captital budegting of time value of money.

1. Capital Budgeting
By- Ayisha Shaikh

2. Meaning
 Capital budgeting is a process of evaluating investments and huge expenses in
order to obtain the best returns on investment.
 An organization is often faced with the challenges of selecting between two
projects/investments or the buy vs replace decision.
 An organization would like to invest in all profitable projects but due to the
limitation on the availability of capital an organization has to choose between
different projects/investments.
 Capital budgeting is the budgeting of capital expense

3. Objectives
 To find out the profitable capital expenditure.
 2. To know whether the replacement of any existing fixed assets gives more return
than earlier.
 3. To decide whether a specified project is to be selected or not.
 To find out the quantum of finance required for the capital expenditure
 To assess the various sources of finance for capital expenditure.
 6. To evaluate the merits of each proposal to decide which project is best.

4. Features
 Capital budgeting involves the investment of funds currently for getting benefits in
the future.
 2. Generally, the future benefits are spread over several years.
 3. The long term investment is fixed.
 4. The investments made in the project is determining the financial condition of
business organization in future.
 5. Each project involves huge amount of funds.
 6. Capital expenditure decisions are irreversible.
 7. The profitability of the business concern is based on the quantum of investments
made in the project.

5. Limitations
 The economic life of the project and annual cash inflows are only an estimation.
The actual economic life of the project is either increased or decreased. Likewise,
the actual annual cash inflows may be either more or less than the estimation.
Hence, control over capital expenditure can not be exercised.
 2. The application of capital budgeting technique is based on the presumed cash
inflows and cash outflows. Since the future is uncertain, the presumed cash inflows
and cash outflows may not be true. Therefore, the selection of profitable project
may be wrong.
 3. Capital budgeting process does not take into consideration of various non-
financial aspects of the projects while they play an important role in successful and
profitable implementation of them. Hence, true profitability of the project cannot
be highlighted.

6.  It is also not correct to assume that mathematically exact techniques always produce
highly accurate results.
 5. All the techniques of capital budgeting presume that various investment proposals
under consideration are mutually exclusive which may not be practically true in some
particular circumstances.
 6. The morale of the employee, goodwill of the company etc. cannot be quantified
accurately. Hence, these can substantially influence capital budgeting decision.
 7. Risk of any project cannot be presumed accurately. The project risk is varying
according to the changes made in the business world.
 8. In case of urgency, the capital budgeting technique cannot be applied.
 9. Only known factors are considered while applying capital budgeting decisions. There
are so many unknown factors which are also affecting capital budgeting decisions. The
unknown factors cannot be avoided or controlled.

7. Capital Budgeting Process

8. Techniques of Capital Budgeting

9. Modern Methods
 Modern Methods are also known as discounted cash flow techniques
 It takes into consideration time value of money
 There are broadly three methods NPV, PI, IRR and Cost Benefit Analysis

10. NET PRESENT VALUE
 The net present value of a project is equal to the sum of discounted cash flows
associated with the project. Symbolically represented as
 NPV = CF0 / (1+r)0 +CF1 / (1+r)1 +CF2 / (1+r)2 +………… CFn / (1+r)n -I
 NPV = 𝒏=𝟏
∞
CFn / (1+r)n - Initial Investment
NPV= Net Present Value (summation of PV of all Cash flows)
CF= Cash flow at the end of the year n
r= Rate of Discount
n= Life of the Project
When NPV Rule
> 1 Accept
< 1 Reject

11. MINI CASESTUDY-2
 2. ABC Ltd has been pondering of the different investment opportunities it has.
Help it to invest in the most profitable one if the rate of interest is 8% p.a. The cash
flow from both the projects are as listed below and the investment required for
each project is Rs. 1,20,000
 PV of cash flow of Project-A= Rs. 1,93,336
 PV of cash flow of Project-B = Rs. 2,24,989
Year Project-A Project-B
1 40,000 50000
2 60,000 30,000
3 75,000 90,000
4 20,000 60,000
5 45,000 55,000

