Appraisal criteria capital budgeting
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Appraisal Criteria – Capital Budgeting. Batch 2013 – 2016 :2 nd Sem MMM / MFM SIMSR. Classification. Evaluation Criteria. Non discounting Criteria. Discounting Criteria. Internal Rate Of Return(IRR). Pay Back Period. Net Present Value(NPV). Accounting Rate of Return (ARR).

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Appraisal Criteria – Capital Budgeting

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Appraisal criteria capital budgeting

Appraisal Criteria – Capital Budgeting

Batch 2013 – 2016 :2ndSemMMM / MFMSIMSR


Classification

Classification

Evaluation Criteria

Non discounting Criteria

Discounting Criteria

Internal Rate

Of Return(IRR)

Pay Back Period

Net Present

Value(NPV)

Accounting Rate

of Return

(ARR)

Annual Capital

Charge

BCR / NBCR


Pay back period

Pay back period

It measures the length of time required to recover the initial outlay in the project.

Eg: If a project with a life of 5 years involves an initial outlay of Rs.20 lakh and is expected to generate a constant annual inflow of Rs.8 lakh, the payback period of the project =20/8 =2.5 yrs.


Pay back period1

Pay back period

Eg: On the other hand if the project is expected to generate annual inflows of, say Rs.4 lakh, Rs.6 lakh, Rs.10 lakh, Rs.12 lakh and Rs.14 lakh over the 5 year period the pay back period will be equal to 3 yrs because the sum of the cash inflows over the first three years is equal to the initial outlay.


Pay back period2

Pay back period

In order to use the payback period as a decision rule for accepting or rejecting the projects, the firm has to decide upon an appropriate cut –off period. Projects with pay back periods less than or equal to the cut –off period will be accepted and others will be rejected.


Pay back period3

  • Cons

  • It fails to consider the time value of money.

  • The cut –off period is chosen rather arbitrarily and applied uniformly for evaluating projects regardless of time span. It may accept too many short –lived projects and too few long-lived ones.

  • It may lead to discrimination against projects which generate substantial cash inflows in later years, the criteria cannot be considered as a measure of profitability

Pay back period

  • Pros

  • It is simple in both concept

    and application.

  • It helps in wedding out

    risky projects by favoring only

    those projects which generate substantial

    inflows in

    earlier years.


Discounted pay back period

Discounted Pay Back Period

To incorporate the time value of money in the calculation of pay back period some firms compute Discounted Pay Back Period.

These firms discount the cash flows before they compute the pay back period.

Eg: If a project involves an initial outlay of Rs.10 lakh and is expected to generate a net annual inflow of Rs.4 lakh for the next 4 yrs……….. Calculate the discounted pay back period represented by n no. of yrs……


Discounted pay back period1

Discounted Pay Back Period

  • 4*PVIFA(12,n) =10………………..(1)

    Assuming the cost of funds to be 12%

    Equation (1) can be re-written as

    PVIFA(12,n) =2.5

    From PVIFA Tables, we find that

    PVIFA(12,3) = 2.402

    PVIFA (12,4) =3.037


Discounted pay back period2

Discounted Pay Back Period

Therefore ‘n’ lies between 3 and 4 and is approximately equal to 3.15 yrs

n =3+(4-3) *(2.500-2.402)

(3.037-2.402)

= 3.15 yrs

But… still this mechanism has a shortcoming…….. As it depends on the choice of an arbitrary cut –off date and ignore all cash flows after that date. In practice, companies do not give much importance to the payback period as an appraisal criteria.


Accounting rate of return arr

ARR = Avg Profit after Tax

Avg book value of the investments

To use it as an appraisal criterion, the ARR of a project is compared with the ARR of the firm as a whole or against some external yard –stick like the average rate of return for the industry as a whole.

