# IRR And NPV - Choice Among Multiple Investment Projects

__Illustration 98__

Let us assume the following. A supervisor of a printing company finds that preliminary investment of printing machinery is $200000. The machinery will be devalued once in five years with scrap value of zero.

He also estimates that increment in revenue or income from the new machinery will be $160000 per year. The addition in costs as an outcome from the new machinery on account of use of direct labour and materials, transportation, extra expense charges, constructing rent related with the new machinery would amount to $90000 every year. Marginal income tax for the industries is 20%.

You are required to determine the following:

- Compute the Net Cash Flow using straight line method of devaluation
- Using IRR - Internal Rate of Return method, should the new investment project be acknowledged or eliminated if the cost of capital comes about 6% per annum.

__Solution__

**(1) Net Cash Flow **= Net
Income before Tax - Income Tax + Devaluation

Thus, to compute net cash flow, we should compute net income before tax as well as depreciation.

Net income before tax = Annual Income – Incremental costs – Depreciation

Annual Income = $160000

Incremental costs = $90000

Depreciation at the rate of 10% under straight line method as the machinery’s life is 5 years.

= 200000 * 10% = 20000

Net income before tax = 160000 – 90000 = $70000

Income tax = 70000 * 20% = 14000

Net cash flow = Net income before tax - income tax + depreciation

= 70000 – 14000 + 20000

= $76000

__Rate of Return Method : IRR__

As per IRR method, rate of return is the discount rate at which present value of cash flow will parity initial cost of investment.

Therefore,

n

Σ __NCFt __= C

t=1 (1+r)
^t

Where NCFt is net cash flow every year, C is the initial cost of investment and r is the rate of return.

As computed above, NCF = $76000

Initial cost = $200000

n = 5 years

Substituting these values in the formula, we have

5

Σ __76000*__ = 200000

t=1 (1+r)
^t

Or,

5

Σ __ 1 __ = __200000__

t=1 (1+r)
^t 76000

= 2.63

5

It should be noted that the term Σ __ 1 __ denotes
the present value of annuity of

t=1 (1+r)
^t

$1 for five years discounted at the rate of r. In order to ascertain the value of r
we have to use the table giving the present value of annuity of $1 in the future period
which is usually termed Present Value Interest Factor PVIF and is provided in the Clarks’ Log
Table.

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