12. Merits of NPV
 It takes into consideration tive value of money
 It considers cash flow stream of the project in its entirety. Ie till the life of the
project
 It perfectly aligns with the financial objective of maximization of wealth of the
shareholders
 The additive property of NPV makes it unique and distinct from all the other
techniques
 Its easy to understand and calculate, whichever project has a higher NPV that
project is considered
 Future investment in the project is also taken into consideration

13.  Project A 1,00,000 45,000
 PROJECT B 1,00,000 40,000
 PROJECT C 50,000 25,000
 PROJECT D 50,000 23,000

14. Demerits of NPV
 Though one of the most popular method of capital budgeting it suffers from the
following demerits
 It is expressed in absolute term and not relative term

15. Profitability Index
 Profitability index is also known as benefit cost ratio
 The formula to calculate it is as follows
PI or BCR = PVB/ I
Where PVB = present value of benefits
I = initial Investment
When PI/BCR Rule is
> 1 Accept
= 1 Indifferent
< 1 Reject

16. Example-1
Year Cashflow
1 25,000
2 40,000
3 40,000
4 50,000
XYZ Ltd. Is expecting the following cashflow from a project which requires an
Investment of Rs.1,00,000, if the rate of interest applicable is 12% p.a

17. Solution
 BCR = PVB/I
 BCR = 25,000 + 40,000 + 40000 + 50,000
(1.12)1 (1.12)2 (1.12)3 (1.12)4
1,00,000
 BCR = 1.145
 Accept the project

18. Merits & Demerits of BCR
Merits
 Considers time value of Money
 It is expressed in relative term and hence comparison of projects with different
outlay can be done
Demerits
 When the cash outlay occurs in other than the initial year it does not take it into
consideration
 Aggregating several smaller projects is not possible because it does not have
addition property

19. Internal Rate of Return
 Internal rate of return calculate the rate of return from the project
 The formula to calculate IRR is
I = CF0 / (1+r)0 +CF1 / (1+r)1 +CF2 / (1+r)2 +………… CFn / (1+r)n
I= 𝒏=𝟏
∞
CFn / (1+r)n
where I = Initial Investment
CF= Cash flow from the project
n= life of the project
r= ? ( Internal Rate of Return)

20. Internal Rate of Return
 This is a trial and error method
When IRR Rule
> Rate of interest Accept
= Rate of interest Indifferent
< Rate of interest Reject

21. Example-2
 PQR Ltd. Is expecting the following cashflow from a project which requires an
Investment of Rs.1,00,000, if the rate of interest applicable is 12% p.a
Year Cashflow
1 30,000
2 30,000
3 40,000
4 45,000

22. Solution
 I= 𝒏=𝟏
∞
CFn / (1+r)n
 1,00,000 = 30,000 + 30,000 + 40000 + 45,000
(1+r)1 (1+r )2 (1+r)3 (1+r)4
 With r= 15%, Rs.100802
 With r= 16%, Rs 98641
 Hence IRR is between 15% and 16%
 With Linear Interpolation
15% + 100802-100000 = 15.37%
100802-98641

23. Merits & Demerits of IRR
Merits
 It takes into consideration time value of money
 It take the cash flow of the project for its entire life
 Its highly relative since its in form of percentage so the changing rate of interest
can be easily compared
Demerits
 Its quite difficult to calculate
 It cannot distinguish between cash outflow and inflow ( table1)
 Smaller projects cannot be compared to larger projects
 It sometimes gives out more than 1 IRR which can be misleading (table-2)

24. Table 1
Year 0 Year1 IRR NPV (@10%)
Project A (4000) 6000 50% 145
Project B 4000 (7000) 75% -236

25. Table 2
Year 0 Year 1 Year 2
(1,60,000) 10,00,000 (10,00,000)
According to IRR Formula
1,60,000 = 10,00,000/(1+r)1 - 10,00,000/(1+r)2
Solving the equation we get
1,60,000r2 -6,80,000r + 1,60,000 = 0
Dividing the whole equation with 40,000 we get
4r2 – 17r + 4 = 0
Solving the equation we get r=0.25 and r=4
Hence the rate of both 25% and 400% stands correct for this equation
When there is cash outflow in more than the initial year you will be getting more than 1
IRR which is misleading

