Weighing Net Present Value and Other Capital Budgeting Criteria Chapter 13 Fin 325, Section 04 - Spring 2010 Washington State University

Introduction In previous chapters we learned how to Calculate the firm’s cost of capital Estimate a project’s cash flows Now, we need to finish the analysis of the project to determine whether the firm should proceed with a potential project.

Capital Budgeting Techniques Most commonly-used methods to evaluate projects: Net Present Value (NPV) Payback (PB) Discounted Payback (DPB) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR) Profitability Index (PI) NPV is generally the preferred technique for most project evaluations There are situations where you may want to use one of the other techniques in conjunction with NPV

Net Present Value NPV represents the “purest” of the capital budgeting rules It measures the amount of value created by the project NPV is completely consistent with the overall goal of the firm: to maximize firm value

NPV is the sum of the present value of every project cash flow (including the initial investment)

NPV Benchmark NPV includes all of the project’s cash flows, both inflows and outflows Since it involves finding the present values of every cash flow using the appropriate cost of capital as the discount rate, anything greater than zero represents the amount of value added above and beyond the required return Accept project if NPV > 0 Reject project if NPV < 0

Example A project has a cost of $25,000, and annual cash flows as shown. Calculate the NPV of the project if the discount rate is 12 percent i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000

Financial Calculator solution: CF0 = (25,000) CF1 = 8,500 CF2 = 12,000 CF3 = 13,500 CF4 = 15,000 I = 12 percent NPV = 11,297.42

Interpretation: Do we like this project? Yes – it has a positive NPV If the market agrees with our analysis, the value of our firm will increase by $11,297 due to this project When will the value-added occur? When the project is complete? NO – it will occur immediately upon the announcement that we are taking the project

NPV Strengths and Weaknesses NPV not only provides a go/no-go decision, but it also quantifies the dollar amount of the value added NPV is not a ratio It works equally well for independent projects and for choosing between mutually-exclusive projects Accept the project with the highest positive NPV Weakness Misinterpretation Comparing NPV to the cost of the project is wrong! Not understanding that the cost is already incorporated into the NPV

Payback Answers the question: How long will it take us to recoup our costs? Has intuitive appeal Remains popular because it is easy to compute Built-in assumptions: Cash flows are normal Assumes cash flows occur smoothly throughout the year

Example Refer to the problem we worked earlier. Compute the payback. 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 Cumulative (25,000) (16,500) (4,500) Payback will occur during the 3rd year Payback = 2 + 4,500/13,500 = 2.33 years

Payback Benchmark Firms set some maximum allowable payback Often set arbitrarily – one of payback’s greatest weaknesses Accept project if calculated payback < Maximum allowable payback Reject project if calculated payback > Maximum allowable payback

Discounted Payback One of the major problems with payback is that it ignores the time value of money It treats all cash flows equally regardless of when they occur Discounted payback fixes this particular problem We convert the raw cash flows to their present values, and then calculate payback like before using these discounted cash flows

Example i=12% Discounted Payback will occur during the 3rd year 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000 CF present values (25,000) 7,589 9,566 9,609 9,533 Cumulative (25,000) (17,411) (7,845) Discounted Payback will occur during the 3rd year Discounted Payback = 2 + 7,845/9,609 = 2.82 years

Discounted Payback benchmark Like payback, management will likely set an arbitrary benchmark Notice that for normal projects DPB will be larger than PB The cash flows that are “chipping away” at the initial cost are the smaller discounted cash flows, so it takes longer Hopefully, the arbitrary benchmark would at least take that effect into account

PB and DPB Strengths and Weaknesses Easy to calculate Intuitive Weaknesses: Both methods have severe weaknesses that make them unsuitable to be the primary method used to select projects PB ignores the time value of money Both methods rely on arbitrary accept/reject benchmarks Both methods ignore cash flows that occur after the payback period. This is perhaps the most serious flaw of all

Internal Rate of Return IRR is the most popular technique to analyze projects Often referred to as “the return on the project” IRR is generally consistent with Net Present Value Problems occur if cash flows are not normal Problems can occur when choosing among mutually exclusive projects

IRR is so closely related to NPV that it is actually defined in terms of NPV IRR is the discount rate that results in a zero NPV

Internal Rate of Return benchmark Once we calculate IRR, we must compare it to the cost of capital (investors’ required return) to see if the project is acceptable We only want to invest in projects where the rate we expect to get (IRR) exceeds the rate investors require (i)

Example Refer to our previous problem. Calculate the IRR of the project. i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000

Financial Calculator solution: CF0 = (25,000) CF1 = 8,500 CF2 = 12,000 CF3 = 13,500 CF4 = 15,000 IRR = ? = 30.08% Do we like this project? Yes – the IRR is greater than the required return

Problems with IRR IRR will be consistent with NPV as long as: The project has normal cash flows Projects are independent NPV profiles The NPV profile is a graph of NPV versus different discount rates It can help us determine if we may encounter a problem with IRR

For normal cash flows, the NPV profile slopes downward IRR can be found where the profile crosses the x-axis (i.e. where NPV = 0, the definition of IRR)

For non-normal cash flows there will be multiple IRRs for the same project IRRs represent the solution to a mathematical series. These solutions are called ‘roots’, and a series will have as many roots as there are sign changes. This is Descartes’ Rule of Signs, discovered in 1637. For us, this means that there will be as many IRRs as there are sign changes in the cash flows.

- + + + + - + + + - - + + - + + Examples: In our normal project, we have one IRR because we have one sign change - + + + + What if a project involves a cleanup at the end? We might have two sign changes (and two IRRs): - + + + - What if a project has to shut down in the 3rd year for maintenance, and then starts up again? We might have three sign changes: - + + - + +

Here is a sample NPV profile for a project with non-normal cash flows Here is a sample NPV profile for a project with non-normal cash flows. Notice that the line crosses the x-axis twice: Fortunately, we can fix the problem of multiple IRRs using a technique called Modified Internal Rate of Return (MIRR)

Calculating MIRR Calculating MIRR is a three-step process: Step 1: Calculate the PV of the cash outflows using the required rate of return. Step 2: Calculate the FV of the cash inflows at the last year of the project’s time line using the required rate of return. Step 3: Calculate the MIRR, which is the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes PVoutflows = PVinflows

Example Calculate the MIRR of the following project: 1 2 3 4 5 i = 9% 1 2 3 4 5 i = 9% -10,000 4,000 6,000 -5,000 12,000 15,000

Step 1: PV of outflows = -13,861 Step 2: FV of inflows = 41,497 Step 3: Calculate MIRR MIRR = 24.52% Exceeds the required return of 9%, so accept project INPUT 5 -13,861 N I/YR PV PMT FV OUTPUT 41,497 24.52

Profitability Index Based on NPV Measures “bang per buck invested” PI benchmark: Accept project if PI > 0 Reject project if PI < 0

Example Calculate the PI of our example Recall that the NPV = $11,297 = 45.19% PI indicates that we should accept the project i=12% 0 1 2 3 4 (25,000) 8,500 12,000 13,500 15,000