1. Project Management Lecture 28 Dr. Arshad Zaheer Source: CASE material and online sources

2. Recap  PERT and CPM  Framework of PERT/CPM  Terminology  Drawing Network Diagrams  Calculation of expected time  Identification of critical path  Gantt charts, Resource loading and leveling  Work Breakdown Structures  Linear Responsibility Charts

3. Outline  Financial Analysis of Projects  Time value of money  Payback Period  Net Present Value (NPV)  Benefit Cost Ratio (BCR)  Internal Rate of Return (IRR)

4. Financial Analysis of Projects

5. Time Value of Money Conceptually, “time value of money” means that the value of a sum of money received today is more than its value received after some time. Conversely, the sum of money received in future is less valuable than it is today. In other words, the present worth of a rupee received after some time will be less than a rupee received today. Since a rupee received today has more value, individuals, as rational human beings, would naturally prefer current receipt to future receipts.

6. Techniques In order to have logical and meaningful comparisons between cash flows that result in different time periods it is necessary to convert the sums of money to a common point in time. There are two techniques for doing this: –Compounding F = P (1 + I) n –DiscountingP =

7. Techniques (Contd) Compounding Technique Interest is compounded when the amount earned on an initial deposit (the initial principal) becomes part of the principal at the end of first compounding period. The term principal refers to the amount of money on which interest is received.

8. TIME VALUE OF MONEY Money can earn interest during the time it is invested, a future return is worth less at the present time. Or An amount of dollar invested now will be worth more when the principal and its accumulated interest are received n years from now

9. F=P(1+i) n F is the future value of the investment P is the present value of the investment i is the annual interest rate n is the number of years.

10. Investment = $ 1,000 (P) Interest = 10 % a year(i) Compounding annually Time = 1 year (n) F=P(1+i) n =$1,000 (1.10) 1 =$1,100 Example

11. If investment is for 2 years F=P(1+i) n =$1,000 (1.10) 2 =$1,210 We can also calculate 2 years compound interest, by investing 1 st years principal and interest. F=P(1+i) n =$1,100 (1.10) 1 =$1,210 Now

12. Quarterly Compounding Interest is paid at the end of each quarter i.e., four times a year Investment = $ 1,000 Interest = 10 % a year Compounding quarterly Time = 2 year F=P(1+i/4) 4(2) =1,000(1.025) 8 =$1,218.4 Example

13. Monthly Compounding Interest is paid at end of each month, twelve times a year Investment = $ 1,000 Interest = 10 % a year Compounding monthly Time = 2 year F=P(1+i/12) 12(2) =1,000(1.00833) 24 =$1,220.3 Example

14. Daily Compounding There are 360 compound periods per year Investment = $ 1,000 Interest = 10 % a year Compounding id done daily Time = 2 year F=P(1+i/360) 360(2) =1,000(1+0.10/360) 720 =$1,221.4 Example

15. DISCOUNTING If the future value of an investment is known we can easily derive its present value, given an interest rate and the number of compounding periods. P=F/(1+i) n How much money to invest now at 10% compounded annually to receive $1,000 in 5 years. P=$1,000/(1.10) 5 =1,000/1.611 =$620.7 Example

16. How much money to invest now at 10% compounded quarterly to receive $1,000 in 5 years. P=$1,000/(1.025) 20 =$ 610.3 --------------------------------------------------------------------------- Example

17. NET PRESENT VALUE The net present value method requires that all cash flows be discounted to their present value, using the firm’s required rate of return. NPV=   (A t /(1+i) t) -C 0  NPV takes into account the time value of money,and regardless of the pattern of cash flows, a single net present value is calculated.

18. Cash flows Years0 1 2 3 Project A-$2,500 $1,000 $1,500 $1,000 Project B-$2,500 -$1,000 $2,500 $2,000 Project A requires initial investment of $2,500 Project B requires initial investment of $2,500 an additional cash outlay of $1000 in the first year Required rate of return is 10% Example

19. NPV A = -2,500+1,000(0.9091)+1,500(0.8264) +1,000(0.7513) =$ 400 NPV B = -2,500-1,000(0.9091)+2,500(0.8264) +2,000(0.7513) =$ 160 Since the NPV of project A is larger so it is better

20. Profitability index The relationship of benefits to the cost of undertaking is provided by the profitability index, or the benefit-cost ratio The ratio of aggregate discounted benefits and aggregate discounted costs Profitability Index=   A t / (1+k) t  C0C0

21. Profitability Index = BCR A = 1,000(0.9091)+1,500(0.8264)+1,000(0.7513) 2500 = 909.1+1239.6 + 751.3 2500 =2900 = 1.16 2500

22. Profitability Index = BCR B = 2,500(0.8264) +2,000(0.7513) -2,500-1,000(0.9091) = 2066 +1502.6 3409.1 = 1.046

23. Internal Rate Of Return The IRR of return for an investment is the rate of return (interest rate) that makes the present value of cash flow equal to the cost of the investment. or The IRR of an investment is the discount rate that makes the NPV of the investment equal to zero. IRR = LDR + (HDR – LDR)NPV of LDR NPV of LDR – NPV of HDR

24. PAYBACK PERIOD Used when firms are concerned with the number of years required to recover the initial outlay of an investment. The payback period is used to evaluate the feasibility of projects in such cases. Payback period is found in two ways Conventional payback Discounted payback

25. Conventional payback The payback period is simply obtained by counting the number of years it takes for cash flow to equal the initial investment

26. Discounted payback This method requires that the cash flow be discounted using the required rate of return, before they are added up to equal the initial investment WHICH ONE IS GREATER?

27. Payback Period (Contd) Project cash flows ($) Year A B C 0-2,400-2,400-2,400 1 600 800 500 2 600 800 700 3 600 800 900 4 600 800 1,100 5 600 800 1,300 Conventional payback (years): 4.0 3.0 3.3 Discounted payback (years) 5.4 3.8 4.1 Net present value(i=10%): -126 633 868

28. Discounted Cash Flows Year AB CABC 0-2,400 i=10%-2,400 16008005000.909545.45727.27454.55 26008007000.826495.87661.16578.51 36008009000.751450.79601.05676.18 460080011000.683409.81546.41751.31 560080013000.621372.55496.74807.2 NPV-126633868 BCR0.951.261.36

29. Discounted Cash Flows Year AA 0-2,400i=6%-2,400 16000.943396566.04 26000.889996534.00 36000.839619503.77 46000.792094475.26 56000.747258448.35 NPV (6%)127

30. IRR (Project A) NPV (10%) = -126 NPV (6%) = 127 IRR = LDR + (HDR – LDR)NPV of LDR NPV of LDR – NPV of HDR = 6 + (10 – 6)*127 127 – (-126) = 8%