Capital budgeting decisions:

Capital Budgeting Decisions
Meaning, Process and Significance, Methods of Project Evaluation and
Selection: ARR, Payback And Discounted Payback, NPV, IRR, Benefit to
Cost Ratio And Terminal Value Method, Risk Analysis In Investment,
Sensitivity Analysis.
31-08-2016 BCH 505 PROJECT FINANCE BY DR N R KIDWAI, INTEGRAL UNIVERSITY 1

Capital Budgeting
In every business there are four basic financial decisions :
• Which projects to take? (Investment decisions)
• How to finance these projects? (Financing decisions)
• How much to return to investors? (Dividend decisions)
• How to manage working capital and its components? (Liquidity decisions)
One duty of a financial manager is to choose investments with satisfactory cash flows and rates of return.
Therefore, a financial manager must be able to decide whether an investment is worth undertaking and
be able to choose intelligently between two or more alternatives. To do this, a sound procedure to
evaluate, compare, and select projects is needed. This procedure is called capital budgeting.
Investments decisions of a firm are generally known as Capital Budgeting or Capital expenditure
decisions
• It have long-term consequences • It often involve substantial outlays • It may be difficult or
expensive to reverse

Type of Proposals/ Projects
Replacement projects: Replacement of equipment/ technologies with objective to reduce costs,
increase efficiency , improve quality etc.
Expansion projects: These investments are meant to increase production and operation capacity
and/ or widen the distribution network. Such investments proposals require explicit forecast of
growth and require more careful analysis than replacement projects.
Strategic/ Diversification projects: These investments are aimed diversification into new products
or services or new markets which are strategically important. It entail substantial risks, involve large
outlays, and require considerable efforts and attention. Given their strategic importance, such
projects require a very thorough evaluation, both quantitative and qualitative.
Research and development projects: Traditionally, R&D projects shared a small proportion of
capital budget. However, in modern era, more funds are allocated for R&D projects specially in
knowledge intensive sectors.

Capital Budgeting Process
Establishing Priorities and objectives
Identification of Investment Proposals
Screening The Proposals
Evaluation and selection
Implementation
Monitoring and Control
Performance audit

Cash Flows
In capital budgeting, the cost and benefits of a proposal are measured in terms of cash
flows.
The term cash flow is used to describe the amount of cash oriented investment and return
generated over time period of the project.
Cash flows are useful approximations of outflow (investment) and inflow (return or
benefits) based on available accounting data.
Components of Cashflows are
(i) Original or Initial cash outflow (Initial investment)
(ii) Operating cash flows (Annual cash flows)
(iii) Terminal cash flow.

Cash Flows
A firm buys an asset costing Rs. 1,00,000 and expects operating profits before depreciation
@ 20% WDV and tax @ 30% of Rs. 30,000 p.a. for the next four years after which the asset
would be disposed off for Rs. 45,000. Find out the each flow for different years
Year Dippr. Asset Value Dippr. @20% PBDT PBT Tax @30% PAT Cash Inflow
1 100000 20000 30000 10000 3000 7000 27000
2 80000 16000 30000 14000 4200 9800 25800
3 64000 12800 30000 17200 5160 12040 24840
4 51200 10240 30000 19760 5928 13832 24072
Depreciated Asset Value = 51200-10240 =40960/-
Taxable Value of Scrap = 45000-40960 = 4040/-
Tax on profit of Scrap =1212/-
Terminal cash Flow = Scrap value- tax = 43788/-

Cash Flows
Year Out flow Inflow
0 100000
1 27000
2 25800
3 24840
4 67860 (24072+43788)

Tools for financial feasibility analysis
Non Discounted cash flow Criteria
Payback period analysis
At what point of time we are making more
money than we are spending ?
Annual rate of Return
annualized net income earned on the average
funds invested in a project.
Discounted cash flow Criteria
Benefit cost ratio analysis
For each rupee how much will be generated?
Net Present value analysis (NPV)
How much is future revenue (or expenditure)
flow worth in today ?
Internal rate of return (IRR) analysis
rate of return on our investment for a fixed
period, during which time we are spending
money and making money

