Strategic Financial Management - Project Appraisal Methods and Techniques

 

Strategic Financial Management

Project Appraisal -

Methods and Techniques

 

Part A: Discussion of basic theories and different methods and techniques of project appraisal (i.e. investment decision) along with all the relevant formulas.

Part B: Six illustrations with solutions.

Part A

Definition of project appraisal

Project appraisal is a cost and benefits analysis of different aspects of proposed project with an objective to adjudge its viability. A project involves employment of scarce resources. An entrepreneur needs to appraise various alternative projects before allocating the scarce resources for the best project. For appraising a project, its economic, financial, technical market, managerial and social aspects are analyzed. The effects of a project appraisal are long reaching and have very definite long term effects because of the capital investment that is always required in any project. Financial institutions carry out project appraisal to assess its creditworthiness before extending finance to a project.

 

Objectives of project appraisal

An enterprise carries out project appraisal analysis to ensure that

1.   The selected projects give maximum return. In other words, total return from the selected projects is more than total return from the projects not selected;

2.   The selected projects return back the initial investments faster than the projects not selected;

3.   The rate of return on investment (ROI) is higher in case of the selected projects than the projects not selected;

4.   The total capital requirement for investing in the selected projects is within the available resources (funds) earmarked for investment in new projects;

5.   The projects so selected for future investment are in line with the overall objectives and goal of the   firm in terms of maximisation of shareholders’ wealth.

 

Methods of project appraisal

Different techniques are used for financial appraisal of the projects / capital investment proposals the most important of which are:

A.     Non-Discounted Cash Flow (or Traditional) Techniques

1.         Average/Accounting Rate of Return (ARR) method,

2.         Pay Back (PB) period method,

3.         Pay Back Reciprocal method, and

4.         Pay Back Profitability method.

 

B.      Discounted Cash Flow Techniques

1.         Net present value (NPV) method,

2.         Internal rate of return (IRR) method,

3.         Modified net present value (MNPV) method,

4.         Modified internal rate of return (MIRR) method,

5.         Profitability index (PI) method,

6.         Discounted pay back (DPB) period method, and

7.         Adjusted net present value method.

 

  ARR (Average Rate of Return) Method

ARR =

[Average PAT ÷ Average investment] × 100

 

 Where,

Average PAT =	(Total of expected PATs for each of the years of the life of the project) ÷ (Number of years of the life of the project)
Average investment =	Additional net working capital + Salvage value + [(Initial investment – Salvage value) ÷ 2]

 

Decision criteria:

For a single project under consideration, the project will be accepted if ARR is higher than the required rate of return (i.e. cost of capital).

 

If there are more than one projects each one of them having ARR which is higher than the required rate of return, the project having the highest ARR will be selected.

 

 Pay Back Period Method

Payback period =

Initial investment ÷ Uniform annual CIAT

 

Where,      CIAT =

Cash inflow after tax

 

The above formula can be applied for calculating payback period only when the cash flow stream is in the nature of annuity for each year of the life of the project, i.e. CIATs are uniform. But if the CIATs are not uniform, then pay back period will be simply the minimum period required to recover the initial investment from the project. In this case, the minimum period required to recover the initial investment can be arrived at by calculating the cumulative CIATs against each year of the life of the project.

 

Decision criteria:

For a single project under consideration, the project will be accepted if the payback period calculated for the project is less than the maximum payback period set by the management. But in case of mutually exclusive projects (each one having a payback period less than the maximum set by the management), the project having the shortest payback period would be selected.

 

 Pay Back Reciprocal Method

Payback reciprocal =	Uniform annual CIAT ÷ Initial investment
Where,      CIAT =	Cash inflow after tax

 

Decision criteria:

Higher the Pay Back Reciprocal better is the project.

 

Pay Back Profitability Method

As the profitability beyond the Pay Back Period is not taken into consideration in Pay Back Period method, the projects with higher Pay Back Period are rejected although such projects with longer life may generate higher benefits after recovering its initial investment. In Pay Back Profitability method the profitability beyond the Pay Back Period is considered and projects generating higher benefits after the recovery of initial investment are considered for selection.

 

Payback profitability =	Total CIAT of the project – Initial Inv.
Where,      CIAT =	Cash inflow after tax

 

 NPV (Net Present Value) Method

NPV =	∑ PV of all CIATs − ∑ PV of all COs
Where, CIAT =	Cash inflow after tax
And CO =	Cash outflow

 

Decision criteria:

For a single project under consideration, the project will be accepted if the NPV of the project is positive, i.e. if NPV > 0.

