1) + (CF2/(1+r)2) + (CFn/(1+r)n) YTM for a bond is like the IRR for a project (only difference - semiannually v. annually payment for YTM) Example: 0 = -100,000 + (50,000/1+r) + (30,000/1+r2) + (40,000/1+r3) + (20,000/1+r4) Calculate w/ financial calculator IRR = 17.17% How to calculate on financial calculator: CF 2nd CLR WORK CF0= -100,000 ENTER, ARROW DOWN CO1= 50,000 ENTER, ARROW DOWN CO2=30,000 same CO3=40,000 same CO4=20,000 same IRR CPT How to calculate on TI-83 or 84 APPS Finance #8 IRR(CF0,{CF1,CF2,CF3,…CFn}) CF0 – negative # Accept or Reject? IRR=17.17% Required rate of return for this project=20% REJECT Required rate of return for this project=15% ACCEPT IRR Criteria: Accept project if IRR is greater than or equal to required rate of return Advantages: most intuitive technique Disadvantages: “Multiple solution” problem CF= -100,000, CF1=200,000, CF2=-50,000 IRR formula: 0=-100,000 + 200,000/(1+r) – 50,000/(1+r)2 Get 2 answers = IRR1, IRR2 “Scale” Problem Project 1: IRR=25% NPV=$75,000 Project 2: IRR=15% NPV=$350,000 If choosing, pick Project 1 if evaluate IRR. Pick 2 if evaluating NPV. NPV & IRR Graph Negative relationship b/t NPV & required rate of return If the required RoR increases, NPV decreases. NPV 0 10% IRR=17.17% 20% Required RoR Probability Index (PI) PI = [(CF1/(1+r)1) + (CF2/(1+r)2) + (CFn/(1+r)n)] / -CF0 Example: What’s the PI if r=15%? PI = [(50,000/(1.15)1) + (30,000/(1.15)2) + (40,000/(1.15)3) + (20,000/(1.15)4)] / 100,000 PI = 1.039 PI = [∑PVs (future)] / -CF0 NPV = CF0 + ∑PVs (futures) Acceptance Criteria: If acceptance criteria: NPV > 0 If acceptance criteria: PI > 1 If IRR = 16%, Required RoR = 15% NPV > 0