Accounting or Average rate of return (ARR)
The ARR is based on the accounting-concept of return on investment or rate of return.
The ARR may be defined as the annualized net income earned on the average funds
invested in a project.
ARR= Average Annual-Profit (after tax) / Average investment in the project
ARR is a measure based on the accounting profit rather than the cash flows and is very
similar to the measure of rate of return on capital employed which is generally used to
measure the over all profitability of the firm
•ARR ignores the time value of money
•ARR also ignores the life of the proposal
•ARR also ignores salvage value of the proposal
•ARR also fails to recognize the size of the investment

Average rate of return (ARR)
Annual rate of Return
ARR= 668/8000 = 0.0835 = 8.35%
A project is accepted if ARR is higher than minimum expected rate of return
ARR does not consider time value of money
year Investment Gross Profit Depreciation Net Profit
1 13334 2000 5332 -3332
2 8000 6000 5332 668
3 2666 1000 5332 4668
Average 8000 668

Payback Analysis
The payback period as name suggest is defined as the number of years required for the
proposal's cumulative cash inflows to be equal to it cash outflows.
In other words, the payback period is the length of time required to recover the initial
cost of the project.
Payback method
• ignores the timing of the occurrence of the cash flows
• ignores the salvage value and the total economic life of the project
• more a method of capital recovery rather than a measure of profitability of a project

Payback Analysis
As per payback period, project A is more attractive
Project A
Year Outflows
Cumulative
out flows
Inflows
Cumulative
In flows
1 200 200 100 100
2 200 400 300 400
3 100 500 300 700
4 500 300 1000
5 500 300 1300
Total 500 1300
Project B
Year Outflows
Cumulative
out flows
Inflows
Cumulative
In flows
1 200 200 100 100
2 200 400 100 200
3 100 500 200 400
4 500 400 800
5 500 500 1300
Total 500 1300

Payback Analysis
A viable project is one that is able to pay back the original investment as early as
possible.
Payback period indicates when, our investment is out of the woods ie When we are
finally making more money in total than we have spent in total.
Projects with long payback are less attractive than those with short payback.
- they tie up capital longer, not enabling its use for other productive purposes.
- they are generally riskier than those with short payback periods
as over a long stretch of time, many things can go wrong.

Net Present Value (NPV) Analysis
or Discounted cash flows analysis
the late 1970s, Americans experienced inflation rates in the 17% per annum range
Inflation provides one example of what is called the time value of money i.e. A rupee
today has a different value than a rupee one year from now.
There is more to time value of money than the force of inflation.
Consider if no inflation, i.e a rupee today has the same purchasing power as a rupee
one year later.
If you have an opportunity to lend Rs 1,000/- to a business at a 10% interest yearly
then at year end you will receive a payment of Rs 1,100/- at the year end when the loan
is paid off.
Your initial investment of Rs 1,000/- has grown by 10% over time.

or Discounted cash flows analysis
FV =PV (1+r)n
where r is interest rate fraction and n is number of completed time slots
Inflation provides one example of what is called the time value of money i.e. A rupee
today has a different value than a rupee one year from now.
There is more to time value of money than the force of inflation.
Consider if no inflation, i.e a rupee today has the same purchasing power as a rupee
one year later.
If you have an opportunity to lend Rs 1,000/- to a business at a 10% interest yearly
then at year end you will receive a payment of Rs 1,100/- at the year end when the loan
is paid off.
Your initial investment of Rs 1,000/- has grown by 10% over time.

