Lecture 15. Thursday Mar 25 th. Advanced Topics in Capital Budgeting

Transcription

1 Lecture 15. Thursday Mar 25 th

2 Equal Length Projects If 2 Projects are of equal length, but unequal scale then: Positive NPV says do projects Profitability Index allows comparison ignoring scale If cashflows are well behaved (outgoings, then ingoings) IRR will also allow comparison. 2

3 Projects of Unequal Lengths A 4 year project (B) and a 3 year project (A) both with the same NPV: Required rate of return 15.00% Periods Project NPV IRR A (99.88) $ % B (100.00) $ % 3

4 Projects of Unequal Lengths A 4 year project (B) and a 3 year project (A) both with the same NPV: IRR Can help if the cashflows are well behaved! Required rate of return 15.00% Periods Project NPV IRR A (99.88) $ % B (100.00) $ % 4

5 Assume we do B three times and A four times Required rate of return 15.00% Periods Project A (1) (99.88) A (2) (99.88) A (3) (99.88) A (4) (99.88) A (100) (59) (59) (59) B (1) (100) B (2) (100) B (3) (100) B (100) (69) (69)

6 Assume we do B three times and A four times Required rate of return 15.00% Periods Project A (100) (59) (59) (59) B (100) (69) (69) A B NPV $10.88 $8.69 IRR 17.85% 17.37% 6

7 The Equivalent Annuity Approach Take the Net Present Values of the Projects at the Required Rate of Return (r) Treat NPV as PVA, r as rate, length of the project as n Calculate the PMT amount 7

8 The Equivalent Annuity Approach The Project with the highest PMT amount is the one which is best, if the projects are repeatable. Our example.. 8

9 The Equivalent Annuity Approach PV of Investment PV of Recovery Cashflow NPV Project A Project A ($99.88) $ $4.58 An Annuity PVA of the Annuity $2.00 $2.00 $2.00 ($4.57) PV of Investment PV of Recovery Cashflow NPV Project B An Annuity PVA of the Annuity Project B ($100.00) $ $ ???? #VALUE! 9

10 The Equivalent Annuity Approach PV of Investment PV of Recovery Cashflow NPV Project A Project A ($99.88) $ $4.58 An Annuity PVA of the Annuity PV of Investment PV of Recovery Cashflow NPV Project B An Annuity PVA of the Annuity $2.00 $2.00 $2.00 ($4.57) Project B ($100.00) $ $ ???? #VALUE! Calculate PMT given n=4, r=15%, PVA =

11 PRS Question If projects are repeatable, do you 1. prefer Project A (PMTA > PMTB) 2. prefer Project B (PMTA < PMTB) 3. prefer neither Project A nor Project B (PMTA = PMTB) 4. have no idea, but I am in class 11

12 Least Cost Decisions - Equal Length Projects If the recovery or revenues from two or more (equal length) projects or from two or more versions of a project are the same Adopt the version of the project where the NPV of the costs is the lowest 12

13 Least Cost Decisions - Unequal Length Projects If the recovery or revenues from projects are the same But Unequal Lives Apply the Equivalent Annuity Approach to the costs Select the project with the lowest equivalent annuity. 13

14 Least Cost Decisions - Unequal Length Projects Required rate of return 15.00% Periods Project NPV A (Recovery) $ A (Costs) (200.00) (12.00) (19.00) (19.00) (19.00) (15.00) ($255.62) A (200.00) $ B (Recovery) $ B (Costs) (170.00) (30.00) (30.00) (30.00) (30.00) ($255.65) B (170.00) $69.56 Assumption is that repeating A or B does not change the stream of recovery cashflows 14

15 Least Cost Decisions - Unequal Length Projects So repeating Required rate of return 15.00% B leads to 120 Periods Project recovery 4 5 in NPV A (Recovery) $ A (Costs) (200.00) (12.00) (19.00) (19.00) period (19.00) (15.00) 5 ($255.62) A (200.00) $ B (Recovery) $ B (Costs) (170.00) (30.00) (30.00) (30.00) (30.00) ($255.65) B (170.00) $69.56 Assumption is that repeating A or B does not change the stream of recovery cashflows 15

16 Least Cost Decisions - Unequal Length Projects Required rate of return 15.00% Periods Project NPV A (Recovery) $ A (Costs) (200.00) (12.00) (19.00) (19.00) (19.00) (15.00) ($255.62) A (200.00) $ B (Recovery) $ B (Costs) (170.00) (30.00) (30.00) (30.00) (30.00) ($255.65) B (170.00) $69.56 Project PVA r n PMT IRR A (Costs) ($255.62) 15% A $ % % B (Costs) ($255.65) 15% B $ % % 16

17 Project A has the lowest Equivalent Annuity of Costs Least Cost Decisions - Unequal Length Projects Required rate of return 15.00% Periods Project NPV A (Recovery) $ A (Costs) (200.00) (12.00) (19.00) (19.00) (19.00) (15.00) ($255.62) A (200.00) $ B (Recovery) $ B (Costs) (170.00) (30.00) (30.00) (30.00) (30.00) ($255.65) B (170.00) $69.56 Project PVA r n PMT IRR A (Costs) ($255.62) 15% A $ % % B (Costs) ($255.65) 15% B $ % % 17

