Introduction to Project
Management
UNIT 3: ORGANIZATIONAL
STRATEGY AND PROJECT
SELECTION
Numeric Models
 Payback model
 NPV
 ROI
Lets calculate
1. Payback Analysis
 It is used to determine the amount of time it will take
to recover the initial investment of a project.
 This may be calculated in two ways:


Even cash flow
Uneven cash flow
Even cash flow example
 Project A has an initial investment of R200 000 and
a project annual cash flow of R25 000.
 Project B has an initial investment of R200 000 and
a project annual cash flow of R50 000.
 Using the formula
 Payback Period = Investment required / Net annual cash flow

Calculate the payback period for each project.
Calculation
 Project A = R200 000/R25 000
= 8 years
 Project B = R200 000/R50 000
= 4 years
 Therefore Project B is a better project. Its has a
shorter payback period.
Uneven cash flow example
 You make an investment of R900 000 and you
generate the following cash inflows:





Year 1
Year 2
Year 3
Year 4
Year 5
R400 000
R350 000
R200 000
R150 000
R100 000
 Calculate how long it will take to recover your initial
investment.
Calculation
 Formula
 Payback
period = A + (B/C)
A = Last period with negative cash flow
B = Absolute value of cumulative cash flow at
the end of period A
C = total cash flow during the period after
period A
Calculation
Year
Cash flow
Cumulative
cash flow
0
(900 000)
(900 000)
1
400 000
(500 000)
2
350 000
(150 000)
3
200 000
50 000
4
150 000
200 000
5
100 000
300 000
Payback period
= A +(B/C)
Payback period = 2 + (150 000/ 200 000) = 2 + 0.75 = 2.75 years
To calculate the number or months:
0.75 x 12 months = 9 months
Therefore payback period = 2 years and 9 months.
DO NOT SAY 2.9 YEARS OR 2.9 MONTHS. THIS WOULD BE INCORRECT.
BACAUSE IT IS 2.75 YEARS . CONVERTED TO YEARS AND MONTHS IT WOULD
BE 2 YEARS AND 9 MONTHS.
2. Net Present Value (NPV)
 Used to calculate the expected net value by
discounting expected future cash inflows and
outflows at present time.
 Additional categories to consider are:


Net flows = difference between inflows and outflows
Discount factor = 1 / (1 + i)n
i = interest rate
 n = number of years from start date

Example
 You are considering an investment in a project that
will cost R200 000. The required rate of return for
your project is 10%. You anticipate a useful life of 5
years for the project. These are the projected cash
flows:





Year 1
Year 2
Year 3
Year 4
Year 5
R40 000
R100 000
R90 000
R40 000
R30 000
Calculation
.
Year
Discount factor
1
1 / (1 + 0.1)1 = 0.9091
0.9091 x R40 000 = R36 364
2
1 / (1 + 0.1)2 = 0.8264
0.8264 x R100 000 = R82 640
3
1 / (1 + 0.1)3 = 0.7513
0.7513 x R90 000 = R67 617
4
1 / (1 + 0.1)4 = 0.6830
0.6830 x R40 000 = R27 320
5
1 / (1 + 0.1)5 = 0.6209
0.6209 x R30 000 = R18 627
Discount Factor = 1 / (1 + i)n
PV
Calculation
.
Year
Inflow
Outflow
Net flow
Discount
factor
PV
1
R40 000
0
R40 000
0.9091
R36 364
2
R100 000
0
R100 000
0.8264
R82 640
3
R90 000
0
R90 000
0.7513
R67 617
4
R40 000
0
R40 000
0.6830
R27 320
5
R30 000
0
R30 000
0.6209
R18 627
Total
R232 568
Initial
investment
(R200 000)
NPV
R32 568
3. Return on Investment (ROI)
 This a % that an investor will receive from his/her
investment.