Project A is more attractive than
Project B, because its true, discounted
profit (Rs 533.18) is greater than the
discounted profit of Project B (Rs
485.24).
Project A
Year Outflows Inflows
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 100 0.9091 181.82 90.91 -90.91
2 200 300 0.8264 165.28 247.92 82.64
3 100 300 0.7513 75.13 225.39 150.26
4 300 0.683 0 204.9 204.9
5 300 0.6209 0 186.27 186.27
Total 500 1300 422.23 955.39 533.16
Project B
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 100 0.9091 181.82 90.91 -90.91
2 200 100 0.8264 165.28 82.64 -82.64
3 100 200 0.7513 75.13 150.26 75.13
4 400 0.683 0 273.2 273.2
5 500 0.6209 0 310.45 310.45
Total 500 1300 422.23 907.46 485.23

Both projects have same NPV
Project A
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 0.9091 181.82 0 -181.82
2 200 0.8264 165.28 0 -165.28
3 100 100 0.7513 75.13 75.13 0
4 200 0.683 0 136.6 136.6
5 500 0.6209 0 310.45 310.45
Total 500 800 422.23 522.18 99.95
Project B
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 50 0.9091 45.455 0 -45.46
2 200 0.8264 165.28 0 -165.28
3 200 100 0.7513 150.26 75.13 -75.13
4 89.65 200 0.683 61.23095 136.6 75.37
5 500 0.6209 0 310.45 310.45
Total 539.65 800 422.226 522.18 99.95

Internal rate of return(IRR) Analysis
Both projects have same NPV
By Excel function IRR of project A is 14
% and Project B is 12 %
Project A
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 -200 0.9091 181.82 0 -181.82
2 -200 0.8264 165.28 0 -165.28
3 -100 100 0.7513 75.13 75.13 0
4 200 0.683 0 136.6 136.6
5 500 0.6209 0 310.45 310.45
Total -500 800 422.23 522.18 99.95
Project B
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 -50 0.9091 45.455 0 -45.46
2 -200 0.8264 165.28 0 -165.28
3 -200 100 0.7513 150.26 75.13 -75.13
4 -89.65 200 0.683 61.23095 136.6 75.37
5 500 0.6209 0 310.45 310.45
Total -539.65 800 422.226 522.18 99.95

Project A
Discounting
factor @ 15%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 0.8696 -173.92 0 -173.92
2 200 0.7561 -151.22 0 -151.22
3 100 100 0.6575 -65.75 65.75 0
4 200 0.5718 0 114.36 114.36
5 500 0.4972 0 248.6 248.6
Total 500 800 -390.89 428.71 37.82
Project B
Discounting
factor @ 15%
PV of
out flows
PV of
In flows
PV of
Net flows
1 50 0.8696 -43.48 0 -43.48
2 200 0.7561 -151.22 0 -151.22
3 200 100 0.6575 -131.5 65.75 -65.75
4 89.65 200 0.5718 -51.2619 114.36 63.1
5 500 0.4972 0 248.6 248.6
Total 539.65 800 -377.462 428.71 51.25
Project A
Year
Outflo
ws
Inflows
Discounting
factor @ 20%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 0.8333 -166.66 0 -166.66
2 200 0.6944 -138.88 0 -138.88
3 100 100 0.5787 -57.87 57.87 0
4 200 0.4823 0 96.46 96.46
5 500 0.4019 0 200.95 200.95
Total 500 800 -363.41 355.28 -8.13
Project B
Discounting
factor @ 20%
PV of
out flows
PV of
In flows
PV of
Net flows
1 50 0.8333 -41.665 0 -41.67
2 200 0.6944 -138.88 0 -138.88
3 200 100 0.5787 -115.74 57.87 -57.87
4 89.65 200 0.4823 -43.2382 96.46 53.22
5 500 0.4019 0 200.95 200.95
Total 539.65 800 -339.523 355.28 15.76

