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Illustration 1 :Zenith Industrial Ltd. are thinking of investing in a

project costing Rs. 20 lakhs. The life of the project is five years and the estimated salvage value of the project is zero. Straight line method of charging depreciation is followed. The tax rate is 50%. The expected cash flows before tax are as follows :

Year 1 2 3 4 5Estimated Cash flow before Depreciation and tax (Rs. lakhs) 4 6 8 8

10You are required to determine the : (i) Payback

Period for the investment, (ii) Average Rate of Return on the investment, (iii) Net Present Value at 10% Cost of Capital, (iv) Benefit-Cost Ratio.

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Illustration 2 :The relevant information for two alternative systems of internal

transportation are given below :(Rs.)

Particulars System 1 System 2Initial investment 60,00,000 40,00,000Annual operating costs 10,00,000 900,000Life 6 years 4 yearsSalvage value at the end 20,00,000 15,00,000Which system would you prefer if the cost of capital is 6%? Justify your

recommendationwith appropriate analysis.[Present value of annuity at 6% for 6 years = 4.917 and for 4 years =

3.465. Present value ofRs. 1.00 at 6% at the end of 6the year 0.705 and that at the end of 4th

year 0.792].

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Capital rationing Capital rationing is a situation where a

constraint or budget ceiling is placed on the total size of capital expenditures during a particular period. Often firms draw up their capital budget under the assumption that the availability of financial resources is limited.

Under this situation, a decision maker is compelled to reject some of the viable projects having positive net present value because of shortage of funds. It is known as a situation involving capital rationing

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The total available budget for a company is Rs. 20 crores and the total cost of the projects is Rs. 25 crores. The projets listed below have been ranked in order of profitability. There is possibility of submitting X project where cost is assumed to be Rs. 13 crores and it has the Profitability Index of 140

Project Cost Profitability index A 60000000 1.50B 5 0000000 1.25C 7 0000000 1.20D 20000000 1.15E 5 0000000 1.10

Which projects, including X, should be acquired by the company?

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In a capital rationing situation (investment limit Rs. 25 lakhs), suggest the most desirable feasible combination on the basis of the following data (indicate justification): Projects B and C are mutually exclusive.Projects Net cash flows NPV

A 1500000 600000B 1000000 450000C 750000 360000D 600000 300000

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S. Ltd., has Rs. 10,00,000 allocated for capital budgeting purpose. The following proposal and associated profitability indexes have been determined.

Which of the above investment should be undertaken? Assume that projects are indivisible and there is no alternative use of the money allocated for capital budgeting?

Projects Cost Profitability Index1 3,00,000 1.222 1,50,000 0.953 3,50,000 1.24 4,50,000 1.185 2,00,000 1.26 64,00,000 1.05

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Alpha Limited is considering five capital projects for the years 2003 and 2004. The company is financed by equity entirely and its cost of capital is 12%. The expected cash flows of the projects are as belows:Projects

Year end cashflows2003 2004 2005 2006

A -70 35 35 20B -40 -30 45 55C -50 -60 70 80D nil -90 55 65E -60 -20 40 50

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All projects are divisible i.e., size of investment can be reduced, if necessary in relation to availability of funds. None of the projects can be delayed or undertaken more than once. Calculate which project Alpha Limited should undertake if the capital available for investment is limited to Rs. 1,10,000 in 2003 and with no limitation in subsequent years. For your analysis,

use the following present value factors :Years 2003 2004 2005 2006Factors 1.00 0.89 0.80 0.71

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Terminal Value MethodAssumption :(1) Each cash flow is reinvested in another project

at a predetermined rate of interest.(2) Each cash inflow is reinvested elsewhere

immediately after the completion of the project.Decision-makingIf the P.V. of Sum Total of the Compound reinvested

cash flows is greater than the P.V. Of the outflows of the project under consideration, the project will be accepted otherwise not.

