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EXCEL MODELING IN CORPORATE FINANCE 5TH EDITION BY CRAIG W. HOLDEN
EXCEL MODELING IN CORPORATE FINANCE 5TH EDITION BY CRAIG W. HOLDEN
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EXCEL MODELING IN CORPORATE FINANCE 5TH EDITIONBY CRAIG W. HOLDEN
,PART 1 TIME VALUE OF MONEY
1 Single Cash Flow
1.1 Present Value
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?
Elaboration 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.
FIG: 1.1 Spreadsheet for Single Cash Flow - Present Value.
How To Create Your Own Spreadsheet Model/method.
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!
1.2 Future Value
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?
Clarificaation 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.
FIG: 1.2 Spreadsheet for Single Cash Flow - Future Value.
How To Create Your Own Spreadsheet Model/method.
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.
, Puzzles
Skill-Createing Puzzles.
1. A single cash flow of $1,673.48 will be received in 4 periods. For this cash flow, the appropriate
discount rate / period is 7.8%. What is the present value of this single cash flow?
2. A single cash flow of $932.47 is available now (in period 0). For this cash flow, the appropriate
discount rate / period is 3.9%. What is the period 4 future value of this single cash flow?
Live In-class Puzzles.
3. Given the partial Present Value spreadsheet SinglepZ.xls, complete step 2 Present Value Using
A Timeline.
Excel Model/MODELING in Corporate Finance 5th Edition
4. Given the partial Future Value spreadsheet SinglefZ.xls, complete step 2 Future Value Using A
Timeline.
2 Annuity
2.1 Present Value
Puzzle. 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?
Clarificaation 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.
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