Chapter 8 NPV and Other Investment Criteria CAPITAL BUDGETING TERMS Capital budgeting is where we start to pull all of the tools and techniques we ve learned so far together (TVM, cash flow analysis, etc.) and use them to address perhaps the most important decision in finance: What assets should we buy? What investments should we make? One of the first steps in selecting among potential investments is to decide what kind of interaction may exist among the opportunities. Project interactions: 1) Independent projects 2) Mutually exclusive projects CAPITAL BUDGETING CRITERIA 1: NET PRESENT VALUE Several measures can be used to quantify the choice among possible capital investment projects. The main ones are: NPV, IRR, and payback period. Net Present Value Net Present Value (NPV) is a measure of the dollar difference between an investment s market value and its cost (i.e., NPV measures the dollar value added). Market value = PV of future cash flows. Also called Discounted Cash Flow analysis (DCF). N CFt NPV = (1 r t t 0 ) NPV is the sum of all the discounted cash flows (with the correct sign!). F301 Page 1
General NPV decision rule: Note: NPV is the best measurement tool for capital budgeting decisions. It is the only capital budgeting technique that is always consistent with the goal of the financial manager. Example: Assume you have the following information for a project. Initial outlay = $1,100 Required return = 10% Year 1 cash flow = $500 Year 2 cash flow = $1,000 NPV = NPV decision rule for mutually exclusive projects: Example -- Two mutually exclusive investment opportunities Assume that we can choose one of the following two projects. The required return is 5%. Project A Project B Discounted Discounted YR cash flows cash flows PV cash flows cash flows PV 0-100 -100-100 -100-100 -100 1 52 52/(1.05) 49.52 41 41/(1.05) 39.05 2 63 63/(1.05) 2 57.14 55 55/(1.05) 2 49.89 3 77 77/(1.05) 3 66.52 110 110/(1.05) 3 95.02 NPV = +73.18 NPV = +83.96 Both projects are value-adding, but are mutually exclusive. Note: With the exception of the NPV technique, all other investment criteria may fail for mutually exclusive projects since they do not quantify project size. F301 Page 2
CAPITAL BUDGETING CRITERIA 2: INTERNAL RATE OF RETURN (IRR) Definition of IRR: CF1 CF2 CF3 NPV = $0 = CF0 2 ( 1 IRR) ( 1 IRR) ( 1 IRR) N CFt Basic IRR equation: 0 t t 0( 1 IRR) 3... Finding the IRR is a trial and error process. Use the cash flow menus on a financial calculator (or use a spreadsheet). Decision rule for IRR: Example: Find the IRR of the following series of cash flows. Year Cash flow 0-200 1 50 2 100 3 150 50 100 150 NPV = 0 200 2 3 Said another way, the IRR is the rate which makes the discounted future cash flows equal to the amount of the initial investment. 50 100 200 2 150 3 F301 Page 3
Solve using trial and error: Discount rate NPV 0% 10% 20% Solve using IRR function on your financial calculator: The relationship between the discount rate, the IRR, and value-added can be illustrated with an NPV profile. NPV profile: A plot of. Example: Construct an NPV profile based on the following cash flows: Year Cash Flow 0 -$275 1 100 2 100 3 100 4 100 First, calculate the NPV of the cash flows for several discount rates. Discount rate 0% 5% 10% 15% 20% 25% NPV Next, find the IRR =. Construct the NPV profile: F301 Page 4
NPV Profile and the Crossover Rate (also called the incremental IRR): The crossover rate is the discount rate which makes the NPV of two projects the same. Crossover rate calculations: Take the differences of the cash flows (each period) between two projects and then calculate the IRR of the newly created series of cash flow differences. e.g.: Project A Project B Period cash flows cash flows Incremental CF 0-500 -400 1 325 325 2 325 200 IRR = IRR = IRR (incremental) = This NPV profile shows the three conclusions that can be drawn about the discount rate and these two projects: F301 Page 5
NPV vs. IRR Form of the cash flows If cash flows are conventional (i.e., the investment is made at t = 0 and benefits, or + CF s, are received over the remainder of the project s life), and If projects are independent, Then IRR decision rule gives same result as General NPV decision rule. e.g. Conventional cash flows Unconventional cash flows t = 0 - - t = 1 + + t = 2 + - t = 3 + + Example: Multiple IRRs With unconventional cash flows, there can be multiple IRRs! Assume you are considering a project with the following cash flows. What is the project s IRR? Year Cash flow 0-252 1 1431 2-3035 3 2850 4-1000 F301 Page 6
There are four IRR solutions here (25%, 33.33%, 42.86%, 66.67%) because of the four changes in cash flow signs over the project s life. Problems with IRR: 1. With mutually exclusive projects: Highest IRR does not imply the highest NPV or value added. 2. If cash flows are unconventional and alternate back and forth between negative and positive more than once, more than one IRR solution is possible. 3. There are some cash flow sequences for which there is no IRR. (i.e., we can t find a rate that forces NPV to be zero). Strong points of IRR: CAPITAL BUDGETING CRITERIA 3: PAYBACK PERIOD Payback period: The length of time until the accumulated cash flows equal or exceed the initial investment. Payback period rule: accept, if a project s payback is less than a desired number of years. Problems with the payback period criterion: 1. Does not consider TVM and project size. 2. Doesn t explicitly consider risk (i.e., no discount rate used). 3. How do we set the cut-off point (desired number of years)? 4. Biased toward short-term investments (ignores cash flows beyond the payback period). F301 Page 7