ROI = (average annual profit/ original investment) x 100
Example
 You make an investment today for R2 000 and it is
worth R2 200 the next year. Calculate the ROI.
 Average annual profit = R2 200 – R2 000 = R200
 ROI = (R200/ R2 000) x 100
= 10%
Lets Practice
Application Questions
1. Read the case study below and answer the
questions that follow:
Aloe Manufacturing Company wishes to buy a new
machine for a five (5) year project. The manager
has to choose between machine A and machine B.
Both machines have the same initial cost (R85
000), but their cash-flows perform differently over
the five (5) year period due to different labour,
material and maintenance costs.
Your cash flow
.
Years
Cash-flow Machine B
1
Cash-Flow Machine
A
R20 000
2
R25 000
R20 000
3
R15 000
R25 000
4
R10 000
R35 000
5
R25 000
R15 000
R15 000
1. Calculate payback period for both machines.
2. Which machine will you choose? Motivate your answer.
Solution
Year
.
Machine A
Machine B
Cash flow
Cumulative
Cash flow
Cash flow
Cumulative
Cash flow
0
(85 000)
(85 000)
(85 000)
(85 000)
1
20 000
(65 000)
15 000
(70 000)
2
25 000
(40 000)
20 000
(50 000)
3
15 000
(25 000)
25 000
(25 000)
4
10 000
(15 000)
35 000
10 000
5
25 000
10 000
15 000
25 000
1. Machine A = 4 + (15 000/ 25 000) = 4 + 0.60 = 4.60 years
Machine B = 3 + (25 000/ 35 000) = 3 + 0.71 = 3.71 years
2. Machine B – It has a shorter payback period
Payback period
= A +(B/C)
Solution
To convert the payback period to years and months:
 Machine A = 4.60 years
The number of months = .60 x 12 = 7.2 months
Therefore payback period = 4 years and 7 months
Or 4 years and 8 months
(THIS DEPENDS ON THE TEXTBOOK OR SOURCE OF INFORMATION YOU ARE USING.
Some books just convert the decimals to the next number. So even though it is 7.2 they take it
to 8 months to avoid any challenges in calculations of recovering the investment.)
DO NOT SAY 4.7 or 4.8 YEARS OR 4.7 or 4.8 MONTHS. THIS WOULD BE INCORRECT.
BACAUSE IT IS 4.71 YEARS . CONVERTED TO YEARS AND MONTHS IT WOULD BE 4
YEARS AND 7 MONTHS or 4 YEARS AND 8 MONTHS.

Machine B = 3.71 years
The number of months = .71 x 12 = 8.52 months
Therefore payback period = 3 years and 9 months
DO NOT SAY 3.9 YEARS OR 3.9 MONTHS. THIS WOULD BE INCORRECT. BACAUSE IT IS
3.71 YEARS . CONVERTED TO YEARS AND MONTHS IT WOULD BE 3 YEARS AND 9
MONTHS.
NB: Follow the method used in the guide.
3. You are considering an investment in a project that
will cost R250 000. The required rate of return for
your project is 10%. You anticipate a useful life of 5
years for the project. These are the projected cash
flows:






Year 1
Year 2
Year 3
Year 4
Year 5
R50 000
R80 000
R90 000
R30 000
R20 000
Solution

Year
Discount factor
1
1 / (1 + 0.1)1 = 0.9091
0.9091 x R50 000 = R45 455
2
1 / (1 + 0.1)2 = 0.8264
0.8264 x R80 000 = R66 112
3
1 / (1 + 0.1)3 = 0.7513
0.7513 x R90 000 = R67 617
4
1 / (1 + 0.1)4 = 0.6830
0.6830 x R30 000 = R20 490
5
1 / (1 + 0.1)5 = 0.6209
0.6209 x R20 000 = R12 418
Discount Factor = 1 / (1 + i)n
PV
Solution
.
Year
Inflow
Outflo
w
Net flow
Discount
factor
PV
1
R50 000
0
R50 000
0.9091
R45 455
2
R80 000
0
R80 000
0.8264
R66 112
3
R90 000
0
R90 000
0.7513
R67 617
4
R30 000
0
R30 000
0.6830
R20 490
5
R20 000
0
R20 000
0.6209
R12 418
Total
R212 092
Initial
investment
(R250 000)
NPV
(R37 908)
4. You make an investment today for R5 000 and it
is worth R5 600 the next year.
Calculate the ROI.
Solution
 Average annual profit = R5 600 – R5 000 = R600
 ROI = (R600/ R5 000) x 100
= 12%