Slides calculate present or future value

Time Value of Money Concepts• Is $1 received today worth the same as $1 to be received one year from today?. Time Value of Money ConceptsMoney received Today: • Can be invested Today to

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Calculate Present or Future Value of Cash Flows

Principles of 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 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

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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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Check on Learning

• How does compound interest differ from simple interest?

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

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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 in the future

• Cash Receipts are positive numbers

• Interest Rate = 8%

• Time in Years = 10

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Unknown amount to be received

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Multiply by the FV Factor

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

$50,000 * 2.159 = $107,950

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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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Check on Learning

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

• How are cash payments represented in the timeline?

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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

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

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

$Investment * (1 + Rate) #Years = $Future Value

$Investment = $Future Value / (1 + Rate) #Years

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• 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

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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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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.

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Check on Learning

• What does Present Value represent?

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

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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

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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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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?

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Practical Exercise

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Time Value of Money Worksheet

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Time Value of Money Worksheet

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Practical Exercise

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