1.2 Future Value

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Problem. A single cash flow of $747.25 is available now (in period 0). For this cash flow, the appropriate

discount rate / period is 6.0%. What is the period 5 future value of this single cash flow?

Solution Strategy. We will calculate the future value of the single cash flow 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 1.2 Spreadsheet for Single Cash Flow - Future Value.

How To Build Your Own Spreadsheet Model.

1. Inputs. Enter the inputs in the range B4:B6.

2. Future Value using a Time Line. Create a time line from period 0 to period 5. Enter the single

cash flow in period 0. Calculate the period 5 future value of each cash flow and sum the future

values as follows.

o Period. Enter 0, 1, 2, …, 5. in the range B9:G9.

o Cash Flows. Enter =B4 in cell B10. Enter $0.00 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. Future Value using the Formula. For a single cash flow, the formula is Future = (Cash Flow) *

(1 + Discount Rate/Period)^(Number of Periods). Enter =B4*(1+B5)^B6 in cell B15.

4. Future Value using the FV Function. The Excel FV function can be used to calculate the future

value of a single cash flow, the future value of an annuity, or the future value of a bond. For a

single cash flow, the format is =-FV(Discount Rate / Period, Number of Periods, 0, Single Cash

Flow). Enter =-FV(B5,B6,0,B4) in cell B18.

The Future Value of this Single Cash Flow is $1,000.00. Notice you get the same answer all three ways:

using the time line, using the formula, or using the FV function!

Comparing Present Value and Future Value, we see that they are opposite operations. That is, one

operation "undoes" the other. The Present Value of $1,000.00 in period 5 is $747.26 in period 0. The

Future Value of $747.26 in period 0 is $1,000.00 in period 5.

Problem. A single cash flow of $747.25 is available now (in period 0). For this cash flow, the appropriate

discount rate / period is 6.0%. What is the period 5 future value of this single cash flow?

Solution Strategy. We will calculate the future value of the single cash flow 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 1.2 Spreadsheet for Single Cash Flow - Future Value.

How To Build Your Own Spreadsheet Model.

1. Inputs. Enter the inputs in the range B4:B6.

2. Future Value using a Time Line. Create a time line from period 0 to period 5. Enter the single

cash flow in period 0. Calculate the period 5 future value of each cash flow and sum the future

values as follows.

o Period. Enter 0, 1, 2, …, 5. in the range B9:G9.

o Cash Flows. Enter =B4 in cell B10. Enter $0.00 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. Future Value using the Formula. For a single cash flow, the formula is Future = (Cash Flow) *

(1 + Discount Rate/Period)^(Number of Periods). Enter =B4*(1+B5)^B6 in cell B15.

4. Future Value using the FV Function. The Excel FV function can be used to calculate the future

value of a single cash flow, the future value of an annuity, or the future value of a bond. For a

single cash flow, the format is =-FV(Discount Rate / Period, Number of Periods, 0, Single Cash

Flow). Enter =-FV(B5,B6,0,B4) in cell B18.

The Future Value of this Single Cash Flow is $1,000.00. Notice you get the same answer all three ways:

using the time line, using the formula, or using the FV function!

Comparing Present Value and Future Value, we see that they are opposite operations. That is, one

operation "undoes" the other. The Present Value of $1,000.00 in period 5 is $747.26 in period 0. The

Future Value of $747.26 in period 0 is $1,000.00 in period 5.