Project Management

Lecture 28

Dr. Arshad Zaheer

Source: CASE material and online sources

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

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

Financial Analysis of

Projects

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.

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

– Discounting P = ni

F

)1(

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.

TIME VALUE OF MONEY

Money can earn interest during the time it is invested, a future return is worth less at the present time.

OrAn amount of dollar invested now will

be worth more when the principal and its accumulated interest are received n years from now

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.

• 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

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 1st years principal and interest.

F=P(1+i)n

=$1,100 (1.10)1

=$1,210

Now

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

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

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

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

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

NET PRESENT VALUEThe net present value method requires that all cash flows be

discounted to their present value, using the firm’s required

rate of return.

NPV= (At/(1+i)t)-C0

NPV takes into account the time value of money,and

regardless of the pattern of cash flows, a single net

present value is calculated.

Cash flows

Years 0 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

NPVA= -2,500+1,000(0.9091)+1,500(0.8264)

+1,000(0.7513)

=$ 400

NPVB= -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

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= At / (1+k)t C0

Profitability Index = BCRA= 1,000(0.9091)+1,500(0.8264)+1,000(0.7513)

2500

= 909.1+1239.6 + 751.3

2500

=2900 = 1.16

2500

Profitability Index = BCRB=

2,500(0.8264) +2,000(0.7513)

-2,500-1,000(0.9091)

= 2066 +1502.6

3409.1

= 1.046

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.

orThe IRR of an investment is the discount rate that

makes the NPV of the investment equal to zero.

IRR = LDR + (HDR – LDR)NPV of LDRNPV of LDR – NPV of HDR

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

Conventional payback

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

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?

Payback Period (Contd)Project cash flows ($)

Year A B C

0 -2,400 -2,400 -2,4001 600 800 5002 600 800 7003 600 800 9004 600 800 1,1005 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

Discounted Cash Flows

Year A B C A B C

0 -2,400 -2,400 -2,400 i=10% -2,400 -2,400 -2,400

1 600 800 500 0.909 545.45 727.27 454.55

2 600 800 700 0.826 495.87 661.16 578.51

3 600 800 900 0.751 450.79 601.05 676.18

4 600 800 1100 0.683 409.81 546.41 751.31

5 600 800 1300 0.621 372.55 496.74 807.2

NPV -126 633 868

BCR 0.95 1.26 1.36

Discounted Cash Flows

Year A A

0 -2,400 i=6% -2,400

1 600 0.943396 566.04

2 600 0.889996 534.00

3 600 0.839619 503.77

4 600 0.792094 475.26

5 600 0.747258 448.35

NPV (6%) 127

IRR (Project A)

NPV (10%) = -126

NPV (6%) = 127IRR = LDR + (HDR – LDR)NPV of LDR

NPV of LDR – NPV of HDR= 6 + (10 – 6)*127

127 – (-126)

= 8%