26. Modified Internal Rate of Return (MIRR)
 The two major shortcomings of IRR namely difficulty to calculate and two IRR has
lead to the formulation of MIRR which nullifies its shortcoming
 MIRR takes into consideration the rate of interest and calculate the return from a
project
 MIRR is simple to calculate
 MIRR gives out single rate of return
 PVC = FV / (1+MIRR)n
 The formula to calculate MIRR is same as the formula to calculate present value

27. MIRR Formula
 Step 1: Calculate PV of all the cash outflow pertaining to the project
 Step 2: Calculate the FV of all the cash inflow pertaining to the project
 Step 3: Use the formula to find MIRR, PVC = FV / (1+MIRR)n
When MIRR Rule
> Rate of interest Accept
= Rate of interest Indifferent
< Rate of interest Reject

28. Example 3
Year 0 1 2 3 4 5 6
Cashflow (120) (80) 20 60 80 100 120
Pentagon Ltd is expecting the following cashflow from a project it is planning to
undertake. You are required to calculate MIRR for the project if the rate of interest is 15%
p.a. Suggest whether the company should go for the project or not

29. Solution
 Step 1: Calculate PV of all the cash outflow pertaining to the project
PV = 120 + {80 /(1.15)} = 189.56
 Step 2: Calculate the FV of all the cash inflow pertaining to the project
FV= 20(1.15)4+ 60(1.15)3+80(1.15)2+100(1.15)1+120 = 467
 Step 3: PVC = FV / (1+MIRR)n
189.56 = 467 / (1+MIRR)6
(1+MIRR)6 = 2.463
1+ MIRR = 1.1615
 Hence MIRR= 16.2% Approx
Since MIRR is greater than the prevailing interest rate of 15% in the market we will
accept the project

30. Pay back Period
 The pay back period is the length of time required to recover the initial outlay on
the project
 This method does not take into consideration time value of money
 This is simple to calculate
 According to this method, the shorter the pay back period the more desirable the
project will be.

31. Example 4
Year Project A Project B
0 (1,00,000) (1,00,000)
1 50,000 20,000
2 30,000 20,000
3 20,000 20,000
4 10,000 40,000
5 10,000 50,000
6 10,000 60,000
Here the Project A has a pay back period of 3 yrs
While Project B has a pay back period of 4 yrs, Hence according to pay back period method
we will go for project A

32. Merits & Demerits of Pay Back Period
Method
 Merits
 Easy to calculate
 It is a rough and ready method to deal with risk
 It is good method if the firm is looking for liquidity
 Demerits
 It does not take into consideration time value of money
 It does not take into consideration cash flow after the pay back period
 It’s a method of capital recovery and not profitability

33. Discounted Payback Method
Example-5
 To address the major flaw of payback period method that it does not consider time
value of money , discounted pay back period method was introduced. Lets assume
that the rate of interest is 10%

34. Solution
Year Project A pvif Discounted
value
Cumulative
0 (1,00,000) (1,00,000) (1,00,000)
1 50,000 0.9091 45,455 (54,545)
2 30,000 0.8264 24,792 (29,753)
3 20,000 0.7513 15,026 (14,727)
4 10,000 0.6830 6830 (7897)
5 10,000 0.6209 6209 (1690)
6 10,000 0.5645 5645 3955
So here the discounted PBP is 5yrs + (1690/5645) months
Hence the Discounted Pay back Period is 5.3 yrs approx.

