# Alternative Investment Rules. Data for Examples

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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 AFM Alternative Investment Rules Slide 1 Data for Examples we will consider the following projects: Project A: cost at (t = 0) = 200,000 period cash flows 100,000 60, ,000 net income 20,000 30,000 20,000 Project B: cost at (t = 0) = 30,000 period cash flows 20,000 10,000 15,000 net income 6,000 3,000 6,000 Project C: cost at (t = 0) = 200,000 period cash flows 180,000 60,000 10,000 assume a discount rate of 10% for all three projects AFM Alternative Investment Rules Slide 2

2 Net Present Value (NPV) Rule definition: NPV = PV future cash flows cost at t = 0 NPV rule: for independent projects: accept if NPV 0 for mutually exclusive projects: accept project with highest NPV 0 calculate NPV A : NPV A = 23,140, NPV B = 7,716 if independent: choose both A and B if mutually exclusive: choose A AFM Alternative Investment Rules Slide 3 Cont d NPV rule analysis: Advantages Disadvantages - 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) notes: 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. AFM Alternative Investment Rules Slide 4

3 NPV profile discount rate r 5% 10% 15% 20% NPV A 44,682 23,140 4,652 (11,343) NPV 50,000 40,000 30,000 20,000 10, ,000 5% 10% 15% 20% r AFM Alternative Investment Rules Slide 5 Internal Rate of Return (IRR) Rule definition: IRR is the discount rate which results in NPV = 0 (basic) IRR rule: for independent projects: accept if IRR OCC for mutually exclusive projects: accept project with highest IRR OCC (if the projects are the same size) calculate IRR A : IRR A = 16.4%, IRR B = 25.2% if independent: choose both A and B if mutually exclusive: project sizes differ, so can t tell AFM Alternative Investment Rules Slide 6

4 IRR rule analysis: Advantages Disadvantages - better than alternatives such as payback, AAR - mutually exclusive - scale - more intuitive than NPV - mutually exclusive - timing - coincides with NPV for simple examples - investing vs. financing - single number summary of - multiple IRRs project s profitability - comparison to discount rate with non-flat term structure notes: most important alternative to the NPV approach IRR discount rate NPV 0 (in simple cases) in simple cases, always yields same decision as NPV for independent projects trial and error calculation (like yield to maturity for bonds) AFM Alternative Investment Rules Slide 7 Cont d IRR problem: mutually exclusive - scale affects mutually exclusive project decisions only do you prefer larger \$ returns or larger % returns? calculate incremental IRR: AFM Alternative Investment Rules Slide 8

5 IRR problem: mutually exclusive - timing affects mutually exclusive project decisions only discount rate r 5% 10% 15% 20% NPV A 44,682 23,140 4,652 (11,343) NPV C 34,489 20,736 8,466 (2,546) NPV 50,000 40,000 A C 30,000 20,000 10, ,000 5% 10% 15% 20% r AFM Alternative Investment Rules Slide 9 Cont d IRR problem: mutually exclusive - timing calculate incremental IRR: AFM Alternative Investment Rules Slide 10

6 IRR problem: investing/lending vs. financing/borrowing affects mutually exclusive and independent projects consider a project D with cash flows exactly the reverse of project A cash flows (e.g. D = borrowing): we find: period Project A -200, ,000 60, ,000 Project D 200, ,000-60, ,000 NPV A = 23,140, NPV D = 23,140 IRR A = 16.4%, IRR D = 16.4% IRR rule is reversed for financing/borrowing type projects: for investing/lending, rule is accept if IRR OCC for financing/borrowing, rule is accept if IRR OCC note: only works if sign of cash flows changes only once AFM Alternative Investment Rules Slide 11 Cont d IRR problem: multiple IRRs affects mutually exclusive and independent projects consider project E: period Project E -4,000 25,000-25,000 we find two IRRs, IRR E = 25% and 400% (verify that each of these discount rates results in NPV = 0) if sign of cash flows changes n times, there can be n different IRRs which IRR is correct? solution: with changing signs, ignore IRR and use NPV AFM Alternative Investment Rules Slide 12

