Capital Budgeting Decision Rules

1. Capital Budgeting Decision Rules NPV IRR MIRR Profitability Index Payback Discounted Payback

2. Net Present Value A. Calculation • Forecast the incremental cash flow generated by the project • Determine the discount rate; which represents the opportunity cost of capital • Calculate the present value of all cash flows • Add discounted values and subtract the investments initial costs B. Decision Rule • Accept projects with NPV > 0 C. Interpretation • The NPV of an investment is the difference between its market value and its cost.

3. The Internal Rate of Return (IRR) A. Calculation • IRR is the discount rate which makes NPV = 0. • Is calculated by iterations or computer. B. Decision Rule • Accept projects with IRR greater than the opportunity cost of capital. C. Interpretation • The IRR is the discount rate that makes the estimated NPV of an investment equal to zero. Why might people prefer to think about the capital budgeting decision in terms of an interest rate rather than a present value?

4. NPV Illustrated (Calculation) 0 1 2 Initial outlay ($1,100) Revenues $2,000 Expenses 1,000 Cash flow $1,000 Revenues $1,000 Expenses 500 Cash flow $500 – $1,100.00 +454.54 +826.45 +$180.99 1 $500 x 1.10 1 $1,000 x 1.102 NPV

5. Internal Rate of Return Illustrated Initial outlay = -$1100 Year Cash flow 1 500 2 1000 • Find the IRR such that NPV = 0 500 1000 0 = -1100 + + (1+IRR)1 (1+IRR)2 500 1000 1100 = + (1+IRR)1 (1+IRR)2

6. NPV Illustrated (concluded) 0 1 2 Initial outlay ($1,100) Revenues $2,000 Expenses 1,000 Cash flow $1,000 Revenues $1,000 Expenses 500 Cash flow $500 – $1,100.00 +414.10 +658.90 $0.00 1 $500 x 1.207448 1 $1,000 x 1.2074482 NPV

7. CF 2nd CLR Work CF0 = -1100 ENTER C01 = 500 ENTER F01 = 1 ENTER C02 = 1000 ENTER F02 = 1 ENTER NPV I = 10 ENTER CPT $180.99 The cash flow registers have the same information as the NPV analysis. IRR CPT 20.74 % NPV using a Financial Calculator

8. Excel Calculations(double click on Excel Sheet)

9. Modified Internal Rate of Return (MIRR) • MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs. • TV is found by compounding inflows at cost of capital. • Thus, MIRR assumes cash inflows are reinvested at cost of capital.

10. MIRR Illustrated (I require to earn at least 10 percent on my investment, do the cash flows provide at least this much in return?) 0 1 2 Initial outlay ($1,100) Revenues $2,000 Expenses 1,000 Cash flow $1,000 Revenues $1,000 Expenses 500 Cash flow $500 Terminal Value: Positive Cash Flows $500 x 1.101 550 1550 PV outflows TV inflows TV PV = (1 + MIRR)2 1550 1100 = (1 + MIRR)2

11. Excel Calculations(double click on Excel Sheet)

12. Profitability Index • The profitability index (PI) is the present value of future cash flows divided by the initial cost. • It measures the “bang for the buck.” PV future CF PI = Initial Cost

13. PI Illustrated (Calculation) 0 1 2 Initial outlay ($1,100) Revenues $2,000 Expenses 1,000 Cash flow $1,000 Revenues $1,000 Expenses 500 Cash flow $500 Initial Cost +454.54 +826.45 +$1280.99 1 $500 x 1.10 1 $1,000 x 1.102 PV of future CF 1,280.99 PV future CF PI = = = 1.1645 1,100.00 Initial Cost

14. Payback Rule A. Calculation: The number of years for the project to return its investment. B. Decision rule • Accept projects with payback less than some specified period C. Interpretation • The payback period is the length of time until the sum of an investment’s cash flows equals its cost. (This does not imply that additional flows are profit.) D. Advantages • Simple to calculate E. Disadvantages • Does not allow for time value of money • Ignores cash flows after cutoff date • Does not consider the risk of the project

15. Payback Rule Illustrated 1 year and 600/1000 of the second years CFs 1. 6 years payback period. If this is less than the cut-off period, the project is acceptable.

16. Discounted Payback Rule Illustrated 1 year and 645.46/826.45 of the second years CFs 1. 78 years discounted payback period. If this is less than the cut-off period, the project is acceptable.

17. Excel Calculations(double click on Excel Sheet)

18. Advantages of NPV Correctly accounts for time value of money Incorporates the risk-adjusted discount rate Always gives the correct accept/reject decision Disadvantages of NPV None - (Unless if a preference by individuals toward another method is considered a disadvantage) Advantages of IRR Easy to understand and compare with other projects. Gives the same accept/reject decisions as NPV for projects that are (1) independent and (2) have conventional cash flows. Disadvantages of IRR Assumes reinvestment of cash flows at IRR Sometimes no IRR exists Does not differentiate between borrowing and lending Can have more than one IRR. Can give the wrong decision when comparing mutually exclusive problems. Can incorrectly rank projects Cannot consider changing interest rate expectations Net Present Value (NPV) and Internal Rate of Return (IRR)

19. Sometimes no IRR exists. .

20. IRR does not differentiate between borrowing and lending (Example 1).

21. IRR does not differentiate between borrowing and lending (Example 2)

22. Can have more than one IRR

23. Problems in Ranking Mutually Exclusive Projects. Mutually exclusive means that either A or B may be taken, but not both.