Calculate Present or Future Value of Cash Flows © Dale R. Geiger 20111.

© Dale R. Geiger 2011 1

Calculate Present or Future Value of Cash Flows

Principles of Cost Analysis and Management


Time Value of Money Concepts

• Is $1 received today worth the same as $1 to be received one year from today?

• Is $1 received today worth the same as $1 to be received one hundred years from today?

• Why or why not?


Terminal Learning Objective

• Action: Calculate Present Or Future Value Of A Variety Of Cash Flow Scenarios

• Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors

• Standard: with at least 80% accuracy • Identify and enter relevant report data to solve Present and

Future Value equations using macro enabled cash flow templates


Time Value of Money Concepts

Money received Today:• Can be invested Today to

earn interest

• Can be spent Today at Today’s prices

Money received in the Future:• Has not yet begun to earn

interest

• Can be spent in the Future at inflated prices


Simple Interest

• Interest earned on Principal onlyPrincipal * Annual Interest Rate * Time in Years

• Invest $1 today at 10% interest for 3 yearsInterest = $1 * .10 * 3 = $.30

• $1 grows to $1.30 over 3 years


Compound Interest or Future Value

• Invest $1 today at 10% Interest for 3 years

• This relationship can be expressed as:Principal * (1 + Annual Interest Rate)Time in Years

$1*(1+.10)3 = $1.33

Principal * 10% (1 year) = Interest New Balance

$1.00 * .10 = $.10 $1.10$1.10 * .10 = $.11 $1.21$1.21 * .10 = $.12 $1.33





$1*(1+.10)3 = $1.33


$1.00 * .10 = $.10 $1.10$1.10 * .10 = $.11 $1.21$1.21 * .10 = $.12 $1.33

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Effect of Interest Rate and Time

0 1 2 3 4 5 6 7 8 9 10 $-

$1.00

$2.00

$3.00

$4.00

$1.21

$2.14

10%

X-Axis = Time in YearsAs Time increases, Future Value of $1 Increases

After 2 years at 10% …..and after 8 years at 10%

© Dale R. Geiger 2011

12


0 1 2 3 4 5 6 7 8 9 10 $-

$1.00

$2.00

$3.00

$4.00

$1.48

$2.14

$3.06

15%10%5%

X-Axis = Time in YearsAs interest rate increases, Future Value of $1 Increases

A higher interest rate causes the future value to increase more in the same 8 years.


13

The Future Value TableFuture Value of $1 (Compound Interest)

Years 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%1 1.020 1.040 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 2 1.040 1.082 1.124 1.166 1.210 1.254 1.300 1.346 1.392 1.440 3 1.061 1.125 1.191 1.260 1.331 1.405 1.482 1.561 1.643 1.728 4 1.082 1.170 1.262 1.360 1.464 1.574 1.689 1.811 1.939 2.074 5 1.104 1.217 1.338 1.469 1.611 1.762 1.925 2.100 2.288 2.488 6 1.126 1.265 1.419 1.587 1.772 1.974 2.195 2.436 2.700 2.986 7 1.149 1.316 1.504 1.714 1.949 2.211 2.502 2.826 3.185 3.583 8 1.172 1.369 1.594 1.851 2.144 2.476 2.853 3.278 3.759 4.300 9 1.195 1.423 1.689 1.999 2.358 2.773 3.252 3.803 4.435 5.160

10 1.219 1.480 1.791 2.159 2.594 3.106 3.707 4.411 5.234 6.192 11 1.243 1.539 1.898 2.332 2.853 3.479 4.226 5.117 6.176 7.430 12 1.268 1.601 2.012 2.518 3.138 3.896 4.818 5.936 7.288 8.916 13 1.294 1.665 2.133 2.720 3.452 4.363 5.492 6.886 8.599 10.699 14 1.319 1.732 2.261 2.937 3.797 4.887 6.261 7.988 10.147 12.839 15 1.346 1.801 2.397 3.172 4.177 5.474 7.138 9.266 11.974 15.407 16 1.373 1.873 2.540 3.426 4.595 6.130 8.137 10.748 14.129 18.488 17 1.400 1.948 2.693 3.700 5.054 6.866 9.276 12.468 16.672 22.186 18 1.428 2.026 2.854 3.996 5.560 7.690 10.575 14.463 19.673 26.623 19 1.457 2.107 3.026 4.316 6.116 8.613 12.056 16.777 23.214 31.948 20 1.486 2.191 3.207 4.661 6.727 9.646 13.743 19.461 27.393 38.338 25 1.641 2.666 4.292 6.848 10.835 17.000 26.462 40.874 62.669 95.396 30 1.811 3.243 5.743 10.063 17.449 29.960 50.950 85.850 143.371 237.376 35 2.000 3.946 7.686 14.785 28.102 52.800 98.100 180.314 327.997 590.668 40 2.208 4.801 10.286 21.725 45.259 93.051 188.884 378.721 750.378 1,469.772