 

In case of two or more competing projects, the project having highest positive NPV would be selected.

 

IRR (Internal Rate of Return) Method

IRR, with respect to an investment project, is that discount rate which equates the present value of anticipated future cash inflows from the project to the initial cost of the project (i.e. cash outflow). Accordingly, IRR is also defined as the discount rate at which the NPV is zero.

IRR can be calculated using either of the following two formulas:

1. IRR =	LR + [(NPV at LR) ÷ (NPV at LR − NPV at HR)] × (HR – LR)
2. IRR =	HR − [(NPV at HR) ÷ (NPV at HR − NPV at LR)] × (HR – LR)

 

Where,

LR =	Lower discount rate
HR =	Higher discount rate
NPV at LR =	Net Present value of CIATs at lower discount rate
NPV at HR =	Net Present value of CIATs at higher discount rate
CIAT =	Cash Inflow after Tax

 

Steps to find out LR and HR

STEP: 1

Find required PVIFA (k, n) which, if multiplied by average CIAT, gives the initial investment so that NPV equals to zero. In other words, PVIFA (k, n) should be such that,

 

PVIFA (k, n) = Initial Investment ÷ Average CIAT.

 

STEP: 2

From the “Present value of an annuity of Rs 1” table find two PVs of an annuity of Rs 1 closest to PVIFA (k, n) for the life of the project (i.e. for ‘n’ years).

 

STEP: 3

From the “Present value of an annuity of Rs 1” table again find the interest rates (i.e. ‘k’ %) corresponding to the two PVs as identified in STEP: 2. If the CIATs are uniform, the interest rate against the higher PV is LR and the interest rate against the lower PV is HR; and STEP: 4 is not required.

Alternative to Steps 1, 2 and 3:

Computation of Internal Rate of Return (IRR) – Shortcut Method – applicable only when there is single cash outflow in the form of initial investment

 

Find out initial LR and initial HR by calculating the value of ‘r’ as follows:

 

STEP: 1

Compute the value of ‘r’ as follows:

r =	[(A/I) ^ {2/ (N+1)} – 1] × 100%

 

Where,

A =	Sum of the inflows
I =	Initial investment (i.e. single outflow)
N =	Number of years of the project life

 

STEP: 2

Calculate NPV taking the rounded off value of ‘r’ as discount rate.

 

STEP: 3

If the NPV calculated in STEP: 2 is (+)ve, increase the discount rate by 1 percentage point and calculate new NPV with this new discount rate. But, if the NPV calculated in STEP: 2 is (−)ve, decrease the discount rate by 1 percentage point and calculate new NPV with this new discount rate.

 

Discount rate as stated in STEP: 2 and in this STEP: 3 are initial discount rates – one is Initial LR and the other is Initial HR in accordance with the value of NPV calculated in STEP: 2.

STEP: 4

Find the NPV of the project using both the approximate interest rates as identified in STEP: 3 above. Now on the basis of the NPVs so calculated three alternative courses of action will follow.

 

First alternative:

If the lower interest rate (Initial LR) gives positive NPV and the higher interest rate (Initial HR) gives negative NPV, the Initial LR is the Final LR and the Initial HR is the Final HR.

 

Second alternative:

If both the NPVs are positive, try a higher interest rate which can be identified as:

New IR =

Initial HR + [(NPV at Initial HR) ÷ (NPV at Initial LR – NPV at Initial HR)]

 

Find NPV using this new-found interest rate.

(a)    If this new NPV is positive, increase the interest rate by one. This process should be carried on until the NPV becomes negative.

(b)    If this new NPV is negative, reduce the interest rate by one. This process should be carried on until the NPV becomes positive. IRR should lie between two such consecutive interest rates that one of the rates (the lower one) gives positive NPV and the other one (the higher one) gives negative NPV.

 

Third alternative:

If both the NPVs are negative, try a lower interest rate which can be identified as:

 

New IR =

Initial LR – [(NPV at Initial LR) ÷ (NPV at Initial HR − NPV at Initial LR)]

 

Find NPV using this new-found interest rate.

(a)    If this new NPV is negative, reduce the interest rate by one. This process should be carried on until the NPV becomes positive.

(b)    If this new NPV is positive, increase the interest rate by one. This process should be carried on until the NPV becomes negative. IRR should lie between two such consecutive interest rates that one of the rates (the lower one) gives positive NPV and the other one (the higher one) gives negative NPV.

