To calculate Present Values,
you need three things:
Amount of Payments - How much will be
received in future?
Time Periods - At what time in the future will the
payments be received?
Interest Rate - What is the risk and opportunity
cost associated with the future values?
The Time Value of Money and Net Present Value
• Having a dollar today is worth more than
having the right to receive a dollar in the
future
• Calculating Present Values will tell you how
much less that dollar in the future is worth
than the dollar today.
How to Calculate!
• You can use the present value tables.
• Multiply the payment to be received by the
factor for the time period and the rate
given.
• PV = Payment x PVIF(rate, # of periods)
Present Value of a Single Payment
Present Value of an Annuity
Net Present Value Method
Open Imaging Company is considering the purchase of a magnetic
resonance imaging (MRI) machine to improve the efficiency of its
Radiology Department. Management must decide between Model M
and Model N. The company’s minimum rate of return is 16 percent
• Model M
– Cost of $17,500
– Estimated residual value of $2,000 after 5 years
– Projected cash inflows of $6,000, $5,500, $5,000, $4,500,
and $4,000 during its five-year life
• Model N
– Cost of $21,000
– Estimated residual value of $2,000 after 5 years
– Projected cash inflows of $6,000 per year for 5 years
Net Present Value Method
• Determine the net present value for Model M
– Must use Table for Present Value of a Single Payment
because of unequal cash flows
Year
1
2
3
4
5
Residual value
Total present value of cash inflows
Less purchase price of Model M
Net present value
The cash outflow for the
purchase is not discounted
because it occurs at time zero
Model M
Net Cash
Inflows
$6,000
5,500
5,000
4,500
4,000
2,000
16%
Factor
.862
.743
.641
.552
.476
.476
Present
Value
$ 5,172.00
4,086.50
3,205.00
2,484.00
1,904.00
952.00
$17,803.50
17,500.00
$ 303.50
The residual value is discounted
because it represents a cash inflow
that will take place at the end of year 5
Net Present Value Method
• Determine the net present value for Model N
– Table for Present Value of an Annuity is used because the
cash inflows are expected to be equal amounts in each year
– However, Table 3 must still be used to determine the present
value of the machine’s residual value
Year
1-5
Residual value
Total present value of cash inflows
Less purchase price of Model N
Net present value
Model N
Net Cash
Inflows
$6,000
2,000
16%
Factor
3.247
.476
Present
Value
$19,644.00
952.00
$20,596.00
21,000.00
( $ 404.00 )
Net Present Value Method
• Results of the two analyses
– Net present value of Model M is $303.50
– Net present value of Model N is ($404.00)
• Model M should be chosen because it
– Has a positive net present value
– Is expected to exceed the company’s minimum rate of return
• Model N should be rejected because it has a
negative net present value
Use Excel to Calculate NPV
• Open a new workbook. Set up rows and columns to
reflect time periods and future payments.
Use Excel to Calculate NPV
Insert the NPV function into the cell
Use Excel to Calculate NPV
Select Function from Category and Menu
Use Excel to Calculate NPV
Use Dialog box to enter interest rate
Use Excel to Calculate NPV
Select range of values for payments
Use Excel to Calculate NPV
• Click OK
• Excel calculates NPV and displays formula in Formula Bar
Use Excel to Calculate NPV
Subtract Present Value of Cost to acquire asset to determine NPV
Slight difference between Excel and tables is due to rounding
Use Excel to Calculate NPV
• Excel is more accurate than tables.
• Can easily perform “what-if” calculations by
changing variables, such as rate, payment,
etc.
• Avoid confusion over which table to use!
• Easy to copy and paste calculations into
other docs for presentation.