Accounting Rate of Return (ARR)


Average investments

Average investments

Average investments = Net working capita + salvage value+ ½ [ initial cost of machine – Salvage Value]


Example

Example


Solution

Solution

Avg annual income =

(30000+20000+10000)/3

= 20000

Avg net book value of investment

= 0 + (90000- 0) /2

= 45000

ARR = (20000) /(45000) *100

=44%

The firm will accept the project if its target avg rate of return is above 44 %


Merits of arr

Merits of ARR

  • Like pay back criterion, ARR is simple both in concept and application. It appeals to the businessmen who find the concept of rate of return familiar and easy to work with rather than absolute quantities.

  • It considers the returns over the entire life of the project and therefore serves as a measure of profitability ( unlike the pay back period which is only a measure of capital recovery)


Demerits of arr

Demerits of ARR

  • First, this criterion ignores the time value of money. Put differently, it gives no allowance for the fact that immediate receipts are more valuable than distant flows and as a result gives too much weight to the more distant flows.

  • The ARR depends on the accounting income and not on the cash flows. Since cash flows and accounting income are often different and investment appraisal emphasizes cash flows, a profitability measure based on accounting income cannot be used as a reliable investment appraisal criterion.


Demerits of arr1

Demerits of ARR

  • Finally the firm using ARR as an appraisal criterion must decide on a yard stick for judging a project and this decision is often arbitrary.Often firms use their current book-return as the yard stick for comparison. In such cases if the current book return of a firm tends to be unusually high or low, then the firm can end upon rejecting good projects or accepting bad projects.


Net present value npv

Net Present Value (NPV)

The Net Present Value is equal to the present value of future cash flows and any immediate cash outflows.

In case of a project, the immediate cash flow will be investment (cash outflow) and the net present value will be therefore equal to the present value of future cash inflows minus the initial investment.


Revision recall net cash flow calculation

Revision…….(Recall Net Cash Flow Calculation)

Q) Sandals inc. is considering the purchase of a new leather cutting machine to replace an existing machine that has a book value of Rs.3,000 and can be sold for Rs.1,500. The estimated salvage value of the old machine in four years would be zero, and it is depreciated on a straight line basis. The new machine will reduce costs (before tax) by Rs.7,000 per year, i.e., Rs.7,000 cash savings over the old machine. The new machine has a four year life, costs Rs.14,000 and can be sold for an expected amount of Rs.2,000 at the end of the fourth year. Assuming straight –line depreciation, and a 40% tax rate, define the cash flows associated with the investment. (assume straight line method of depreciation for tax purposes)


Solution1

Solution


Working notes

Working Notes

Computation of depreciation:

Existing leather –cutting machine

Rs.3,000/4= Rs.750 pa

New leather –cutting machine

Rs.12,000/4= Rs.3,000 pa

Incremental depreciation = Rs.2,250 pa


Brain gym back to npv

Brain Gym…..(back to NPV)

  • Now consider the project just described . Compute the net present value of the project, if the cost of the funds to the firm is 12%…….


Solution to brain gym

Solution to Brain Gym

NPV = Rs.[-12,500+(4554+4065+3631+4516)]

= Rs[.-12500 +16766]

= Rs.4266


Npv rationale

NPV ……Rationale

A project will be accepted if its NPV is positive and rejected if its NPV is negative

What if the NPV works out to be exactly zero???

It it happens, theoretically speaking the decision –maker is

supposed to be indifferent between accepting or rejecting

the project. But in practice, NPV in the neighborhood of zero

calls for a close review of the projections made in respect of

such parameters that are critical to the viability of such

marginally viable projects.


Pros and cons

Pros and Cons

  • Cons

  • Difficulty in comprehending the concept’s application

  • Most non-financial

    executives and business

    men find ‘ Rate on Capital

    Employee's or ‘ Average

    Rate of Return’ easy to interpret compared to

    absolute values like the NPV

Pros

  • Conceptually sound, takes into account

    time value of money

  • Considers the cash

    flow stream entirely

  • NPV is congruent

    with the objectives of

    investment decision making

    viz., maximization of shareholder’s wealth


Benefit cost ratio bcr

Benefit –Cost Ratio (BCR)

The benefit cost ( or the profitability Index) is defined as follows:

