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1 Alternative Investment Rules (Text reference: Chapter 6) Topics data for examples net present value (NPV) rule internal rate of return (IRR) rule payback rule discounted payback rule average accounting return (AAR) rule profitability index (PI) rule techniques used in practice 1 Data for Examples: we will consider the following projects: Project A: cost at = 200,000 period cash flows 100,000 60, ,000 net income 20,000 30,000 20,000 Project B: cost at = 30,000 period cash flows 20,000 10,000 15,000 net income 6,000 3,000 6,000 Project C: cost at = 200,000 period cash flows 180,000 60,000 10,000 assume a discount rate of 10% for all three projects 2

2 Net Present Value (NPV) Rule definition: NPV PV future cashflows cost at rule: accept if NPV. More specifically, independent projects: accept if NPV mutually exclusive projects: accept project with highest NPV calculate NPV : NPV 23,140, NPV 7,716 if independent: choose both A and B if mutually exclusive: choose A only 3 NPV rule analysis: notes: - based on cash flow - must forecast all cash flows - considers all cash flows - can be hard to estimate discount rate - discounts cash flows (and incorporates time value of money) accepting positive NPV projects benefits shareholders by increasing the PV of their wealth an NPV profile is useful for analyzing the sensitivity of the NPV to the appropriate discount rate. The profile plots NPV as a function of the discount rate. 4

3 NPV profile discount rate 5% 10% 15% 20% NPV 44,682 23,140 4,652 (11,343) 50k 40k 30k 20k 10k -10k 5% 10% 15% 20% 5 Internal Rate of Return (IRR) Rule definition: IRR is the discount rate which results in NPV rule: accept if IRR is greater than the opportunity cost of capital. More specifically, independent projects: accept if IRR OCC mutually exclusive projects: accept project with highest IRR OCC calculate IRR IRR %, IRR % if independent: choose both A and B if mutually exclusive: project sizes differ, so can t tell (IRR says B, NPV says A) 6

4 IRR rule analysis: notes: - better than alternatives such as payback, AAR - mutually exclusive - scale - more intuitive than NPV - mutually exclusive - timing - coincides with NPV for - investing or financing / simple examples lending or borrowing - single number summary of - multiple IRRs project s profitability - comparison to discount rate if not constant over time (term structure of interest rates) most important alternative to the NPV approach IRR discount rate implies NPV in simple cases, always yields same decision as NPV for independent projects trial and error calculation (like yield to maturity for bonds) 7 IRR problem: mutually exclusive - scale affects mutually exclusive project decisions only do we prefer larger $ returns or larger % returns? calculate incremental IRR 8

5 IRR problem: mutually exclusive - timing affects mutually exclusive project decisions only discount rate 5% 10% 15% 20% NPV 44,682 23,140 4,652 (11,343) NPV 34,489 20,736 8,466 (2,546) 50k 40k 30k 20k 10k -10k 5% 10% 15% 20% 9 IRR problem: mutually exclusive - timing calculate incremental IRR 10

6 IRR problem: investing/lending vs. financing/borrowing affects mutually exclusive and independent project decisions consider a project D with cash flows exactly the reverse of project A cash flows (e.g. D = borrowing): period Project A -200, ,000 60, ,000 Project D 200, ,000-60, ,000 we find NPV 23,140, NPV 23,140 IRR %, IRR % IRR rule is reversed for financing/borrowing type projects: if CFs negative first, then investing/lending, rule is accept if IRR OCC if CFs positive first, then financing/borrowing, rule is accept if IRR OCC note: only works if sign of CFs changes only once 11 IRR problem: multiple IRRs affects mutually exclusive and independent project decisions consider project E: we find two IRRs! period Project E -4,000 25,000-25,000 IRR % and IRR % verify that letting equal IRR results in NPV in both cases if sign of cash flows changes times, there can be different IRRs! which IRR is correct? solution: with changing signs, ignore IRR and use the NPV rule 12

7 IRR problem: not constant over time affects mutually exclusive and independent project decisions term structure of interest rates states that rates (and so discount rates) vary depending on the timing of future CFs recall NPV can t compare IRR to the entire term structure of interest rates solution if term structure of interest rates becomes important, ignore IRR and use the NPV rule 13 Payback Period Rule definition: the payback period is the time required for the investment to pay back its cost rule: accept if payback period less than some acceptable threshold period (e.g. 2 years). More specifically, independent projects: accept payback threshold mutually exclusive projects: accept shortest payback threshold calculate payback for Project A payback periods, payback periods if independent: choose B only if mutually exclusive: choose B only 14

8 payback period rule analysis: notes: - simple rule (easy to use) - ignores time value of money - may be important for firms - ignores CFs after cutoff period with liquidity problems - ignores risk differences between projects - arbitrary payback threshold compute fractional years gives the number of years to recover investment cost becomes unreliable as time value of money becomes more important (i.e. larger number of periods, larger interest rate) 15 Discounted Payback Period Rule definition: the discounted payback period is the time required for an investment to pay back its cost, after discounting the project CFs rule: accept if less than threshold period (e.g. 2 years). More specifically, independent projects: accept if discounted payback threshold mutually exclusive projects: accept shortest discounted payback threshold calculate discounted payback for Project A discounted payback periods, discounted payback periods if independent: choose neither if mutually exclusive: choose neither 16

9 discounted payback period rule analysis: notes: - simple rule (easy to use) - arbitrary payback threshold - useful for firms - ignores CFs after cutoff period with liquidity problems - ignores some risk differences - considers timing of CFs between projects - can be hard to estimate discount rate discounted payback period payback period if we have already discounted all CFs, might as well compute NPV and use NPV rule 17 Average Accounting Return (AAR) Rule definition: average project earnings after taxes and depreciation, divided by average book value of investment during its life rule: accept if AAR specifically, acceptable return threshold (e.g. 10%). More independent projects: accept project if AAR threshold mutually exclusive projects: accept project with highest AAR threshold calculate AAR for Project A AAR %, AAR % if independent: choose both A and B; if mutually exclusive: choose B 18

10 average accounting return (AAR) rule analysis: - simple rule (easy to use) - does not use cash flows - sensitive to accounting methods and estimates - ignores timing of cash flows - arbitrary threshold rate - ignores risk differences between projects 19 Profitability Index (PI) Rule definition: PI rule: accept project if PI PV of CFs subsequent to initial investment initial investment 1. More specifically, independent projects: accept project if PI 1 mutually exclusive projects: accept project with highest PI 1 calculate PI for Project A PI, PI if independent: choose both A and B if mutually exclusive: since project sizes are different, can t tell (PI says choose B, NPV says choose A) 20

11 profitability index (PI) rule analysis: notes: - reflects time value of money - mutually exclusive - ignores scale - considers all cash flows - can be hard to estimate discount rate if PI 1, then NPV 0! can overcome the scale problem by looking at PI of incremental cash flows (A - B) useful when there is capital rationing rank projects according to PIs, and invest in projects with highest PIs until all capital is exhausted NPV rule is just as easy to use as PI (and doesn t suffer from scale problems) 21 Techniques used in Practice see text pp based on a 1995 survey of CFOs of large Canadian industrial firms, discounted cash flow methods (IRR, NPV) are the most popular methods payback is also quite popular most firms use NPV or IRR along with payback or AAR payback is most popular among small firms and for firms with CEOs who do not have an MBA firms in industries where cash flows are easier to forecast are more likely to use IRR or NPV 22

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