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