BCR = PV/ I

Where ,

PV – present value of future cash flows

I – Initial Investment


Nbcr variant of bcr

NBCR: Variant of BCR

NBCR, net benefit cost ratio is defined as:

NBCR = NPV /I

= (PV –I)/I

= (PV/I) –1

= BCR -1


Brain gym

Brain Gym

  • Calculate the BCR and NBCR of the previous example

Ans ) BCR = 16766/12500 =1.34

NBCR = 4266/12500 =0.34


Decision rule based on bcr nbcr

Decision Rule based on BCR/NBCR

If Decision Rule

BCR >1(NBCR>0) Accept the project

BCR<1(NBCR<0) Reject the project

Since the BCR measures the present value per rupee of outlay,it is considered to be a useful criterion for ranking a set of projects in the order of decreasingly efficient use of capital


Limitations of bcr

Limitations of BCR

  • First, it provides no means for aggregating several smaller projects into a package that can be compared with a large project

  • Second, when the investment outlay is spread over more than one period, this criterion cannot be used.


Brain gym1

Brain Gym

Zeta Ltd is considering 4 projects – A , B C and D with the following characteristics

The funds available for investment are limited to Rs.20 lakh

and the cost of funds to the firm is 14%. Rank the 4 project(s) in terms of the NPV and BCR criteria.Which project(s) will you recommend given the limited supply of funds?


Solution to brain gym1

Solution to Brain Gym

The NPVs of the 4 projects are as follows:

The BCR of the 4 projects are as follows:


Which project should be accepted

Which project should be accepted??

Based on the NPV and BCR criteria, all 4 projects are acceptable as both NPV and BCR are positive.

But what if all the 4 projects need to be taken by the firm?

It can not be due to limited availability of funds.

either Zeta has to accept project A or a package consisting

of projects B, C and D but not both.


Limitation of bcr application

Limitation of BCR…. application

The decision will depend upon which option maximizes the shareholder’s wealth. In this sort of a decision –making situation, the BCR becomes inapplicable because there is no way by which we can aggregate the BCRs of the projects B, C and D.

On the other hand NPVs of projects B, C and D can be aggregated and compared with the NPV of project A to arrive at a decision.


Internal rate of return irr

Internal Rate Of Return (IRR)

The internal rate of return is that rate of interest at which the net present value of a project is equal to zero, or in other words, it is the rate which equates the present value of the cash inflows to the present value of the cash outflows.

While under the NPV method the rate of discounting is known (the firm’s cost of capital) under IRR this rate which makes NPV zero has to be found out


Brain gym2

Brain Gym

A project has the following pattern of cash flows:

What is the IRR of this project?


Solution to brain gym2

Solution to Brain Gym

  • To determine the IRR, we have to compute the NPV of the project for different rates of interest until we find that rate of interest at which the NPV of the project is equal to zero or sufficiently close to zero. To reduce the number of iterations involved in this trial and error process, we can use the following short –cut procedure:


Steps to irr calculation

Steps to IRR calculation

Step 1

Find the average annual net cash flow based on the given future net cash flows.In our eg. it turns out to be

(5+5+3.08+1.20)/4 =3.57

Step 2

Divide the initial outlay by the average annual net cash flow ie, 10/3.57 =2.801


Steps to irr calculation1

Steps to IRR calculation

Step 3

From the PVIFA table find that the interest rate at which the PVIFA of Re 1 will be nearly equal to 2.801 in 4 yrs ie, the duration of the project ( remember this is only a hint for finding the IRR, which actually needs to be found out by hit and trial method)


Steps to irr calculation2

Steps to IRR calculation

  • The NPV at r =15%

    -10+ (5*0.870)+(5*0.756)+(3.08*0.658)

    +(1.2*0.572) = 0.84

  • The NPV at r =18%

    -10+ (5*0.848)+(5*0.719)+(3.08*0.609)

    +(1.2*0.516) = 0.33

  • The NPV at r =20%

    -10+ (5*0.833)+(5*0.694)+(3.08*0.579)

    +(1.2*0.482) = 0

    We find that at r=20%, the NPV is zero and therefore the IRR of the project is 20%


The decision

The decision

To use IRR as an appraisal criterion, we require information on the ‘ cost of capital or funds employed’ in the project.