IRR of Project A is 19% and of Project B
is 23 %
a project's IRR is higher than the
prevailing interest rate, then it may be
smart to invest in it.
IRR model assumes that money
employed is utilized all the time and is
not remain unutilized at all.
Project A
Discounting
factor @ 19%
PV of
out flows
PV of
In flows
PV of
Net flows
1 -200 0.8403 -168.06 0 -168.06
2 -200 0.7062 -141.24 0 -141.24
3 -100 100 0.5934 -59.34 59.34 0
4 200 0.4987 0 99.74 99.74
5 500 0.419 0 209.5 209.5
Total -500 800 -368.64 368.58 -0.06
Project B
Discounting
factor @ 10%
PV of
out flows
PV of
In flows
PV of
Net flows
1 -50 0.813 -40.65 0 -40.65
2 -200 0.661 -132.2 0 -132.2
3 -200 100 0.5374 -107.48 53.74 -53.74
4 -89.65 200 0.4369 -39.1681 87.38 48.21
5 500 0.3552 0 177.6 177.6
Total -539.65 800 -319.498 318.72 -0.78

Benefit to Cost ratio
The benefit-cost ratio is nothing more than a measure of benefit divided by a measure of cost.
Measure of benefit can be anything: financial profit/ cost savings, happiness, error reduction, throughput
time, and so on.
Practically, the measure of benefit is revenue - or in non- revenue generating situations, cost savings.
Benefit-cost ratio (B/C) > 1.0 Revenue is greater than expenditures. i.e. investment is profitable.
Benefit-cost ratio (B/C) = 1.0. Revenue and expenditures offset each other.
Consequently, you are facing a breakeven situation.
Benefit-cost ratio (BE) < 1.0. In this case, expenditures outstrip revenue. You are losing money. Example: BIC
= Rs 40,000/Rs 50,000 = 0.8 Interpretation: For each dollar you are spending on this project, you are only
gaining 80 cents of revenue. Thus you are losing money.

Benefit to Cost ratio
Discounted B/C for project A
= 428.71/390.89 =1.09
Discounted B/C for project B
= 428.71/377.46 =1.14
B/C for project A = 800/500 =1.6
B/C for project B = 800/539.65 =1.48
Benefit-cost ratio analysis using discounted cash flow
data, the computing what in finance is called the
profitability index.
Project A
Discounting
factor @ 15%
PV of
out flows
PV of
In flows
PV of
Net flows
1 200 0.8696 173.92 0 -173.92
2 200 0.7561 151.22 0 -151.22
3 100 100 0.6575 65.75 65.75 0
4 200 0.5718 0 114.36 114.36
5 500 0.4972 0 248.6 248.6
Total 500 800 390.89 428.71 37.82
Project B
Discounting
factor @ 15%
PV of
out flows
PV of
In flows
PV of
Net flows
1 50 0.8696 43.48 0 -43.48
2 200 0.7561 151.22 0 -151.22
3 200 100 0.6575 131.5 65.75 -65.75
4 89.65 200 0.5718 51.26 114.36 63.1
5 500 0.4972 0 248.6 248.6
Total 539.65 800 377.46 428.71 51.25

Benefit to Cost ratio for non-revenue generating
project
Many projects that are carried out are not revenue generating
Ex. . a typical information technology (IT) project in an organization
This can improve revenue performance indirectly, as the organization reduces operating costs. But it is
not directly tied to generating revenue
Benefit-cost ratio analysis for this involves cost saving instead of revenue generation.

B/C ratio : pitfalls
There are a number of pitfalls associated with benefit-cost analyses that are
important to know.
B/C ratios do not provide information on the size of the numbers being
reviewed.
EX: Project A BIC = 3.1 Project B BIC = 2.7 Project A's is
better
Project A BIC = 3100/1000 = 3.1 Project B BIC = 2,700,000/1,000,000 = 2.7
Since B/C is a ratio, sense of the size of the numbers vanishes. . For most
organizations, Project B is more attractive than A, as B has substantial
revenue.
For valid comparisons among the B/C ratios of different projects, One must
know the actual size of the numbers that are used to compute the ratios.

