2.1 Present Value
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Problem. An annuity pays $80.00 each period for 5 periods. For these cash flows, the appropriate
discount rate / period is 6.0%. What is the present value of this annuity?
Solution Strategy. We will calculate the present value of this annuity in three equivalent ways. First, we
will calculate the present value using a time line, where each column corresponds to a period of calendar
time. Second, we use a formula for the present value. Third, we use Excel’s PV function for the present
value.
FIGURE 2.1 Spreadsheet for Annuity - Present Value.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:B6.
2. Annuity Present Value using a Time Line. Create a time line from period 0 to period 5.
Determine the annuity cash flows in periods 1 through 5. Calculate the present value of each cash
flow and sum the present values as follows.
o Period. Enter 0, 1, 2, …, 5. in the range B9:G9.
o Cash Flows. Enter $0.00 in cell B10. Enter =$B$4 in cell C10 and copy it across.
o Present Value of Each Cash Flow = (Cash Flow) / ((1 + Discount Rate/Period) ^
Period). Enter =B10/((1+$B$5)^B9) in cell B11 and copy it across. The $ signs in $B$5
lock the column and row when copying.
o Present Value = Sum over all periods of the Present Value of Each Cash Flow. Enter
=SUM(B11:G11) in cell B12.
3. Annuity Present Value using the Formula. The formula for Annuity Present Value =
(Payment) * (1 - ((1 + Discount Rate/Period) ^ (-Number of Periods))) / (Discount Rate/Period).
Enter =B4*(1-((1+B5)^(-B6)))/B5 in cell B15.
4. Annuity Present Value using the PV Function. The Excel PV function can be used to calculate
the present value of an annuity using the following format =-PV(Discount Rate / Period, Number
of Periods, Payment, 0). Enter =-PV(B5,B6,B4,0) in cell B18.
The Present Value of this Annuity is $336.99. Notice you get the same answer all three ways: using the
time line, using the formula, or using the PV function.
Problem. An annuity pays $80.00 each period for 5 periods. For these cash flows, the appropriate
discount rate / period is 6.0%. What is the present value of this annuity?
Solution Strategy. We will calculate the present value of this annuity in three equivalent ways. First, we
will calculate the present value using a time line, where each column corresponds to a period of calendar
time. Second, we use a formula for the present value. Third, we use Excel’s PV function for the present
value.
FIGURE 2.1 Spreadsheet for Annuity - Present Value.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:B6.
2. Annuity Present Value using a Time Line. Create a time line from period 0 to period 5.
Determine the annuity cash flows in periods 1 through 5. Calculate the present value of each cash
flow and sum the present values as follows.
o Period. Enter 0, 1, 2, …, 5. in the range B9:G9.
o Cash Flows. Enter $0.00 in cell B10. Enter =$B$4 in cell C10 and copy it across.
o Present Value of Each Cash Flow = (Cash Flow) / ((1 + Discount Rate/Period) ^
Period). Enter =B10/((1+$B$5)^B9) in cell B11 and copy it across. The $ signs in $B$5
lock the column and row when copying.
o Present Value = Sum over all periods of the Present Value of Each Cash Flow. Enter
=SUM(B11:G11) in cell B12.
3. Annuity Present Value using the Formula. The formula for Annuity Present Value =
(Payment) * (1 - ((1 + Discount Rate/Period) ^ (-Number of Periods))) / (Discount Rate/Period).
Enter =B4*(1-((1+B5)^(-B6)))/B5 in cell B15.
4. Annuity Present Value using the PV Function. The Excel PV function can be used to calculate
the present value of an annuity using the following format =-PV(Discount Rate / Period, Number
of Periods, Payment, 0). Enter =-PV(B5,B6,B4,0) in cell B18.
The Present Value of this Annuity is $336.99. Notice you get the same answer all three ways: using the
time line, using the formula, or using the PV function.