18 Project A has the lowest Equivalent Annuity of Costs Least Cost Decisions - Unequal Length Projects Project A has the highest Equivalent Annuity of all cashflows Required rate of return 15.00% Periods Project NPV A (Recovery) $ A (Costs) (200.00) (12.00) (19.00) (19.00) (19.00) (15.00) ($255.62) A (200.00) $ B (Recovery) $ B (Costs) (170.00) (30.00) (30.00) (30.00) (30.00) ($255.65) B (170.00) $69.56 Project PVA r n PMT IRR A (Costs) ($255.62) 15% A $ % % B (Costs) ($255.65) 15% B $ % % 18

19 Inflation Price Inflation is the value of money decreasing in terms of the goods it can buy as the prices of those goods increase. Price Deflation is the value of money increasing 19

20 Inflation PV ( 1+r ) = 1 FV Price 5 *1 years ( + inflation ago my apartment rate) = rental was $620 per month 0 1 Now $725 per month $620 *( ) = $640 $640 *( ) = $660 $660 *( ) = $681 $681 *( ) = $703 $703 *( ) = $725 Price 20

21 Inflation Similar Math to TVM Inflation Compounds like interest Calculate average compounding rate of inflation with formula 3.10 r = ( PV) 1 n 1 FV n 21

22 Inflation r = ( PV) 1 n 1 FV n Similar Math to TVM n = years = 5 FVn is rental after 5 years PV was rental at time Zero (five years ago. 22

23 Inflation r = ( PV) 1 n 1 FV n r ( ) Similar Math to TVM = 1 n = years = 5 r ( ) FVn is rental after 5 years PV was rental at time Zero (five r r years ago = 1 = = = % 23

24 Inflation and Project Build to Rent Assume no inflation in rental project is 5 years duration. Required Rate of return is 6% per annum or (6/12)% per month or r= PV of Rental is PVA of annuity Period n = (5*12) = 60 months PMT or A = $550 Mode is Begin since you pay rent at start of month! 24

25 Inflation and Project Build to Rent PRS Question n=60, PMT = $550, r=0.5%, Mode Begin, PVA =??? 1. $28, $28, $110, $110, I have no idea, but I am in class 25

26 Inflation and Project Build to Rent If the rental is replicable, i.e. every month for ever Then the cashflow from the rental is a perpetuity due PVPdue = (A/r) + A PVPdue = $110,

27 Inflation and Project Build to Rent If the rental is replicable, and growing at 3% per annum! Then the cashflows are a Growth Perpetuity due PVCGPdue = (A/(r-g)) + A 27

28 Inflation and Project Build to Rent DUE = ( r g) + PVCGP { CF } CF PVCGP DUE 1 1 { A ( r g) } A = + 28

29 Inflation and Project Build to Rent DUE = ( r g) + PVCGP { CF } CF PVCGP DUE 1 1 { A ( r g) } A = + r = 6% p.a. = 0.5% monthly g = 3% p.a. = 0.25% monthly A = $550 monthly rental 29

30 Inflation and Project Build to Rent DUE = ( r g) + PVCGP { CF } CF PVCGP DUE 1 1 { A ( r g) } A = + r = 6% p.a. = 0.5% monthly g = 3% p.a. = 0.25% monthly A = $550 monthly rental PVCGP PVCGP DUE DUE = = { $550 ( )} $220, $550 30

31 Inflation and Project Build to Rent Think about 5 years rental with 3% inflation Switch to Excel N.B. if you calculate as 60 period annuity with 3% interest rate, PVA = $30, (diff = $340.18) reflecting the fact that inflation is compounding annually and interest is compounding monthly in the annuity calculations. 31

32 Inflation and Project Build to Rent No Inflation PVA5 = $28, (6%!) Perpetuity Due = $110,550 (3%!) Inflation 3% p.a. PVA5 = $30, (3%!) Perpetuity Due = $220,550 (3%) 32

33 Inflation The rate of inflation negates the discount rate Inflation makes money less valuable in goods The interest rate rewards risk taken and compensates for inflation 33

34 The Fisher Effect A theory Nominal Interest Rate comprises: A Real Component Compensation for expected inflation 34

35 The Fisher Effect Consumer Price Inflation Australia 2.4% Britain 2.5% U.S. 1.9% Japan 0.4% Source - The Economist Feb 7 th

36 Fisher Effect Capital If you plan in Nominal Dollars then Use a Nominal Required Rate of Return (i.e. rent $550, r = 6%) If you plan in Real Dollars then Use a Real Required Rate of Return (i.e. rent increasing, r = 3%) 36

37 The Fisher Effect Capital If, before you considered inflation, you wanted 6% as the Required Rate of Return If inflation is expected to be 3% you probably should be using 9% as the Nominal Required Rate of Return 37

38 Fisher Effect Capital If you plan in Nominal Dollars then Use a Nominal Required Rate of Return (i.e. rent $550, r = 9%) If you plan in Real Dollars then Use a Real Required Rate of Return (i.e. rent increasing, r = 6%) 38

39 Capital Rationing and The Profitability Index Like every other commodity, Capital is a constrained resource. Make sure you look at pages 224 to 225 in the text 39