1.1 Present Value

К оглавлению1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 
68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 
85 86 87 88 89 90 91 92 93 94 95 96 97 

Problem. A single cash flow of $1,000.00 will be received in 5 periods. For this cash flow, the

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

Solution Strategy. We will calculate the present value of this single cash flow 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 1.1 Spreadsheet for Single Cash Flow - Present Value.

How To Build Your Own Spreadsheet Model.

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

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

cash flow in period 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 and copy it to the range C10:F10. Enter =B4 in cell

G10.

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 as B and the row as 5 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. Present Value using the Formula. For a single cash flow, the formula is Present Value = (Cash

Flow) / ((1 + Discount Rate/Period) ^ Period). Enter =B4/((1+B5)^B6) in cell B15.

4. Present Value using the PV Function. The Excel PV function can be used to calculate the

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

For a single cash flow, the format is =-PV(Discount Rate / Period, Number of Periods, 0, Single

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

The Present Value of this Single Cash Flow is $747.26. Notice you get the same answer all three ways:

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

Problem. A single cash flow of $1,000.00 will be received in 5 periods. For this cash flow, the

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

Solution Strategy. We will calculate the present value of this single cash flow 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 1.1 Spreadsheet for Single Cash Flow - Present Value.

How To Build Your Own Spreadsheet Model.

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

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

cash flow in period 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 and copy it to the range C10:F10. Enter =B4 in cell

G10.

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 as B and the row as 5 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. Present Value using the Formula. For a single cash flow, the formula is Present Value = (Cash

Flow) / ((1 + Discount Rate/Period) ^ Period). Enter =B4/((1+B5)^B6) in cell B15.

4. Present Value using the PV Function. The Excel PV function can be used to calculate the

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

For a single cash flow, the format is =-PV(Discount Rate / Period, Number of Periods, 0, Single

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

The Present Value of this Single Cash Flow is $747.26. Notice you get the same answer all three ways:

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