**MBA 643Managerial FinanceLecture 5: Capital Budgeting** Decision Rules Spring 2006 Jim Hsieh

**Investment Criteria for Capital Budgeting** • How should a firm make an investment decision? • What is the underlying goal? • What assets should we buy? Should we take the project(s)? • What is the right decision criterion? • These questions are correlated. • We focus on the last question in this lecture.

**Net Present Value** • Definition: The net present value (NPV) of an investment is the PV of the cash flows from the investment less the cost of the investment. • NPV = - Initial cost + PV(expected future CFs) • A generic form: • C: Cash flow (could be positive or negative) • T: Time period of the investment • r: Discount rate

**More on the Discount Rate, r** • Discount rate = Opportunity cost of capital • Expected rate of return given up by investing in a project • Reflects the risk of the cash flows from the project • Important: The discount rate does NOT reflect the risk of the firm or the risk of the firm’s previous projects.

**Net Present Value Rule** • Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost. • Rule:Accept the project if NPV>0; Reject the project if NPV<0 • Accept all projects with positive NPVs. • If managers can only accept one project, choose the one with the highest NPV. • For mutually exclusive projects

**Example 1A – NPV Rule** • Your firm is considering whether to invest in a new product. The costs associated with introducing this new product and the expected cash flows over the next four years are listed below. (Assume these cash flows are 100% likely). The appropriate discount rate for these cash flows is 20% per year. Should the firm invest in this new product? Costs:($ million) Promotion and advertising 100 Production & related costs 400 Other 100 Total Cost 600 • Initial Cost: $600 million and r = 20% • The cash flows ($million) over the next four years: Year 1: $200; Year 2: $220; Year 3: $225; Year 4: $210 • Should the firm proceed with the project?

**Example 1A – NPV Rule (cont’d)** 1/(1.20)1 166.67 1/(1.20)2 152.78 1/(1.20)3 130.21 1/(1.20)4 101.27 (49.07)

**Example 2A – NPV Rule** • As a financial manager, you have to choose one of the two projects available to your company. Which project should you choose? Both projects have the opportunity cost of capital, r=10%. 1/1.1 9.09 63.63 1/1.12 49.59 41.32 1/1.13 60.11 15.02 18.79 19.97

**Other Capital Budgeting Rules-- The Payback Rule** • Payback period = The length of time until the accumulated cash flows from the investment equal or exceed the original cost • Payback Rule: A project should be accepted if its payback period is less than the pre-specified cutoff period. Otherwise, reject it.

**Example 1B – The Payback Rule** • It has been decided that the project should be accepted if the payback period is 3 years or less. Should you accept the project? • Exercise: What are the payback period for projects L and S in Example 2A? Answer: PaybackL=2.4 years; PaybackS=1.6 years (400) (180) 45 255 2+180/225=2.8

**Weaknesses of the Payback Rule** • Martin Co. has 3 projects available. If you were the manager of the company, which project should you choose? • The payback rule ignores time value of money. • It also ignores cash flows occurring after the payback period. 2 2 2 +7,249 -264 -347

**Other Capital Budgeting Rules-- The “Discounted” Payback** Rule • Discounted payback period = The length of time until the accumulated “discounted” cash flows from the investment equal or exceed the original cost • Discounted Payback Rule: A project should be accepted if its discounted payback period is less than the pre-specified cutoff period. Otherwise, reject it.

**Example 1C – The Discounted Payback Rule** • It has been decided that the project should be accepted if the payback period is 3 years or less. Should you accept the project? r = 20% 1/(1.20)1 (433.33) 1/(1.20)2 (280.56) 1/(1.20)3 (150.35) 1/(1.20)4 (49.07) N/A

**Other Capital Budgeting Rules-- The Internal Rate of Return** (IRR) Rule • IRR is the discount rate, r, that makes the NPV equal to zero. • It makes the PV of future cash flows equal to the initial cost of the investment.

**The IRR Rule** • Rule: Invest in any project if its IRR is higher than the required rate of return (discount rate). • IRR is difficult to calculate. • Need to use a financial calculator or Excel spreadsheet. • Could first calculate NPV, and then use the answer to get a first good guess about the IRR.

**Example 1D – The IRR Rule** • In Excel -> Tools -> Goal Seek

**Example 1D – The IRR Rule** NPV 50 Crossover rate: r = 8.68 NPV = 22.32 40 30 20 10 r=23.56 Discount rate, % 5 10 15 20 25 30 -10 r=18.13 Project L Project S

**Comparing IRR with NPV** • IRR and NPV rules lead to identical decisions IF the following conditions are satisfied: • Cash flows are “conventional”: The first cash flow (the initial investment) is negative and all the remaining cash flows are positive. • Project is independent: The decision to accept or reject the project does not affect the decision to accept or reject any other projects. • When one or both of these conditions are violated, IRR and NPV could lead to different conclusions!

**Potential Problems with the IRR Rule-- (1). Unconventional** Cash Flows • Example 3: A strip-mining project requires an initial investment of $60. The cash flow in the first year is $155. In the second year, the mine is depleted, but the firm has to spend $100 to restore the land. • NPV = -$60 + 155/(1 + r) – 100/(1 + r)2 Discount Rate (r) NPV 0.00% –$5.00 10.00 – 1.74 20.00 – 0.28 25.00 0.00 30.00 0.06 33.33 0.00 40.00 – 0.31 • Generally, the number of possible IRRs is equal to the number of changes in the sign of the cash flows. IRR #1 IRR #2

**Potential Problems with the IRR Rule-- (2). Mutually** Exclusive Projects • Mutually exclusive projects: If taking one project implies another project is not taken, the projects are mutually exclusive. The one with the highest IRR may not be the one with the highest NPV. • Example 1D • Example 4: Project A has a cost of $500 and cash flows of $325 for two periods, while project B has a cost of $400 and cash flows of $325 and $200 in years 1 and 2, respectively.

**Example 4 (cont’d)** 19.43% 22.17% Project B appears to be better because of the higher return. But …

**Example 4 (cont’d)** Discount RateNPV(A) NPV(B) 0.00% $150.00 $125.00 5.00 104.32 100.00 10.00 64.05 60.74 15.00 28.36 33.84 20.00 -3.47 9.72 • Which project is preferred depends on the discount rate. • Project A has a higher NPV at a 10% discount rate • Project B has a higher NPV at a 15% discount rate.

**The IRR Rule – Conclusion** • Advantages • Closely related to NPV • Easy to understand and communicate • Disadvantages • May result in multiple answers • May lead to incorrect decisions • Not always easy to calculate • Very Popular: People like to talk in terms of returns • 99% using IRR rule versus 85% using NPV rule

**Evaluating Equipment with Different Economic Lives** • Example 5: As a production manager, you need to choose between two machines, L and S. The two machines are designed differently but have identical capacity and do exactly the same job. Which machine should you choose? • Machines L and S need to be replaced every 3 and 2 years, respectively. 25.69 21.00

**Evaluating Equipment with Different Economic Lives** • Definition: Equivalent annual cost (EAC): The present value of a machine’s costs calculated on an annual basis. • EAC = Present value of costs/annuity factor • EAC rule: Choose the machine that has the lowest equivalent annual cost.

**Example 5 (cont’d)** • For Machine L: 3-year annuity factor = 1/0.06-1/[0.06*1.063] = 2.673 EACL = 25.69/2.673 = $9.61 • For Machine S: 2-year annuity factor = 1/0.06-1/[0.06*1.062] = 1.833 EACL = 21.00/1.833 = $11.46 • Machine L is a better choice because it has lower annual cost.