B/C ratio : pitfalls
2. B/C ratios do not provide information on when payback occurs. Consider the following two ratios:
Project A B/C = 3.1 Project B B/C = 2.7
Again, Project A appears to be more attractive than Project B.
If Project A realizes a B/C of 3.1 after five years, it is less attractive than Project B, if B realizes its
B/C ratio in two years.
3. The easiest quantitative data to acquire is basic business data derived from estimated budgets and,
possibly, on anticipated revenues. Hard-to-measure factors are often ignored when computing the ratios.
For example, the main benefit of a project may be what is called a second-order benefit - e.g., this project,
while not profitable in itself, will provide the groundwork for major revenue streams generated on future
projects.
Another benefit might be improved public perceptions of the company's activities.
None of these pitfalls is fatal. With B/C, analysts should be aware of their existence and should strive to deal
with them so that the analyses are valid.

Return on Investment (ROI)
The ROI is nothing more than a measure of NPV expressed as percentage of present value of cost.
ROI = (NPV/PV of cost)x 100= (discounted B/C -1)x 100
ROI> 0 Revenue is greater than expenditures. i.e. investment is profitable.
ROI= 0. Revenue and expenditures offset each other.
Consequently, you are facing a breakeven situation.
ROI< 0. In this case, expenditures outstrip revenue. You are losing money.

Terminal Value (TV)
The other variant of the NPV technique is known as the TV technique. In this case, a new
dimension is added to the NPV technique. As already discussed in the NPV technique,
the future cash flows are discounted to make them comparable.
In the TV technique, the future cash flows are first compounded at the expected rate of
interest for the period from their occurrence till the end of the economic life of the
project. The compounded values are then discounted at an appropriate discount rate to
find out the present value. This present value is compared with the initial outflow to
find, out the suitability of the proposal.

Terminal Value (TV)
Project A
Year Outflows Inflows Net flow
Compounding
factor @ 8%
Compounded
Net flow @ 8%
TV=PV of compounded Netflow
(discounted @ 8%)
Discounting
factor @ 10%
PV of Net
flows
0 100 -100 1.4693 -146.93 1
1 200 100 -100 1.3605 -136.05 0.9091 -90.91
2 200 300 100 1.2597 125.97 0.8264 82.64
3 100 300 200 1.1664 233.28 0.7513 150.26
4 300 300 1.08 324 0.683 204.9
5 300 300 1 300 0.6209 186.27
Total 600 1300 700.27 434.8 433.16
Project B
Year Outflows Inflows Net flow
Compounding
factor @ 8%
Compounded
Net flow @ 8%
TV=PV of compounded Net flow
(discounted @ 8%)
Discounting
factor @ 10%
PV of Net
flows
0 100 -100 1.4693 -146.93 1
1 200 100 -100 1.3605 -136.05 0.9091 -90.91
2 200 100 -100 1.2597 -125.97 0.8264 -82.64
3 100 200 100 1.1664 116.64 0.7513 75.13
4 400 400 1.08 432 0.683 273.2
5 500 500 1 500 0.6209 310.45
Total 500 1300 639.69 397.18 385.23

Discounted Payback Period
This method is a combination of the original payback method and the
discounted cash flow technique.
In this method, the cash flows of the project are discounted to find their
present values. The present value of the cash inflows is then compared with
the present value of the outflow, in order to identify the period taken to
recover the initial cost or the present value of outflow.
This method thus, takes care of the main drawback of the pay back period
method and allows the consideration of the time value of money of cash flows.
However, it still does not take into account those cash inflows, which occur
subsequent to the payback period

Risk Analysis
 Risk is inherent in almost every business decision
 Risk refers to variability
 Capital budgeting decision involves cost and benefits over a long period of time
 Financial analysis has two phases
 feasibility analysis
 Risk analysis
 Sources of Risk
 Project Specific Risk: factors specific to project like quality, production
 Corporate Risk: action of competitors
 Industry specific Risk: technological developments and regulatory charges
 Market risk: Changes in microeconomic factors have impact project
 International risk: in case of foreign projects or political risk

