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Net Prese

nt Value

PAZ-Paddon Development Email: paz4Tunnel@hotmail.ca http://accountingexplained.com/managerial/capital-budgeting/npv

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Net Present Value

• Net Present Value is the present value of net cash inflows generated by a project including salvage value, if any, less the initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts for time value of money by using discounted cash inflows.• Before calculating NPV, a target

rate of return is set which is used to discount the net cash inflows from a project. Net cash inflow equals total cash inflow during a period less the expenses directly incurred on generating the cash inflow.

To discount you go to the left from FV and calculate the PV, this is called discounting.

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Net Present Value

• Calculation Methods and Formulas• The first step involved in the calculation of

NPV is the determination of the present value of net cash inflows from a project or asset. • The net cash flows may be even (i.e. equal

cash inflows in different periods) or uneven (i.e. different cash flows in different periods). • When they are even, present value can be

easily calculated by using the present value formula of annuity.• However, if they are uneven, we need to

calculate the present value of each individual net cash inflow separately.• In the second step we subtract the initial

investment on the project from the total present value of inflows to arrive at net present value.

Calculation Methods and Formulas

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Net Present Value

• When cash inflows are even:

• NPV = R × 1 − (1 + i) -n − Initial Investment i Investment • In the above formula,• R is the net cash inflow expected

to be received each period;• i is the required rate of return

per period;• n are the number of periods

during which the project is expected to operate and generate cash inflows.

Thus we have the following two formulas for the calculation of NPV:

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Net Present Value

• When cash inflows are uneven:

NPV = R1 + R2 + R3 + ... −Initial Investment

(1 + i) 1 (1 + i) 2 (1 + i)3

• Where,• i is the target rate of return per

period;• R1 is the net cash inflow during

the first period;• R2 is the net cash inflow during

the second period;• R3 is the net cash inflow during

the third period, and so on ...

NPV = R1 + R2 + R3 + ... − Initial Investment

(1 + i) 1 (1 + i) 2 (1 + i)3

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Net Present Value

• Decision Rule• Accept the project only if its

NPV is positive or zero. • Reject the project having

negative NPV. •While comparing two or more

exclusive projects having positive NPVs, accept the one with highest NPV.

NPV = R1 + R2 + R3 + ... − Initial Investment

(1 + i) 1 (1 + i) 2 (1 + i)3

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Net Present Value• Examples• Example 1: Even Cash Inflows: Calculate the net present value of a project which requires an

initial investment of $243,000 and it is expected to generate a cash inflow of $50,000 each month for 12 months. Assume that the salvage value of the project is zero. The target rate of return is 12% per annum.• Solution• We have,

Initial Investment = $243,000Net Cash Inflow per Period = $50,000Number of Periods = 12Discount Rate per Period = 12% ÷ 12 = 1%• Net Present Value

= $50,000 × (1 − (1 + 1%)^-12) ÷ 1% − $243,000= $50,000 × (1 − 1.01^-12) ÷ 0.01 − $243,000≈ $50,000 × (1 − 0.887449) ÷ 0.01 − $243,000≈ $50,000 × 0.112551 ÷ 0.01 − $243,000≈ $50,000 × 11.2551 − $243,000≈ $562,754 − $243,000≈ $319,754

• Example 2: Uneven Cash Inflows: An initial investment on plant and machinery of $8,320 thousand is expected to generate cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the present value of the investment if the discount rate is 18%. Round your answer to nearest thousand dollars.

• Solution• PV Factors:• Year 1 = 1 ÷ (1 + 18%)^1 ≈ 0.8475• Year 2 = 1 ÷ (1 + 18%)^2 ≈ 0.7182• Year 3 = 1 ÷ (1 + 18%)^3 ≈ 0.6086• Year 4 = 1 ÷ (1 + 18%)^4 ≈ 0.5158• The rest of the problem can be solved more efficiently in table format as show below:• Year 1 2 3 4 • Net Cash Inflow $3,411 $4,070 $5,824 $2,065 • Salvage Value 900 • Total Cash Inflow $3,411 $4,070 $5,824 $2,965 • × Present Value Factor 0.8475 0.7182 0.6086 0.5158 • Present Value of Cash Flows $2,890.68 $2,923.01 $3,544.67 $1,529.31 • Total PV of Cash Inflows $10,888 • − Initial Investment − 8,320 • Net Present Value $2,568 thousand

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Net Present Value

• Advantage and Disadvantage of NPV• Advantage: Net present value

accounts for time value of money. Thus it is more reliable than other investment appraisal techniques which do not discount future cash flows such payback period and accounting rate of return.• Disadvantage: It is based on

estimated future cash flows of the project and estimates may be far from actual results.•Written by Irfanullah Jan