35. Post Pay back Period Method
 Its very simple method where all the cashflow of the project is taken into
consideration
 The formula to Calculate Post Payback period
 PPBP = Total Cash Flows – Initial Investment
 Project A PPBP = 1,30,000 – 1,00,000 = Rs 30,000
 Project B PPBP = 2,10,000-1,00,000 = Rs. 1,10,000

36. Accounting Rate of Return
 The accounting rate of return also known as the average rate of return is calculated
as
= Av. Profit after tax
Av. Book value of Investment
Here the numerator is the average annual post tax profit over the life of investment
The denominator is the average of book value of the investment in the project
When ARR Rule
> Rate of interest Accept
= Rate of interest Indifferent
< Rate of interest Reject

37. Example-6
Year Book Value of Invstment Profit After Tax
1 90,000 20,000
2 80,000 22,000
3 70,000 24,000
4 60,000 26,000
5 50,000 28,000

38. Solution
ARR= Av. Profit after tax
Av. Book value of Investment
Step 1: Calculate Average PAT = 20,000+22,000+24,000+26,000+28000 = 24000
5
 Step 2: Calculate Average BV of Investment
 = 90,000+80,000+70,000+60,000+50,000 =70,000
5
ARR= 24,000/70,000 = 0.3428
ARR= 34.28%
Accept The Project

39. Merits & Demerits of ARR
 Merits
 It is simple to calculate
 It is based on accounting information which is readily available
 It takes into consideration benefits over the entire life of the project
 Demerits
 It is based on accounting profit and cash flow
 It does not take into consideration time value of money

40. Capital Budgeting techniques in Practice
 Over the time NPV and IRR are the most widely used techniques
 Firms typically use multiple evaluation methods
 ARR and PBP are widely used as a supplementary methods
 Weighted Average Cost of Capital (WACC) is widely used as the discount rate by
the firms
 The most widely used discount rate is 15%
 Risk assessment and adjustment techniques have gained popularity and are
adjusted by increasing the discount rate

41. Techniques in Practice
Method % of Companies considering it
Internal Rate of Return 85%
Payback Period 67.5%
Net Present Value 66.3%
Breakeven Analysis 58.2%
Profitability Index 35.1%
According to a research conducted by researchers about the different techniques and
importance given to those techniques by companies, the following was revealed

42. Question 1
Year Cashflow
0 (1,00,000)
1 20,000
2 30,000
3 40,000
4 50,000
5 30,000
The expected cash flow from a project is as follows. The cost of capital is 12% per
annum. Calculate the following a) NPV b) BCR c) IRR d) MIRR e) Payback Period
f)Discounted Payback period

43. Solution
 NPV- Rs. 19060
 BCR= 1.19
 IRR=18.69%
 MIRR=15.97%
 PBP= 3.2 YEARS
 DPBP- 3.9 YEARS

44. Question 2
 What is the Internal rate of return for a project that involves an outlay of
Rs.30,00,000 now which will result in an annual cashflow of Rs 6,00,000 for a period
of 7 yrs?

45. Solution 2
IRR= 9% TO 10%

46. Question 3
 Calculate the Internal rate of return of the project which has the following cash flow
Year Cash flow
0 (3000)
1 9000
2 (3000)

47. Case Study -1
 Alpha Ltd has been using a machine that needs an urgent overhauling, the
company is also considering the option of outsourcing the production or
purchasing a new smaller machine. Help the company take the most profitable
decision. Calculate MIRR, PI and NPV if the rate of interest is 12%pa.
Year Outsource the
production
Purchase a
smaller machine
Overhaul the
current machine
0 (15000) (15000) (15000)
1 11000 3500 42000
2 7000 8000 (4000)
3 4800 13000 -

48. Case Study 2
 ABC Ltd is considering two mutually exclusive projects with the following cash flow
if the cost of capital is 12%
Year Project P Project Q
0 (1000) (1600)
1 (1200) 200
2 (600) 400
3 (250) 600
4 2000 800
5 4000 100
Which Project should the company choose. Which technique will you use to find out the
profitable project and why ?

49. Case Study- 3
Year Project A Project B Project C
0 (6000) (6000) (6000)
1 3000 1000 2000
2 2000 2000 2000
3 1000 3000 2000
4 4000 6000 5000
a)Which project will you choose according to payback period technique.
b) Will you go for post payback period method or discounted payback period method if
the rate of interest applicable is 12% and why ?