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Illustration :

Original Investment Rs. 40,000 Life of the project 4 years Cash Inflows Rs. 25,000 for 4 years Cost of Capital 10% p.aExpected interest rates at which the cash

inflows will be reinvested :Year-end 1 2 3 4% 8 8 8 8

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RISK AND UNCERTAINLY IN CAPITAL BUDGETING

Capital budgeting requires the projection of cash inflow and outflow of the future. The future in always uncertain, estimate of demand, production, selling price, cost etc., cannot be exact.

For example: The product at any time it become obsolete therefore, the future in unexpected. The following methods for considering the accounting of risk in capital budgeting. Various evaluation methods are used for risk and uncertainty in capital budgeting are as follows:

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(i) Risk-adjusted cut off rate (or method of varying discount rate)

(ii) Certainly equivalent method.(iii) Sensitivity technique.(iv) Probability technique(v) Standard deviation method.(vi) Co-efficient of variation method.(vii) Decision tree analysis.

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(i) Risk-adjusted cutoff rate (or Method of varying)

This is one of the simplest method while calculating the risk in capital budgeting increase cut of rate or discount factor by certain percentage an account of risk.

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Example 1 The Ramakrishna Ltd., in considering the purchase of a

new investment. Two alternative investments are available (X and Y) each costing Rs. 150000. Cash inflows are expected to be as follows:

Cash Inflows Year Investment X Investment Y Rs. Rs.1 60,000 65,0002 45,000 55,0003 35,000 40,0004 30,000 40,000

The company has a target return on capital of 10%. Risk premium rate are 2% and 8% respectively for investment X and Y. Which investment should be preferred?

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Answer

Project X Project Y

Years

Discounting factor= Cost of

capital + Risk premium Rate(10%

+2%=12%)

Cash inflows

Present Value

of CFAT

Discounting factor= Cost of capital + Risk premium Rate(10%

+8%=18%)

Cash inflows

Present Value

of CFAT

1 0.893 60000 0.847 85000

2 0.797 45000 0.718 55000

3 0.712 35000 0.609 40000

4 0.636 30000 0.516 40000

TOTAL PRESENT VALUE OF

CFAT TOTAL PRESENT VALUE OF CFAT

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(ii) Certainly equivalent methodIt is also another simplest method for

calculating risk in capital budgeting. It reduces expected cash inflows by certain amounts. it can be calculated by multiplying the expected cash inflows by certainly equivalent co-efficient in order to convert the uncertain cash inflow to certain cash inflows.

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Exercise 14There are two projects A and B. Each involves an

investment of Rs. 50,000. The expected cash inflows and the certainly co-efficient are as under:

Risk-free cutoff rate is 10%. Suggest which of the two projects. Should be preferred

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Step 1: calculate certainly cash inflows at certainly co efficient factors.

Step 2: calculate present value of cash inflows at discounting rate.

Step 3: Calculate NPV and take decision.

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Project AYears

Cash inflows

(1)

Certainly Co

efficient(2)

Certainly cash

inflows=3(1X2)

(4)Present

value factors

(5)PV certainly

cash inflows

1 35000 0.8 0.9092 30000 0.7 0.8263 20000 0.9 0.751

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Project BYears

Cash inflows

(1)

Certainly Co

efficient(2)

Certainly cash

inflows=3(1X2)

(4)Present

value factors

(5)PV certainly

cash inflows

1 25000 0.9 0.9092 35000 0.8 0.8263 20000 0.7 0.751

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(iii) Sensitivity techniqueWhen cash inflows are sensitive under different

circumstances more than one forecast of the future cash inflows may be made. These inflows may be regarded on ‘Optimistic’, ‘most likely’ and ‘pessimistic’. Further cash inflows may be discounted to find out the net present values under these three different situations.

If the net present values under the three situations differ widely it implies that there is a great risk in the project and the investor’s is decision to accept or reject a project will depend upon his risk bearing activities.

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Mr. Ritik is considering two mutually exclusive project ‘X’ and ‘Y’. You are required to advise him about the acceptability of the projects from the following information

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The net present values on calculated above indicate that project Y is more risky as compared to project X. But at the same time during favourable condition, it is more profitable also. The acceptability of the project will depend upon Mr. Selva’s attitude towards risk. If he could afford to take higher risk, project Y may be more profitable.