7 IRR problem: non-flat term structure affects mutually exclusive and independent projects a non-flat term structure implies that discount rates vary depending on the timing of future cash flows recall NPV = T t=0 C t (1 + r t ) t can be hard to compare IRR to the entire term structure of interest rates example: two year project, IRR = 5%, r 1 = 4%, r 2 = 6% solution: if term structure of interest rates is important, ignore IRR and use NPV AFM Alternative Investment Rules Slide 13 Payback Rule definition: the payback period is the time required for an investment to recover its cost payback rule: for independent projects: accept if payback threshold for mutually exclusive projects: accept project with shortest payback threshold calculate payback for Project A: payback A = 2.36 periods, payback B = 2 periods if independent: choose B only if mutually exclusive: choose B only AFM Alternative Investment Rules Slide 14

8 payback rule analysis: Advantages Disadvantages - simple rule (easy to use) - ignores time value of money - may be important for firms - ignores cash flows after threshold with liquidity problems - ignores risk differences between projects - arbitrary payback threshold notes: 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 discount rate) AFM Alternative Investment Rules Slide 15 Discounted Payback Rule definition: the discounted payback period is the time required for an investment to recover its cost, after discounting the project cash flows discounted payback rule: for independent projects: accept if discounted payback threshold for mutually exclusive projects: accept project with shortest discounted payback threshold calculate discounted payback for Project A: AFM Alternative Investment Rules Slide 16

9 discounted payback for A = 2.72 periods, for B = 2.32 periods if independent: choose neither if mutually exclusive: choose neither discounted payback period rule analysis: notes: Advantages Disadvantages - simple rule (easy to use) - arbitrary payback threshold - useful for firms - ignores cash flows after threshold with liquidity problems - ignores some risk differences - considers timing of cash flows between projects - can be hard to estimate discount rate discounted payback period > payback period if we have already discounted all cash flows, just use NPV AFM Alternative Investment Rules Slide 17 Average Accounting Return (AAR) Rule definition: AAR is average project earnings after taxes and depreciation, divided by average book value of investment during its life AAR rule: for independent projects: accept project if AAR threshold mutually exclusive projects: accept project with highest AAR threshold calculate AAR for Project A: AFM Alternative Investment Rules Slide 18

10 AAR A = 23.3%, AAR B = 33.3% if independent: choose both A and B if mutually exclusive: choose B average accounting return (AAR) rule analysis: Advantages Disadvantages - 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 AFM Alternative Investment Rules Slide 19 Profitability Index (PI) Rule definition: PI = PI rule: PV of cash flows after initial investment initial investment for independent projects: accept if PI 1 for mutually exclusive projects: accept project with highest PI 1 (if they are the same size) calculate PI for Project A: PI A = 1.12, PI B = 1.26 if independent: choose both A and B if mutually exclusive: project sizes differ, so can t tell AFM Alternative Investment Rules Slide 20

11 PI problem: mutually exclusive - scale affects mutually exclusive project decisions only calculate incremental PI: AFM Alternative Investment Rules Slide 21 Cont d profitability index (PI) rule analysis: Advantages Disadvantages - reflects time value of money - mutually exclusive - ignores scale - considers all cash flows - can be hard to estimate discount rate notes: if PI > 1, then NPV > 0! can overcome the scale problem by looking at PI of incremental cash flows useful when there is capital rationing (i.e. insufficient capital to undertake all desirable projects) rank projects according to PIs, and invest in projects with highest PIs until all capital is used NPV rule is just as easy to use as PI (and doesn t suffer from scale problems) AFM Alternative Investment Rules Slide 22

12 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 AFM Alternative Investment Rules Slide 23

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