Techniques of Risk Analysis
Techniques for risk
analysis
Analysis of Stand
alone Project
Analysis of
Contextual Risk
Sensitivity Analysis Scenario Analysis
Break Even Analysis Hillier Model
Simulation Analysis Decision tree analysis
Corporate Risk
Analysis
Market Risk Analysis

Measures of Risk
Range : Range of variance is difference of maximum and minimum value
Mean or average 𝑥 = 𝐸 𝑥 = 𝑖 𝑝𝑖 𝑥𝑖
Standard deviation : standard deviation (𝜎 ) is defined as 𝜎 = 𝐸 𝑥 − 𝑥 2 = 𝑖 𝑝𝑖 𝑥 − 𝑥 2
Coefficient of Variation: standard deviation (𝜎 ) is not adjusted for scale. Coefficient of
variation is adjusted for scale and is defined as 𝐶𝑉 =
𝜎
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑀𝑒𝑎𝑛 𝑣𝑎𝑙𝑢𝑒
Semi Variance: since investors are concerned with negative variations only so computing
variance with only negative errors (outcome less than mean) gives semi variance
standard deviation (𝜎 ) is defined as
𝑠𝑒𝑚𝑖 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝐸 𝑥 − 𝑥 2 𝑓𝑜𝑟 𝑜𝑛𝑙𝑦 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 < 𝑥

Measures of Risk
NPY ( thousands) x Probability p px x- 𝑥 𝑥 − 𝑥 2 p x sq. error
200 0.3 60 -340 115600 34680
600 0.5 300 60 3600 1800
900 0.2 180 360 129600 25920
mean NPV ( 𝑥) 540 Sq. variance 62400
std deviation 249.8
For the example, Range = 900-200 = 700 K
𝑀𝑒𝑎𝑛 𝑁𝑃𝑉 = 0.3 𝑥 200 + 0.5 𝑥 600 + 0.2 𝑥900 = 540
𝜎 = 𝐸 𝑥 − 𝑥 2 = 0.3 𝑥 (−340)2+0.5 𝑥 602 + 0.2 𝑥 3602 = 249.8 𝐾
Coefficient of Variation, 𝐶𝑉 =
249.8
540
= 0.46
Semi standard deviation= 0.3 𝑥 (−340)2= 186.2 𝐾

Measures of Risk
• Standard deviation is most commonly employed as measure of risk in finance.
• For computing mean and dispersion variables, probability distribution is required,
• If sufficient records for similar ventures are available, probability distribution is
quite ‘objective,
• If sufficient records are not available, probability distribution is quite ‘subjective’,
Prospective on risk
There are three perspectives of the risk
• Stand alone risk: risk of the project when viewed in isolation
• Firm risk or Corporate risk: contribution of a project to the risk of the firm
• Systematic risk or market risk: risk of a project from view point of diversified investor

Sensitivity analysis
Sensitivity analysis is ‘what if’ analysis
NPV = -20000+4000 x PVIFA
= -20000+4000 x 5.65
= 2600 K
Cash flows depends on various factors and can
vary widely.
So optimistic and pessimistic estimates for
variables defined and NPV calculated
Cash Flow of ABC LTD project
(in thousands) Year 0 year 1-10
1Investment 20000
2Sales 18000
3
Variable cost
( 2/3 of sales) 12000
4Fixed cost 1000
5Depreciation 2000
6Pre tax profit 3000
7Taxes (@ 33.3 %) 1000
8PAT 2000
9
cash flow from operation
(PAT+ depreciation) 4000
10Net cash flow 2000 4000
Cost of capital 12%
Accumulated PV indexing
factor (PVIFA) @ 12 % 5.65