The Value of $1 at 10% interest after 8 years is $2.14The Factors are pre-calculated on the FV Table.



Check on Learning

• How does compound interest differ from simple interest?

• How does number of years affect the future value of an investment?


Demonstration Problem

• If I invest $50,000 today at 8%, what will it be worth in 10 years?

• Steps:1. Identify the key variables

• Cash flow• Interest rate• Time in years

2. Build a timeline3. Multiply cash flow by FV factor from the Table


Identify Key Variables

• Cash Flows• $50,000 to be paid now• Cash Payments are negative numbers• Some unknown amount to be received ten years

in the future• Cash Receipts are positive numbers

• Interest Rate = 8%• Time in Years = 10


Build a Timeline

0 1 2 3 4 5 6 7 8 9 10

-60

-40

-20

0

20

40

60

80

100

120

$50,000 to be invested now

$

$

X-Axis = Time in Years

Unknown amount to be received in 10

years

K

K $50K

?

18

Multiply by the FV FactorFuture Value of $1 (Compound Interest)

Years 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%1 1.020 1.040 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 2 1.040 1.082 1.124 1.166 1.210 1.254 1.300 1.346 1.392 1.440 3 1.061 1.125 1.191 1.260 1.331 1.405 1.482 1.561 1.643 1.728 4 1.082 1.170 1.262 1.360 1.464 1.574 1.689 1.811 1.939 2.074 5 1.104 1.217 1.338 1.469 1.611 1.762 1.925 2.100 2.288 2.488 6 1.126 1.265 1.419 1.587 1.772 1.974 2.195 2.436 2.700 2.986 7 1.149 1.316 1.504 1.714 1.949 2.211 2.502 2.826 3.185 3.583 8 1.172 1.369 1.594 1.851 2.144 2.476 2.853 3.278 3.759 4.300 9 1.195 1.423 1.689 1.999 2.358 2.773 3.252 3.803 4.435 5.160

10 1.219 1.480 1.791 2.159 2.594 3.106 3.707 4.411 5.234 6.192 11 1.243 1.539 1.898 2.332 2.853 3.479 4.226 5.117 6.176 7.430 12 1.268 1.601 2.012 2.518 3.138 3.896 4.818 5.936 7.288 8.916 13 1.294 1.665 2.133 2.720 3.452 4.363 5.492 6.886 8.599 10.699 14 1.319 1.732 2.261 2.937 3.797 4.887 6.261 7.988 10.147 12.839 15 1.346 1.801 2.397 3.172 4.177 5.474 7.138 9.266 11.974 15.407 16 1.373 1.873 2.540 3.426 4.595 6.130 8.137 10.748 14.129 18.488 17 1.400 1.948 2.693 3.700 5.054 6.866 9.276 12.468 16.672 22.186 18 1.428 2.026 2.854 3.996 5.560 7.690 10.575 14.463 19.673 26.623 19 1.457 2.107 3.026 4.316 6.116 8.613 12.056 16.777 23.214 31.948 20 1.486 2.191 3.207 4.661 6.727 9.646 13.743 19.461 27.393 38.338 25 1.641 2.666 4.292 6.848 10.835 17.000 26.462 40.874 62.669 95.396 30 1.811 3.243 5.743 10.063 17.449 29.960 50.950 85.850 143.371 237.376 35 2.000 3.946 7.686 14.785 28.102 52.800 98.100 180.314 327.997 590.668 40 2.208 4.801 10.286 21.725 45.259 93.051 188.884 378.721 750.378 1,469.772