 

Decision criteria:

IRR is the maximum rate of interest which an organisation can afford to pay on the capital invested in a project. Therefore, a project is acceptable, if its IRR is greater than the cost of capital (k). On the other hand, a project should be rejected, if its IRR is less than the cost of capital (k). But if the IRR of a project is equal to the cost of capital (k), the firm may remain indifferent, i.e. the project may be or may not be accepted.

 

Symbolically,

1.         If IRR > k, the project is acceptable,

2.         If IRR < k, the project is not acceptable, and

3.         If IRR = k, the project may be or may not be accepted.

 

In case of two or more competing projects, the project giving the highest IRR (which should also necessarily be higher than the cost of capital) would be selected.

 

MNPV (Modified NPV) Method

Under this method, it is assumed that each cash flow is re-invested in another project at a certain rate of interest. It is also assumed that each cash inflow is re-invested elsewhere immediately until the termination of the project. In other words, under this method, the cash inflows are compounded forward rather than discounting them backward as followed in NPV method. These compounded values are to be calculated till the termination of the project and total of all these compounded values is called Terminal Value of the Project. The terminal value of the project is then discounted at an appropriate discount rate (normally, cost of capital) to find out the present value. This present value of terminal value of the project is compared with the present value of the cash outflows to arrive at the Modified NPV of the project and to find out the justifiability of the project.

 

Therefore, Modified NPV = PV of TV of the Project – PV of the Cash Outflows

 

Decision criteria:

In case of a single project, the project will be accepted if the Modified NPV is positive. In case of mutually exclusive projects, the project with the highest positive Modified NPV would be selected.

 

MIRR (Modified IRR) Method

Modified internal rate of return (MIRR) is a method of evaluating the profitability of capital investment proposals. MIRR can be calculated using the following two formulas:

 

1.   MIRR =	[(∑ PV of all CIATs) ÷ (∑ PV of all Cash Outflows)]^(1/n) x (1+i) – 1
2.   MIRR =	[Terminal Value of the Project ÷ (∑ PV of all Cash Outflows)]^(1/n) – 1

 

 Where,

PV =	Present value, discount rate being the cost of capital
n =	Number of years of the project
i =	Cost of capital of the company

 

Decision criteria:

MIRR is the maximum rate of interest which an organisation can afford to pay on the capital invested in a project. Therefore, a project must be accepted if its MIRR is higher than the cost of capital (k). On the other hand, a project shall be rejected if its MIRR is less than the cost of capital (k). But if the MIRR of a project is equal to the cost of capital (k), the firm may remain indifferent.

 

In case of mutually exclusive projects, the project giving the highest MIRR (which should also necessarily be higher than the cost of capital) would be selected.

 

 PI (Profitability Index) Method

PI =	∑ PV of all CIATs ÷ ∑ PV of all COs
Where, CIAT =	Cash inflow after tax
And CO =	Cash outflow

 

Decision criteria:

For a single project under consideration, the project will be accepted if the PI is more than one. But the project will be rejected in case the PI is less than one. However, if the PI is equal to one, the firm may remain indifferent.

 

In case of mutually exclusive projects (each one having its PI > 1), the project having highest PI would be selected.

 

Discounted Pay Back Period Method

Under this method the present values of all cash outflows and inflows are computed at an appropriate discount rate (normally, cost of capital). The present values of all inflows are cumulated in order of time. The time period at which the cumulated present value of cash inflows equals to the present value of cash outflows is known as discounted payback period.

 

Decision criteria:

For a single project under consideration, the project will be accepted if the discounted payback period calculated for the project is less than the maximum discounted payback period set by the management.

 

In case of mutually exclusive projects (each one having a discounted payback period less than the maximum set by the management), the project having the shortest discounted payback period would be selected.

 

Adjusted NPV (Adjusted Net Present Value) Method

This method considers the tax advantage (savings in tax) due to use of borrowed fund in financial appraisal of projects by incorporating the impact of debt financing in case of a new investment proposal. Formula for Adjusted NPV is as given below:

 

Adjusted NPV =

Base Case NPV – Issue Cost (i.e. Floatation Cost) for issue of share capital + Total PV of Tax Shields on interest payments

 

 Where,

Base Case NPV =	PV of all CIATs (assuming all-equity financing) – Initial Investment
CIAT =	Cash inflow after tax

 

Decision criteria:

For a single project under consideration, the project will be accepted if the Adjusted NPV of the project is positive.

 

In case of mutually exclusive projects, the project having highest positive Adjusted NPV would be selected.

