cmabdtheblogger: Financial Management - Capital Budgeting

Financial Management

Capital Budgeting – IRR Method

Part A:

Discussion about (a) what is capital budgeting, (b) what is project appraisal, (c) what are the different methods of project appraisal, (d) what are the different types of cash flows and how CIAT (Cash Inflow After Tax) is computed under different situations, and (e) general theory of computation and explanation of IRR (Internal Rate of Return) Method.

Part B:

Four Illustrations with solutions

Part A

Definition of capital budgeting

Capital budgeting is a process of identifying, evaluating and selecting the project/s to be taken up for execution, out of many such projects to choose from, in such a way that the selection of the project/s satisfies the following requirements:

1. The selected project/s give/s the best possible returns. In other words, total return from the selected project/s is more than total return from the projects not selected;

2. Net present value of cash flows from the project/s selected is greater than that from the projects not selected;

3. The selected project/s return/s back the initial investments faster than the projects not selected;

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

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

6. The project/s so selected for future investment is/are in line with the overall objectives and goal of the firm in terms of maximisation of shareholders’ wealth.

Definition of project appraisal

Project appraisal is evaluating a proposed project by undertaking a cost and benefits analysis of different aspects of the project with an objective of determining 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.

Methods of project appraisal

Different techniques are used for appraisal of the projects / capital investment proposals. They are classified into Non-Discounted Cash Flow (or Traditional) and Discounted Cash Flow techniques.

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

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

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.

Definition of IRR

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.

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

Cash inflow after tax (CIAT)

CIAT is calculated using either of the following two formulas:

CIAT =

PAT + Depreciation +

Interest (1 – t)

[Note: Here PAT is

after charging interest]

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) × Rate of capital gains tax]	×××
LESS: Tax on capital gain [(Sale proceeds – Cost of acquisition) × Rate of capital gains tax]	×××
LESS: Tax on profit on sale of asset [(Cost of acquisition – Book value of 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 × Normal rate of tax]	×××
LESS: Tax on short term capital gain [STCG × 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.

Part B

Illustration: 1

A company proposes to install a machine involving capital cost of Rs 3, 60,000. The life of the machine is 5 years and its salvage value at the end of the life is nil. The machine will produce the net operating income after depreciation of Rs 68,000 per annum. The company’s tax rate is 45%.

The “Present Values of annuity of Rs 1” for 5 years at different discount rates are as under:

Discount Rate	Present Value
14%	3.433
15%	3.352
16%	3.274
17%	3.199
18%	3.127

Calculate the internal rate of return (IRR) of the proposal, and suggest the company regarding whether the machine should be installed or not considering the fact that the cost of capital of the company is 12%.

Solution: 1

Link for downloading Solution: 1 in PDF

Illustration: 2

Zenith Industries Limited is 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 inflows before tax are as follows:

Year	Cash Inflow Before Tax
1	Rs 4 Lakhs
2	Rs 6 Lakhs
3	Rs 8 Lakhs
4	Rs 8 Lakhs
5	Rs 10 Lakhs

Determine the internal rate of return of the project under consideration, and give suitable advice to the company in this regard assuming that the cost of capital of the company is 12%.

Solution: 2