2.2 Future 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 period 5 future value of this annuity?
Solution Strategy. We will calculate the future value of this annuity in three equivalent ways. First, we
will calculate the future value using a time line, where each column corresponds to a period of calendar
time. Second, we use a formula for the future value. Third, we use Excel’s FV function for the future
value.
FIGURE 2.2 Spreadsheet for Annuity - Future Value.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:B6.
2. Annuity Future 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$4 in cell C10 and copy it across.
o Future Value of Each Cash Flow = (Cash Flow) * (1 + Discount
Rate/Period)^((Number of Periods) - (Current Period)). Enter =B10*(1+$B$5)^($B$6-
B9) in cell B11 and copy it across. The exponent ($B$6-B9) causes the period 0 cash
flow to be compounded 5 times into the future, the period 1 cash flow to be compounded
4 times into the future, the period 2 cash flow to be compounded 3 times into the future,
etc. The $ signs in $B$5 and $B$6 lock the column and the row when copying.
o Future Value = Sum over all periods of the Future Value of Each Cash Flow. Enter
=SUM(B11:G11) in cell B12.
3. Annuity Future 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+B5)^B6)-1)/B5 in cell B15.
4. Annuity Future Value using the FV Function. The Excel FV function can be used to calculate
the future value of an annuity with the using format =-FV(Discount Rate / Period, Number of
Periods, Payment, 0). Enter =-FV(B5,B6,B4,0) in cell B18.
The Future Value of this Annuity is $450.97. Notice you get the same answer all three ways: using the
time line, using the formula, or using the FV 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 period 5 future value of this annuity?
Solution Strategy. We will calculate the future value of this annuity in three equivalent ways. First, we
will calculate the future value using a time line, where each column corresponds to a period of calendar
time. Second, we use a formula for the future value. Third, we use Excel’s FV function for the future
value.
FIGURE 2.2 Spreadsheet for Annuity - Future Value.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:B6.
2. Annuity Future 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$4 in cell C10 and copy it across.
o Future Value of Each Cash Flow = (Cash Flow) * (1 + Discount
Rate/Period)^((Number of Periods) - (Current Period)). Enter =B10*(1+$B$5)^($B$6-
B9) in cell B11 and copy it across. The exponent ($B$6-B9) causes the period 0 cash
flow to be compounded 5 times into the future, the period 1 cash flow to be compounded
4 times into the future, the period 2 cash flow to be compounded 3 times into the future,
etc. The $ signs in $B$5 and $B$6 lock the column and the row when copying.
o Future Value = Sum over all periods of the Future Value of Each Cash Flow. Enter
=SUM(B11:G11) in cell B12.
3. Annuity Future 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+B5)^B6)-1)/B5 in cell B15.
4. Annuity Future Value using the FV Function. The Excel FV function can be used to calculate
the future value of an annuity with the using format =-FV(Discount Rate / Period, Number of
Periods, Payment, 0). Enter =-FV(B5,B6,B4,0) in cell B18.
The Future Value of this Annuity is $450.97. Notice you get the same answer all three ways: using the
time line, using the formula, or using the FV function.