If we define IRR as ‘r’ and cost of funds employed as ‘k’,then the decision rule based on IRR will be:

Accept the project if r> k

Reject the project if r< k

If r=k, it is a matter of indifference


Merits of irr

Merits of IRR

  • It takes into account the time value of money.

  • It considers the cash flow stream over the entire investment horizon.

  • Like ARR, it makes sense to businessmen who prefer to think in terms of rate of return on capital employed.


Limitations of irr

Limitations of IRR

  • IRR is uniquely defined only for a project whose cash flow pattern is characterized by cash outflow(s) followed by cash inflows ( such projects are called simple investments). If the cash flow stream has one or more cash outflows interspersed with cash inflows, there can be multiple internal rates of return. This point can be clarified with the help of the following table where four projects with different patterns of cash flows are given:


Illustration of limitation of irr

Illustration of Limitation of IRR

  • Projects A and B are simple investments and therefore will have unique IRR values. But projects C and D can have multiple internal rates of return because their cash flows and outflows are interspersed. For such projects IRR cannot be a meaning full criterion of appraisal.( Work out the IRRs and see the limitation)


Limitations of irr1

Limitations of IRR

  • The IRR criterion can be misleading when the decision-maker has to choose between mutually exclusive projects that differ significantly in terms of outlays.

    In spite of these defects, IRR is still the best criterion today to appraise a project financially. Financial Institutions insist that projects having substantial outlay specially in the medium and large scale sectors must show the computation of IRR in the Detailed Project Report (DPR), which they appraise before sanctioning financial assistance.


Annual capital charge

Annual Capital Charge

  • This appraisal criterion is used for evaluating mutually exclusive projects or alternatives which provide similar service but have differing patterns of costs and often unequal life spans, eg, choosing between fork –lift transportation and conveyor-belt transportation.


Steps involved in calculation

Steps Involved in Calculation

Step 1

Determine the present value of the initial investment and operating costs using the cost of capital(k) as the discount rate.

Step 2

Divide the present value by PVIFA(k,n) where ‘n’ represents the life span of the project. The quotient is defined as the annual capital charge or the equivalent annual cost.

Once the annual capital charge for the various alternatives are defined, the alternative which has the minimum annual capital charge is selected


Brain gym3

Brain Gym

  • Hindustan Forge Ltd is evaluating two alternative systems: A and B , for internal transportation. While the two systems serve the same purpose, system A has a life of 7 years and system B has a life s of 5 years. The initial outlay and operating costs(in Rs.) associated with these systems are as follows:


Brain gym4

Brain Gym

Calculate the annual capital charge associated with these

two systems,if the cost of capital is 12%. ( You can assume

that the net salvage values of the two system at the end of

their economic lives will be zero.


Solution to brain gym3

Solution to Brain Gym

Present value of costs associated with system A

= Rs.10,00,000+(100000*0.893)+(125000

*0.797)+(150000*0.712)+(175000*0.636)

+(200000*0.567)+(225000*0.507)+

(200000*0.452)

= 17,24,900

Annual capital charge associated with system A

= 17,24,900/ [PVIFA(12,7)] = Rs.3,77,936


Solution to brain gym4

Solution to Brain Gym

Present value of costs associated with system B

= Rs.8,00,000+(75000*0.893)+(100000

*0.797)+(120000*0.712)+(140000*0.636)

+(100000*0.567

= 11,77,855

Annual capital charge associated with system B

= 11,77,855 / [PVIFA(12,5)] = Rs.3,26,728


Conclusion

Conclusion

Since the annual capital charge associated with system B is lower than that of system A , system B is preferred.

A wide variety of measures are used in practice for appraising investments. But whatever method is used, the appraisal must be carried out in explicit, well defined , preferably standardized terms and should be based on sound economic logic.


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