Time value of Money, Present Value of Future Money, Future value of Presesnt Money, Net Present Value, Benefit cost Ratio, Internal Rate of Return

1. Investment Analysis
(Capital Budgeting)
(NPV, BCR & IRR)
Presented By
Dr. Devyanee K.Nemade
Assistant Professor
Dr.PDKV, Akola

2. Investment in Agriculture is of two
types.
The first type involves operating
investment such as seed, feed, fertilizers
etc. and
Second one is concerned with
capital assets such as land, machine,
projects etc.

3. Time value of Money:
Future value of Present Money:
A rupee today is worth more
than a rupee in future.

4. One person
(Amount available today) Rs. 1,00,000/-
Bank
Bank deposited amount 1,00,000/-
After One year 10% 10,000/-
----------------
1,10,000/-
10% After Two year 10% 11,000/-
-----------------
1,21,000/-

5. Future value of Present money
The Future value of present
investment in the project is
calculated by using the following
formula of compound interest.
FV = PV (1+r)n
For 1st year 1,00,000(1+ 0.10)1 = 1,10,000
For 2nd year 1,00,000(1.10)2 = 1,21000
For 3nd year 1,00,000(1.10)3 = 1,33,100

6. Present Value of Future money:
The Present value of future sum is the
current value of investment to be received in
the future.
FV 1
PV = -------- or FV -------
(1+r)n (1+r)n
For 1st year
1,10,000 1
-------------- or 1,10,000 x ---------
(1+ 0.10)1 (1.10)1
= 1,10,000 x 0.909
= 1,00,000

7. For 2nd year
1,21,000 1
= -------------- = 1,21,000 x ---------
(1+ 0.10)2 (1.10)2
= 1,21,000 x 0.826
= 1,00,000
For 3rd year
1,33,100 1
= -------------- = 1,33,100 x ---------
(1+ 0.10)3 (1.10)3
= 1,33,100 x 0.751
= 1,00,000

8. Broadly there are two methods of
project appraisal,
viz: A. Undiscounted measures
B. Discounted measures.
Undiscounted measures:
1. Ranking by Inspection
2. Pay back period
3. Average Annual proceeds of Rupee
Outlay

9. Ranking by Inspection:
This project are with the same
investment and the same net value of
production, but with difference in the
length of the period, then the project with
longer duration is preferred to the one
with shorter time period.

10. Pay Back period:
Another simple method of ranking
a project is the length of time required to
get back the investment on the project.
Investment of the project in rupees(I)
P = -------------------------------------------------
Annual cash revenue in rupees(E)
This preference of a particular
project is based on the lesser payback
period.

11. Calculation of Pay Back Period
Year Cash Flow(in Rs)
Project A Project B
0 - 20,000 - 20,000
1 5000 4000
2 5000 4000
3 5000 4000
4 5000 4000
5 5000 4000
6 5000 4000
Initial Investment = Rs. 20,000/-

12. Rs. 20,000
Project A = ------------------ = 4 Years
Rs. 5000
Rs. 20,000
Project B = ------------------ = 5 Years
Rs. 4000

13. Average Rate of return/
Average Annual proceeds of Rupee Outlay:
Average Income/Average Profit = 20,000/-
Average Investment = 2,00,000/-
Average profit
= ---------------------- x 100
Average investment
20,000
= ---------------------- x 100
2,00,000
= 10%
Average profit = 1,00,000 / 5 = 20,000/-

14. Discounted Measures
1. Net present worth
2. Benefit cost Ratio
3. Internal rate of return

15. 1. Net present worth:
- It is the discounted cash flows are the
best estimates to decide on the worth of
the project.
- The present worth of the costs is
subtracted from the present worth of the
benefits in order to arrive at the Net
Present Worth of the project every year.

16. Measurement of the Cash Flows of the
Project:
- From the Annual stream of Gross
benefits of the project, the capital
invested and the other Input costs like
labour, machinery, fertilizers, pesticides,
management etc. are deducted .
- Financial analysis aims at estimation of
returns to all resources employed in the
project.

17. Net present Value:
Ram Project Cash Inflows/ Cash Income
(Rs. 1,00,000 ) 1st year = 60,000
2nd year = 40,000
3rd year = 50,000
Bank(Rs. 1,00,000) Ist Year
10 % interest 1,10,000
- 60,000
---------------------
50,000 +10% = 55,000/-
IInd Year IIIrd year
55,000 16,500
- 40,000 50,000
------------- ----------------
15,000 + 10% 33,500 (Net value)
= 16,500

18. IIIrd year Amount = 33500/-
Net cash flow in 3rd year (P3)
3rd Year NPV = --------------------------------------
(1+ i)3
33500
= -----------
(1+0.10)3
= 25, 169/-

