Module
3: Net Present Value (NPV)
Net
Present Value
the
A Capital-budgeting decision criterion defined as the present value of
the future net cash flows after tax less the project's initial outlay.
where
= the annual free cash flow in time period t
k = the appropriate discount rate; that is, the required rate of return or cost of capital
IO = the initial cash outlay
n = the project's expected life
NPV is
equal to the present value of its annual after tax net cash flows less
the investment’s initial outlay.
Accept : NPV > or = 0
Reject : NPV < 0
NPV Illustration of Investment in New Machinery
|
Free
Cash Flow
|
|
|
Initial
Outlay
|
$40,000
|
|
Year
2
|
15,000
|
|
Year
3
|
14,000
|
|
Year
4
|
13,000
|
|
Year
5
|
12,000
|
|
Year
6
|
1,1000
|
Calculation for NPV Illustration of Investment
in new Machinery
|
Free
Cash Flow
|
Present
Value Factor
at 12 Percent |
Present
Value
|
|
|
Year
1
|
$15,000
|
.893
|
$13,395
|
|
Year
2
|
14,000
|
.797
|
11,158
|
|
Year
3
|
13,000
|
.712
|
9,256
|
|
Year
4
|
12,000
|
.636
|
7,632
|
|
Year
5
|
11,000
|
.567
|
6,237
|
|
Present
Value
of Cash Flows |
$47,678
|
||
|
Initial
Outlay
|
-40,000
|
||
|
Net
Present Value
|
$7,678
|
Good Point of NPV
1. It deals with Cash Flow
2. It is sensitive to the true timing of benefits resulting from project
3. It considers time value of money
4. Accepting positive NPV increases the value of the firm, and is consistent with goal of wealth’s maximization.
Weak
Point of NPV
It requires long-term forecasts of the incremental cash flows.
Example NPV Problem of Computer System
The required rate of return demanded by the firm is 10 percent.
To determine the system's net present value, the 3 year $15,000 cash flow
annuity is first discounted back to the present at 10 percent. From Appendix
E in the back of this book, we find that PVIFA IS 2.487. Thus,
the present value of this $15,000 annuity is $37,305 ($15,000x2.487).
|
Free
Cash Flow
|
Free
Cash Flow
|
||
|
Initial
Outlay
|
-$30,000
|
Year
2
|
15,000
|
|
Year
1
|
15,000
|
Year
3
|
15,000
|
Spreadsheets
and the Net Present Value
actual NPV= Excel calculated
NPV-initial outlay
This can be input into a spreadsheet cell as: NPV (rate, inflow
1 ,inflow 2 , .... inflow 29)- initial outlay