 

Equivalent Annual Benefit (EAB) and

Equivalent Annual Cost (EAC)

 

Equivalent Annual Benefit (EAB) means Annualised Net Benefit and Equivalent Annual Cost (EAC) means Annualised PV of Total Cost. Equivalent Annual Benefit method and Equivalent Annual Cost method should be adopted when economic lives of two or more projects are different.

 

 Formulas for EAB:

1.	EAB =	NPV of the project ÷ PVIFA(k, n)
2.	EAB =	NPV of the project × CRF

 

Formulas for EAC:

1.	EAC =	PV of Total Cost of the Project ÷ PVIFA(k, n)
2.	EAC =	PV of Total Cost of the Project × CRF

 

 Where,

1.	CRF =	Capital Recovery Factor
2.	CRF =	1 ÷ PVIFA(k, n)

 

Types of cash flows

Cash flows associated with an investment proposal may be classified into three components:

(i)         Initial cash outflow (i.e. initial investment)

(ii)       Annual operating cash inflow (i.e. cash inflow after tax, in short CIAT)

(iii)     Terminal cash inflow

 

Initial investment – Initial investment comprises:

(a)          Initial cost of the new project / asset,

(b)          Installation charges, and

(c)          Working capital introduced.

 

Cash inflow after tax (CIAT)

CIAT is calculated using either of the following two formulas:

1.	CIAT =	PAT + Depreciation + Interest (1 – t) [Note: Here PAT is after charging interest]
2.	CIAT =	EBIT (1 – t) + Depreciation

 

If CIBT (Cash inflow before tax) is given in the problem along with depreciation, etc., CIAT will be calculated as follows:

STEP 1:

PBT =

CIBT – Depreciation

 

STEP 2:

PAT =

PBT – Tax

 

STEP 3:

CIAT =

PAT + Depreciation + Interest (1 – t)

 

Therefore, if CIBT is given and there is no interest cost,

CIAT =

[(CIBT – D) – T] + D; where, D = Depreciation and, T = Tax

 

Terminal cash inflow

Terminal cash inflow consists of

(i)               Working capital recovered, and

(ii)             Net cash inflow from the sale of scrap.

 

Net cash inflow from the sale of scrap can be calculated as follows:

A.     If the Income-Tax Rules regarding depreciation on block of assets are not required to be followed –

Particulars	Rs
Proceeds from the sale of scrap	×××
ADD: Tax on capital loss [(Cost of acquisition – Sale proceeds) x Rate of capital gains tax]	×××
LESS: Tax on capital gain [(Sale proceeds – Cost of acquisition) x Rate of capital gains tax]	×××
LESS: Tax on profit on sale of asset [(Cost of acquisition – Book value of the asset) × Normal rate of tax	×××
NET CASH INFLOW FROM THE SALE OF SCRAP	×××

 

Important note:

Under straight line method of depreciation, book value and sale proceeds in the terminal year of the project are same. Therefore, there will be no tax benefit or tax loss on capital loss or capital gain respectively under the straight line method of depreciation.

 

B.      If the Income-Tax Rules regarding depreciation on block of assets are required to be followed –

Particulars	Rs
Proceeds from the sale of scrap	×××
ADD: Tax on short term capital loss [STCL x Normal rate of tax]	×××
LESS: Tax on short term capital gain [STCG x Normal rate of tax]	×××
NET CASH INFLOW FROM THE SALE OF SCRAP	×××

Important notes:

1.         Under section 50 of the Income Tax Act, there cannot be any long term capital gain / loss on disposal of depreciable assets.

2.         There will be short term capital gain / loss on disposal of depreciable assets only in case of the following two situations –

 

Situation one:

Under section 50(1), there will be short term capital gain, if on the last day of the previous year WDV of the block of assets is zero. No depreciation will be allowed under this situation.

 

Situation two:

Under section 50(2), there will be short term capital gain or loss, if the block of assets is empty on the last day of the previous year. No depreciation will be allowed under this situation.

 

3.   There will be no short term capital gain / loss if the disposal of depreciable assets does not fall under any of the above two situations. In this case depreciation will be allowed under section 32 of the Income Tax Act.

Capital rationing

Capital rationing means distribution of limited capital in favour of more acceptable proposals. It refers to a situation where a firm is not in a position to invest in all the available profitable projects due to the limited financial resources in the form of capital. Under this situation a firm is compelled to reject some of the viable projects having positive net present value because of shortage of funds. Therefore, the firm has to select a feasible combination of proposals that will give the maximum return to the shareholders by maximising the total net present value from the available projects.