Sensitivity analysis
• NPV calculated by varying one variable at a time
• NPV is more sensitive to sales and least sensitive to fixed cost. For more sensitive variable, it
may be explored how variability of the factor can be contained.
• In real situation, many variable may change at a time so interpretation of results is subjective
Sensitivity of NPV to variations in the value of key variables in ABC LTD project
Range (in thousands) NPV
Pessimistic Expected Optimistic Pessimistic Expected Optimistic Variation
1 Investment 24000 20000 18000 -1400 2600 4600 6000
2 Sales 15000 18000 21000 -1147 2600 6366 7513
3
Variable cost
as percentage
70 66.67 65 340 2600 3730 3390
4 Fixed cost 1300 1000 800 1470 2600 3353 1883

Break-Even analysis
• It tells what is minimum value of key variables/
revenues so that project does not ‘lose money’
• Variable cost to sales ratio= 12/18= 0.667
• Contribution to margin ratio =0.333
• Accounting break even=
𝐹𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡+𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑡𝑜 𝑚𝑎𝑟𝑔𝑖𝑛 𝑟𝑎𝑡𝑖𝑜
=
1000+2000
0.333
= 9000 𝐾
• For sales 0f 9000 K , PBT, PAT will be zero
• At accounting break even project gives zero % return
(in thousands) Year 0
year
1-10
1Investment 20000
2Sales 18000
3
Variable cost
( 2/3 of sales) 12000
4Fixed cost 1000
5Depreciation 2000
7Taxes (@ 33.3 %) 1000
8PAT 2000
9
Cost of capital 12%

Financial Break-Even analysis
• Focus is on NPV and not on accounting profit
• Variable cost =0.667 x sales
Contribution = 0.333 x sales
Fixed cost = 1000
Depreciation =2000
PBT = 0.333 x sales-3000
Tax = 0.333 x (0.333 x sales-3000)=0.111 x sales - 1000
PAT = 0.667 x (0.333 x sales-3000)=0.222 x sales - 2000
Cash flows = PAT+ depreciation= 0.222 x sales
PV of cash flows= Cash flows x PVIFA= 1.255 x sales
Breakeven NPV = 20000- 1.255 x sales= 0
so Breakeven sales= 15936 K
(in thousands) Year 0
year
1-10
1Investment 20000
2Sales 18000
3
Variable cost
( 2/3 of sales) 12000
4Fixed cost 1000
5Depreciation 2000
7Taxes (@ 33.3 %) 1000
8PAT 2000
9
Cost of capital 12%

Hiller Model : Un correlated cash flows
interest rate = 12 %
Expected NPV, 𝑁𝑃𝑉 = 𝑡=1
3 𝐴 𝑡
(1+𝑟) 𝑡 =
5000
1.12
+
4000
(1.12)2 +
5000
(1.12)3 = 4464.3 + 3188. 8 + 3558.9 = 11211.9
Standard deviation 𝜎 𝑁𝑃𝑉 = 𝑡=1
3 𝜎𝑡
2
(1+𝑟)2𝑡 =
2400000
1.122 +
1600000
1.124 +
2400000
1.126 = 2036.18
Analytical derivation to find expected NPV and standard deviation of NPV
Year 1 Year 2 Year 3
Net Cash flow (Rs) Probability Net Cash flow (Rs) Probability Net Cash flow (Rs) Probability
3000 0.3 2000 0.2 3000 0.3
5000 0.4 4000 0.6 5000 0.4
7000 0.3 6000 0.2 7000 0.3
Mean 5000 4000 5000
Standard variance 2400000 Standard variance 1600000 Standard variance 2400000

Project selection under risk
• Judgemental Evaluation: Accept or reject the project based on the risk and return
characteristics without any formal method for incorporating risk in decision making
• Payback period requirement: payback period requirement is applied to control risk.
• Risk adjusted discount method:
• If the risk of the project is equal to risk of existing investment, discount rate is average
cost of capital
• If the risk of the project is greater than risk of existing investment, discount rate is higher
than average cost of capital

Capital budgeting decisions:

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