The Factor of $1 at 8% interest for 10 years is 2.159$50,000 * 2.159 = $107,950



Using the Formula

• The formula proves that the answer from the table is correct:

$50,000 * (1 + .08)10 = $107,946• The difference of $4 is caused by rounding in

the table


ProofYear Principal * 8 % = Interest New Balance

1 $50,000 * .08 = $4,000 $54,0002 $54.000 * .08 = $4,320 $58,3203 $58,320 * .08 = $4,666 $62,9864 $62,986 * .08 = $5,039 $68,0245 $68,024 * .08 = $5,442 $73,4666 $73,466 * .08 = $5,877 $79,3437 $79,343 * .08 = $6,347 $85,6908 $85,690 * .08 = $6,855 $92,5459 $92,545 * .08 = $7,404 $99,949

10 $99,949 * .08 = $7,996 $107,945


Check on Learning

• What is the first step in solving a future value problem?

• How are cash payments represented in the timeline?


Future Value vs. Present Value

• Future Value answers the question:• To what value will $1 grow in the Future?

• Present Value answers the question:• What is the value Today of $1 to be received in the

Future?-or-

• How much must be invested today to achieve $1 in the Future?


Future Value vs. Present Value

$0.00$0.10$0.20$0.30$0.40$0.50$0.60$0.70$0.80$0.90$1.00

1 3 5 7 9 11 13 15 17 19

Periods

Present Value of $1 at 10%

$0.00$1.00$2.00$3.00$4.00$5.00$6.00$7.00$8.00

1 3 5 7 9 11 13 15 17 19

Periods

Future Value of $1 at 10%

A dollar to be received in the future is worth less than a dollar received today

The value of a dollar received today will increase in the future


Present Value Concepts

• What is the value Today of $1 to be received one year in the Future?

• How much must be invested Today to grow to $1 one year from Today?

• The answer to these two questions is the same!



• Discount Rate represents interest or inflation• Assume a rate of 10%• What is the cost expression for this relationship?

$Investment Today + Interest = $1.00-or-

$Investment + ($Investment * .10) = $1.00$Investment * (1+ .10) = $1.00

$Investment = $1/(1.10)$Investment = $.91


Proof

• Plug $.91 in to the original equation:$.91 + ($.91 * .10) = $1.00

$.91 + .09 = $1.00• This relationship is fairly simple for one

period, but what about multiple periods?



• How much must be invested today to achieve $1.00 three years from today?

• What is the cost expression for this relationship?$Investment * (1 + Rate) #Years = $Future Value$Investment = $Future Value / (1 + Rate) #Years

-or-$Investment * (1+.10) 3 = $1.00$Investment = $1.00 / (1+.10) 3

$Investment = $.75






$Investment = $.75



• The Investment amount is known as the Present Value

• The Present Value relationship is expressed in the formula:

Future Cash Flow * 1/(1 + Rate) #Years

-or-$1 * 1/(1.10)3 = $.75


Proof

• There is also a table shortcut for Present Value


$.75 * .10 = $.075 $.83$.83 * .10 = $.083 $.91$.91 * .10 = $.091 $1.00


The Present Value TablePresent Value of $1

Years 2% 4% 6% 8% 10% 12% 14% 16% 18%1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 2 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 3 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 4 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.516 5 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 6 0.888 0.790 0.705 0.630 0.564 0.507 0.456 0.410 0.370 7 0.871 0.760 0.665 0.583 0.513 0.452 0.400 0.354 0.314 8 0.853 0.731 0.627 0.540 0.467 0.404 0.351 0.305 0.266 9 0.837 0.703 0.592 0.500 0.424 0.361 0.308 0.263 0.225