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(iv) Probability techniqueProbability technique refers to the each

event of future happenings are assigned with relative frequency probability. Probability means the likelihood of future event. The cash inflows of the future years further discounted with the probability. The higher present value may be accepted.

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Example

Years

Project 1

Probability

Project 2 Probability

0 10000 - 10000 -

1 10000 0.2 12000 0.2

2 18000 0.6 16000 0.6

3 8000 0.2 14000 0.2

Cost of capital is 15%

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(v) Standard deviation method

Two Projects have the same cash outflow and their net values are also the same, standard durations of the expected cash inflows of the two Projects may be calculated to measure the comparative and risk of the Projects. The project having a higher standard deviation in said to be more risky as compared to the other.

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From the following information, ascertain which project should be selected on the basis of standard deviation.

Years

Project 1

Probability

Project 2 Probability

1 3200 0.2 3200 0.12 5500 0.3 5500 0.43 7400 0.3 7400 0.44 8900 0.2 8900 0.1

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N= sum of all probabilities

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Inflows(1)

Deviation(d)

from mean(

2)

Square deviation

(3)

Probability

(4)(f)

Weighted

deviation

(3*4)

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Inflows(1)

Deviation(d)

from mean(

2)

Square deviation

(3)

Probability

(4)(f)

Weighted

deviation

(3*4)

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Mr. Kumar in considering an investment proposal of Rs.40,000. The expected returns during the life of the investment are as under:

Year I Event Cash Inflow Probability(i) 16,000 0.3(ii) 24,000 0.5(iii) 20,000 0.2

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Example 1From the following information, calculate the

pay-back periods for the 3 projects. Which requires Rs. 2,00,000 each? Suggest most profitable project.

Year Project I Project II Project III1 50,000 60,000 35,0002 50,000 70,000 45,0003 50,000 75,000 85,0004 50,000 45,000 50,0005 50,000 ------ 35,000

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Example 2The machine cost Rs. 1,00,000 and has

scrap value of Rs. 10,000 after 5 years. The net profits before depreciation and taxes for the five years period are to be projected that Rs. 20,000, Rs. 24,000, Rs. 30,000, Rs. 26,000 and Rs. 22,000. Taxes are 50%. Calculate pay-back period and accounting rate of return.

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Example 3A company has to choose one of the following two

actually exclusive machine. Both the machines have to be depreciated. Calculate NPV.

Cash inflowsYear Machine X Machine Y

0 –20,000 –20,0001 5,500 6,2002 6,200 8,8003 7,800 4,3004 4,500 3,7005 3,000 2,000

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Example 4A machine cost Rs. 1,25,000. The cost of capital

is 15%. The net cash inflows are as under:Year Rs.

1 25,0002 35,0003 50,0004 40,0005 25,000

Calculate internal rate of return and suggest whether the project should be accepted of cost.

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Example 5Which project will be selected under NPV and IRR?

A BCash outflow 2,00,000 3,00,000Cash inflows at the end of1 Year 60,000 40,0002 Year 50,000 50,0003 Year 50,000 60,0004 Year 40,000 90,0005 Year 30,000 1,00,000Cost of capital is 10%.

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Example 6SP Limited company is having two projects,

requiring a capital outflow of Rs. 3,00,000. The expected annual income after depreciation but before tax is as follows:

Depreciation may be taken as 20% of original cost and taxation at 50% of net income:

You are required to calculate:(a) Pay-back period (b) Net present value(c) According rate of return (d) Net present

value index.(e) Internal rate of return.

Years 1 2 3 4 5Rs 90000 80000 70000 60000 50000

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Example From the following information, select which project is

better.Cash Inflows (Year) I II

0 –20,000 –20,0001 7,000 8,0002 7,000 9,0003 6,000 5,000

Risk less discount rate is 5%. Project I is less risks as compared to project II. The management consider risk premium rates at 5% and 10% respectively appropriate for discounting the cash inflows.

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There are two mutually exclusive projects I and II. Each projects requires an investment of Rs. 60,000. The following are the cash inflows and certainly co-efficient are as follows.

Risk-free cutoff rate is 10%. Evaluate which project will be considered