19. P1 P2 Pn
NPV = --------- + --------- +……… --------- - C
(1+i) t1 (1+i) t2 (1+i) tn
Where,
P1 = Net cash flow in first year
i = Discount rate
t = time period
C = Initial cost investment
60,000 40, 000 50,000
NPV = --------- + --------- + --------- - 1,00,000
(1.10)1 (1.10) 2 (1.10) 3
NPV = 25,169/-

20. Estimation of NPW for Agriculture Project
Year Mango Orchard(One ha)
Cost in
Rs.
Return
in Rs.
Net
income
Discount
factor at
12%
NPV/
NPW
At the end of
the 6th year
25,000 - -25,000
7th 4,250 10,260 6,010
8th 4,792 12,550
9th 5,368 14,530
10th 5,975 16,275
11th 6,456 19,396
12th 7,187 21,470
NPV or NPW

21. 1
NPV up to 6th year = P1 ---------
(1+ i)1
NPV 7th year =
NPV 8th year =
NPV 9th year =
NPV 10th year =
NPV 11th year =
NPV 12th year =
NPV =

22. Benefit cost Ratio
• It is compare the present worth of cost
with present worth of benefits.
• It is most common methods of selecting
projects.
• It is, to choose the projects, having B-C
ratio of more than one, when discounted
at opportunity cost of capital and the
given project is opted for implementation.

23. Benefit Cost Ratio:-
Present worth of the gross returns
= ------------------------------------------------
Present worth of the costs

24. Benefit – Cost Ratio for Agriculture Project
Year Mango Orchard(One ha)
Cost in
Rs.
Return
in Rs.
Discount
factor at
12%
Present
worth of
the cost
Present
worth of
the gross
returns
At the end of
the 6th year
25,000 - Cost X
D.F.
Returns
X D.F.
7th 4,250 10,260
8th 4,792 12,550
9th 5,368 14,530
10th 5,975 16,275
11th 6,456 19,396
12th 7,187 21,470
Total

25. Benefit Cost Ratio:-
Present worth of the gross returns
= ------------------------------------------------
Present worth of the costs
31,278.04
= -----------------
24,093.70
= 1.30

26. Internal Rate of return:
• IRR is the time value of money is accounted.
• IRR provides the knowledge of actual rate of
return from the different projects.
• IRR is known as Yield of the investment or
Marginal efficiency of capital.
• When NPW(Net cash flow) is set equal to zero,
the equation is solved for ‘i’. This is the IRR.
• The IRR must be found out by trial and error
with some approximation.

27. Formula
Lower Difference
IRR = Discount + between X
Rate the two
discount rates
Present worth of the cash flow at
the lower discount rate
----------------------------------------------
Absolute difference between the
present worths of the cash flow
at the two discount rates

28. Internal Rate of Return:
Company Invest Project Return
IRR ≥ Cost of Capital = Accept
IRR < Cost of Capital = Rejected
1,00,000/-
(Capital)
Bank
(Required rate of return)
Cost of capital 10%

29. Internal Rate of Return:
Cost of Project: Rs. 1,00,000/-
Estimated cash flows :
1st Year = 50,000/-
2nd Year = 35,000/-
3rd Year = 45,000/-
Required Rate of return = 10 %
50,000 35,000 45,000
NPV @ 10 % = ----------- + ---------- + ------------ - 1,00,000
(1.10)1 (1.10)2 (1.10)3
= 8,189/-

30. Required Rate of return = 12 %
50,000 35,000 45,000
NPV @ 12 % = ----------- + ---------- + ------------ - 1,00,000
(1.12)1 (1.12)2 (1.12)3
= 4,575/-
Required Rate of return = 15 %
50,000 35,000 45,000
NPV @ 15 % = ----------- + ---------- + ------------ - 1,00,000
(1.15)1 (1.15)2 (1.15)3
= - 468/-

31. Interpolating IRR: Select, + ve - ve
12 % 15 %
NPV
12 % 4575
0
15 % (468)
-------- ---------
03% 5043
IRR = Select 12 %
5043 3%
4575 ? 4575 x 3
4575 x 3 --------------
= 12 + -------------- 5043
5043
= 12.75 %

32. Interpolating IRR + ve - ve
10 % 15 %
NPV
10 % 8189
0
15 % (468)
-------- ---------
05% 8657
IRR = Select 10 %
8657 5%
8189 ? 8189 x 5
8189 x 5 --------------
= 10 + -------------- 8657
8657
= 14.72 %

33. Formula
Lower Difference
IRR = Discount + between X
Rate the two
discount rates
Present worth of the cash flow at
the lower discount rate
----------------------------------------------
Absolute difference between the
present worths of the cash flow
at the two discount rates

34. Formula
4575
IRR = 12 + 03 X ---------------
4575 + 468
4575
= 12 + 3 X ----------
5043
= 12 + 3 X (0.9027)
= 12 + 2.721
= 14.72

35. Conclusion:
- Result are near about same, no more
difference i.e. discount rate -
12% & 15% = 12.75
and 10% & 15% = 14.72
- It means no more gap selected.
- Select only one positive value and
one negative value i.e. 12% &15%.