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 flowsModel M

Year

Net Cash Inflows

16% Factor

Present Value

1 $6,000 .862 $ 5,172.00 2 5,500 .743 4,086.50 3 5,000 .641 3,205.00 4 4,500 .552 2,484.00 5 4,000 .476 1,904.00 Residual value 2,000 .476 952.00 Total pres ent value of cash inflows $17,803.50 Less purchase price of Model M 17,500.00 Net present value $ 303.50

The cash outflow for the purchase is not discounted because it occurs at time zero

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

Model N

Year Net Cash Inflows

16% Factor

Present Value

1-5 $6,000 3.247 $19,644 .00 Residual value 2,000 .476 952.00 Total present value of cash inflows $20,596.0 0 Less purchase price of Model N 21,000.00 Net present value ( $ 404.0 0 )

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 NPVInsert the NPV function into the cell

Use Excel to Calculate NPVSelect Function from Category and Menu

Use Excel to Calculate NPV

Use Dialog box to enter interest rate

Use Excel to Calculate NPVSelect 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 NPVSubtract 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.