Slides 2 3 calculate present or future value of a variety o

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... Compound Int

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Calculate Present or Future Value

of Cash Flows

Intermediate Cost Analysis

and Management

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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?

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Terminal Learning Objective

• Action: Calculate Present or Future Value of a Variety of

Cash Flow Scenarios

• Condition: You are training to become an ACE with

access to ICAM course handouts, readings, and

spreadsheet tools 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

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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

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Simple Interest

• Interest earned on Principal only

Principal * Annual Interest Rate * Time in Years

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

Interest = $1 * 10 * 3 = $.30

• $1 grows to $1.30 over 3 years

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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

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Effect of Interest Rate and Time

X-Axis = Time in Years

As Time increases, Future Value of $1 Increases

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

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$3.06

15% 10% 5%

As interest rate increases, Future Value of $1 Increases

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

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The Future Value Table

The Value of $1 at 10% interest after 8 years is $2.14

The Factors are pre-calculated on the FV Table.

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Identify Key Variables

• Cash Flows

• $50,000 to be paid now

• Cash Payments are negative numbers

• Some unknown amount to be received ten years

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$50,000 to be invested now

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Multiply by the FV Factor

The Factor of $1 at 8% interest for 10 years is 2.159

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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

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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?

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Future Value vs Present Value

The value of a dollar received today will

increase in the future

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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!

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• Assume a rate of 10%

• What is the cost expression for this relationship?

$Investment Today + Interest = $1.00

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• 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?

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

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• The Investment amount is known as the

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• There is also a table shortcut for Present Value

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

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The Present Value Table

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

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As Time increases, Present Value of $1 Decreases

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

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$0.68

5% 10% 15%

As Time increases, Present Value of $1 Decreases

A higher discount rate causes the present value to decrease more

in the same 8 years.

A higher discount rate causes the present value to decrease more

in the same 8 years.

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Learning Check

• What does Present Value represent?

• How does the Present Value table differ from the Future Value table?

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Demonstration Problem

• What is the Present Value of a $60,000 cash flow

to be received 6 years from today assuming 12% discount rate?

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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

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Unknown Present Value

$

$60,000 to be received in 6 years

K

?

$60K

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Multiply by the PV Factor

The Factor of $1 at 12% discount for 6 years is 0.507

$60,000 * 0.507 = $30,420

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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

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Practical Exercise

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Time Value of Money Worksheet

Enter key variables in the blank white cells to generate the graph shown below

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Time Value of Money Worksheet

The spreadsheet tool also calculates Present Value

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Practical Exercise

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