 

There are two methods of capital rationing under the two different situations in terms of divisibility of the projects. The methods of capital rationing are:

1.   Capital rationing when projects are divisible, and

2.   Capital rationing when projects are indivisible.

 

Capital rationing when projects are divisible

Selection of projects under this situation will require the taking of the following steps:

STEP − 1:

Calculate the profitability index (PI) or the internal rate of return (IRR) of each project.

 

STEP − 2:

Rank the projects in descending order of PI or IRR calculated in step − 1 above.

 

STEP − 3:

Prepare a statement showing the cumulative initial investment against the projects arranged in order of their rankings.

 

STEP − 4:

Select the optimal combination of the projects in such a way that the total amount of initial investment required for all the selected projects is equal to the total available investible capital. Since the projects are divisible, the last project in terms of the rankings of the projects may be selected partially utilising the balance of the available capital.

 

Capital rationing when projects are indivisible

Selection of projects under this situation will require the taking of the following steps:

STEP − 1:

Make a list of feasible combinations of the projects in such a way that the total amount of initial investment required for any of the combinations does not exceed the total fund available for investment and at the same time maximum possible amount of the available investible fund is utilised for each of the combinations of the projects.

 

STEP − 2:

Select the combination of the projects whose aggregate NPV is the maximum and consider it as the optimal project mix.

Part B

Illustration: 1

Z Limited has two projects under consideration A & B, each costing Rs 60 lakhs. The projects are mutually exclusive. Life of project A is 4 years & of project B is 3 years. Salvage value is nil for both the projects. Income Tax rate is 33.99%. Cost of capital is 15%. Profit before depreciation and tax (PBDT) of the two projects for 4 years are as follows:

      (Rs in Lakhs)

At the end of the year	Project: A	Project: B
1	60	100
2	110	130
3	120	50
4	50	-

 

PV Factors for 4 years at 15% Discount Rate are as under:

Year	1	2	3	4
PV Factors	0.870	0.756	0.658	0.572

 

Advise which project should be taken up on the basis of NPV of the projects.

 

Solution: 1

Illustration: 2

A company is considering a new project for investment purpose. The cost of the project and estimated cash inflows for 4 years are as follows:

	Rs
Project cost	1,10,000
Cash inflows:
Year 1	60,000
Year 2	20,000
Year 3	10,000
Year 4	50,000

 

Calculate the Internal Rate of Return of the project.

 

Solution: 2

Illustration: 3

A company has two projects under consideration. Initial investment and estimated cash inflows of the projects for 4 years are as follows:

 

	Project: I (Rs)	Project: II (Rs)
Investment	2,20,000	2,20,000
Cash inflows:
Year 1	62,000	1,42,000
Year 2	80,000	80,000
Year 3	1,00,000	82,000
Year 4	1,40,000	40,000

Cost of capital: 10%. Calculate Modified Net Present Value (MNPV) and Modified Internal Rate of Return (MIRR) of the projects and suggest about which project should be selected. (Assume rate of reinvestment as 14%.)

 

Solution: 3

Illustration: 4

A company has two projects under consideration. Initial investment and estimated cash inflows of the projects are as follows:

	Project: P (Rs)	Project: Q (Rs)
Investment	50,00,000	50,00,000
Cash inflows:
Year 1	75,00,000	20,00,000
Year 2		20,00,000
Year 3		70,00,000

Cost of capital: 12%. Calculate Equivalent Annual Benefit (EAB) of the projects and suggest about which project should be selected.

 

Solution: 4

Illustration: 5

A company wants to buy a machine and it has two machines under consideration to choose from. The necessary details of the two machines are as follows:

	Machine: I	Machine: II
Cost of machine (Rs)	75,000	50,000
Annual operating cost (Rs)	12,000	20,000
Life of machine (Years)	5	3

 

Cost of capital: 12%. Calculate Equivalent Annual Cost (EAC) of the machines and suggest about which machine should be bought.

 

Solution: 5

Illustration: 6

A company is considering a project requiring Rs 50 Lakhs of investment. Expected cash flow is Rs 10 Lakh per annum for 8 years. The rate of return required by the equity investors from the project is 15%. The company is able to raise Rs 24 Lakhs of debt finance carrying 14% interest for the project. The debt is repayable in equal annual instalments over the eight year period – the first to be paid at the end of the first year. The Income Tax rate is 40%. (Assume floatation cost to be 5%.)

Calculate Adjusted Net Present Value of the project.

Solution: 6