10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 11 0.804 0.650 0.527 0.429 0.350 0.287 0.237 0.195 0.162 12 0.788 0.625 0.497 0.397 0.319 0.257 0.208 0.168 0.137 13 0.773 0.601 0.469 0.368 0.290 0.229 0.182 0.145 0.116 14 0.758 0.577 0.442 0.340 0.263 0.205 0.160 0.125 0.099 15 0.743 0.555 0.417 0.315 0.239 0.183 0.140 0.108 0.084 16 0.728 0.534 0.394 0.292 0.218 0.163 0.123 0.093 0.071 17 0.714 0.513 0.371 0.270 0.198 0.146 0.108 0.080 0.060 18 0.700 0.494 0.350 0.250 0.180 0.130 0.095 0.069 0.051

The Present Value of $1 at 10% to be received in 3 years is $.75

37


0 1 2 3 4 5 6 7 8 9 10 $-

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$0.83

$0.47 10%

X-Axis = Time in YearsAs Time increases, Present Value of $1 Decreases

$1 to be received in 2 years at 10% …..and in 8 years at 10%


38


0 1 2 3 4 5 6 7 8 9 10 $-

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$0.33

$0.47

$0.68 5%10%15%

X-Axis = Time in YearsAs Time increases, Present Value of $1 Decreases

A higher discount rate causes the present value to decrease more in the same 8 years.



Check on Learning

• What does Present Value represent?• How does the Present Value table differ from

the Future Value table?


Demonstration Problem

• What is the Present Value of a $60,000 cash flow to be received 6 years from today assuming 12% discount rate?

• Steps:1. Identify the key variables

• Cash flow• Discount rate• Time in years

2. Build a timeline3. Multiply cash flow by the Factor from the PV Table


Identify Key Variables

• Cash Flow• $60,000 to be received in the Future• Is equal to some unknown amount Today

• Discount Rate = 12%• Time in Years = 6


Build a Timeline

0 1 2 3 4 5 60

10

20

30

40

50

60

70

UnknownPresent Value

$

X-Axis = Time in Years

$60,000 to be received in 6 years

K

?

$60K


Multiply by the PV FactorPresent Value of $1

Years 2% 4% 6% 8% 10% 12% 14% 16% 18%1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 2 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 3 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 4 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.516 5 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 6 0.888 0.790 0.705 0.630 0.564 0.507 0.456 0.410 0.370 7 0.871 0.760 0.665 0.583 0.513 0.452 0.400 0.354 0.314 8 0.853 0.731 0.627 0.540 0.467 0.404 0.351 0.305 0.266 9 0.837 0.703 0.592 0.500 0.424 0.361 0.308 0.263 0.225

10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 11 0.804 0.650 0.527 0.429 0.350 0.287 0.237 0.195 0.162 12 0.788 0.625 0.497 0.397 0.319 0.257 0.208 0.168 0.137 13 0.773 0.601 0.469 0.368 0.290 0.229 0.182 0.145 0.116 14 0.758 0.577 0.442 0.340 0.263 0.205 0.160 0.125 0.099 15 0.743 0.555 0.417 0.315 0.239 0.183 0.140 0.108 0.084 16 0.728 0.534 0.394 0.292 0.218 0.163 0.123 0.093 0.071 17 0.714 0.513 0.371 0.270 0.198 0.146 0.108 0.080 0.060

The Factor of $1 at 12% discount for 6 years is 0.507$60,000 * 0.507 = $30,420


Using the Formula

• The formula proves that the answer from the table is correct:

$60,000 * 1/(1 + .12)6 = $30,398• The difference of $22 is caused by rounding in

the table


ProofYear Principal * 8 % = Interest New Balance

1 30,420 * .12 = $3,650 $34,070 2 34,070 * .12 = $4,088 $38,159 3 38,159 * .12 = $4,579 $42,738 4 42,738 * .12 = $5,129 $47,866 5 47,866 * .12 = $5,744 $53,610 6 53,610 * .12 = $6,433 $60,044


Check on Learning

• How does time affect the present value of a cash flow?

• How does the discount rate affect the present value of a cash flow?


Practical Exercise


Time Value of Money Worksheet

Enter key variables in the blank white cells to generate

the graph shown below


Time Value of Money Worksheet

The spreadsheet tool also calculates Present Value


Practical Exercise

Calculate Present or Future Value of Cash Flows © Dale R. Geiger 20111.

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Transcript of Calculate Present or Future Value of Cash Flows © Dale R. Geiger 20111.