1) The document discusses cash flow analysis techniques for project evaluation including net present value (NPV), net future value (NFW), and true (discounted cash flow) rate of return (TRR). 2) It provides examples of calculating NPV and determining if projects are justified based on positive NPV. It also shows how to calculate the break-even interest rate that makes a project's NPV equal to zero. 3) The final example demonstrates calculating a project's TRR and comparing it to the required rate of return to determine if the project gains or loses money. The annuity rule is used to calculate the present value of a series of cash flows.

1. Project Management, Economics and
Implementation
Cash Flow
Cairo University
Faculty of Engineering
Credit Hours System
PPC-C Courses
Eng. Nourhan Hisham

3. This is the money going into your company and the
money going out, where the net cash flow is cash
flow in – cash flow out.
Cash Flow

4. Cash
Flow,
$
Years
Cash Flow Diagram

5. • Net Present Value (NPV) or NPW
- It is the total present value (PV) of a time series of cash
flows. It is a standard method for using the time value of
money to appraise long-term projects.
- We can use the NPV or NPW to judge on projects
• Net Future Worth (NFW)
- It is the total future value (FV) of a time series of cash
flows. It is a standard method for using the time value of
money to appraise long-term projects.
- We can use the NFW to judge on project
Cash Flow

6. Cash Flow

7. Cash Flow
Year Cash Flow, $ NPV, $ NFW, $
0 (80,000)
1 20,000
2 20,000
3 20,000
4 20,000
5 20,000
6 20,000
Total

8. Cash Flow

9. 1) A corporation must decide whether to introduce a new product line.
The new product will have startup costs, operational costs, and
incoming cash flows over nine years. This project will have an
immediate (t=0) cash outflow of $100,000 (which might include
machinery, and employee training costs). Other cash outflows for
years 1-9 are expected to be $5,000 per year. Cash inflows are
expected to be $30,000 each for years 1-9. All cash flows are after-
tax, and there are no cash flows expected after year 9. The interest
rate is 10%, calculate the NPV and mention whether to do the project
or not, also draw a cash flow diagram.
Solution:
Here at year zero. $100,000 was spent as an out-cash flow, and
each year inflow is $30,000 and out is $5000 so net inflow each
year is $25,000.
The following table shows the NPV of each cash flow and the NPV
of the whole project is the summation of all the NPV of all the cash
flows

10. The sum of all these present values is the net present value,
which equals $44,000. Since the NPV is greater than zero, it
would be better to invest in the project than to do nothing, and the
corporation should invest in this project if there is no alternative
with a higher NPV.
Year Cash flow Present Value
T=0 -100,000 -100,000 $-100,000
T=1 25,000 25,000/(1 + 0.1) $22,727
T=2 25,000 25,000/(1 + 0.1)^2 $20,661
T=3 25,000 25,000/(1 + 0.1)^3 $18,783
T=4 25,000 25,000/(1 + 0.1)^4 $17,075
T=5 25,000 25,000/(1 + 0.1)^5 $15,523
T=6 25,000 25,000/(1 + 0.1)^6 $14,112
T=7 25,000 25,000/(1 + 0.1)^7 $12,829
T=8 25,000 25,000/(1 + 0.1)^8 $11,663
T=9 25,000 25,000/(1 + 0.1)^9 $10,604
Total $44,000

13. 2) Suppose that $150,000 were invested for research and
development in a certain firm 1 year ago and research is now
completed, as a result of this research, annual savings of $65,000 or
the next 4 years will occur, would the project be justified at I = 10%?
Also find the value of i (rate on return) that makes the project justified
if the investment was made 2 years ago instead of 1 year ago.
The NPV is positive and = $41,041 so the project is justified at rate of
return = 10%
Solution:
a)

14. Solution:
b)
Equate the NPV with zero and by trial and error get the value of i,
it will be the value which makes the project just justified as it
neither lose nor make profit.

15. 3) A proposed project has the following data:
Initial fixed investment of $200,000, WCI of $20,000 and final
salvage value of $20,000 and the series of cash flow are:
Determine TRR
Solution:
Before we solve there are some points to be taken:
• TRR is called true rate of return and it is just another name for the
DCFRR (Discounted Cash Flow Rate of Return) which is value of
rate of return i at NPW = 0 and NFW = 0
• Both the WCI & the salvage value are returned at the end of the
project, so both values are added here on the cash of year 7
• Any value between brackets means it is a negative value or out
cash flow

16. Solution:
Equate the NPW with zero and get value of I, either by trial and
error or using calculator.

17. 4) Consider the following project, working at rate of return (I) =
15%, evaluate the Project using the TRR technique
Solution:
At TRR or DCFRR the NPW = 0, and if rate of return I is >
DCFRR…..this means loss and if rate of return is < DCFRR… this
means profit Year Cash flow T=0
So, what we will do is that we will calculate TRR and compare it
with rate of return given and see whether the project gains or
loses.

18. Solution:
The previous equation is hard to be solved using calculator so we
will use trial and error, equate the NPW with zero to get the
DCFRR
DCFRR = 17.4 %
Since that the rate of return is 15 % and less than the DCFRR, the
project is justified

19. Note:
In this problem we used the annuity rule in order to calculate NPW
of the cash flows from year 6 to 15, this rule is as follows:
P = R ((1 + i)n – 1)/ i (1 + i)n ) where P is present worth , R is the
repeated cash flow. N is the number of years.
In our problem n = 10 , = (15- 6 + 1) because year 6 is included,
then we multiplied by 1/(1 + i )^5, because the annuity rule gets the
P value at the beginning of year 6 which is nearly at the end of year
5 so we just want to get this value back 5 years not 6!
NFW may be easier in this problem. Try this way!

20. Special Thanks to Dr.Amira Khaled