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In: Finance

Proof that the NPV rule is equivalent to the rate of return rule if the investment...

Proof that the NPV rule is equivalent to the rate of return rule if the investment period is 1 Year.

Solutions

Expert Solution

Let’s consider an example to prove equivalency of NPV and IRR decision rule of investment.

Project A requires a cash flow of $ 10,000 and gives a positive cash flow of $ 11,500 in first year.

Rate of return of the firm is 9 %. NPV can be computed as:

Year

Cash Flow

Project A (C)

PV Factor Computation

PV Factor @ 9 % (F)

PV (=C x F)

0

($10,000)

1/(1+0.9)^0

1

($10,000)

1

$11,500

1/(1+0.9)^1

0.917431193

$10,550

NPV

$550

NPV is $ 550.

Computations of IRR using excel:

A

B

1

Year

Cash Flow

(Project A)

2

0

($10,000)

3

1

$11,500

4

IRR

15.00%

Insert Formula “=IRR (B2:B3) in cell B4 which will display IRR as 15 %.

For positive NPV of Project A, IRR is also higher than required rate of return.

Hence both NPV and IRR rules are agree to accept the project.

This is all for single project.

Consider another project.

Project B requires a cash flow of $ 15,000 and gives a positive cash flow of $ 20,000 in first year.

Required return is same.

NPV is computed as:

Year

Cash Flow (Project B) CB

PV Factor Computation

PV Factor @ 9 % (F)

PV (=CB x F)

0

($15,000)

1/(1+0.9)^0

1

($15,000)

1

$20,000

1/(1+0.9)^1

0.917431193

$18,349

NPV

$3,349

NPV of project B is $3,349

Computations of IRR using excel:

A

B

1

Year

Cash Flow (Project B)

2

0

($15,000)

              3

1

$20,000

4

IRR

33.33%

Insert Formula “=IRR (B2:B3) in cell B4 which will display IRR as 33.33 % which is higher than required rate of return 9 %.

Project B is also accepted as NPV is positive and IRR is higher than required rate.

If both projects A and B are independent decision of NPV and IRR rule are same.

If these two projects are mutually exclusive, as per NPV and IRR rules to evaluate the projects, Project B should be selected as it has higher NPV and IRR than Project A.

Hence it is proved that NPV rule is equivalent to Rate of return rule if investment period is 1 year.


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