1. Calculate Present or Future Value of a Variety of Cash Flows Scenarios
Principles of Cost Analysis and Management
Show Slide #1: Calculate Present or Future Value of a Variety of Cash Flows Scenarios
References:
FM Financial Management Operations, Apr 14
Handouts and Excel Spreadsheets
Facilitator Material: Each primary facilitator should possess a lesson plan, slide deck, course handouts, and practical exercises with Answer Key, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14. All required printed reference material, and technical manuals will be provided by the Schoolhouse.
Learner Material: Learners should possess all required printed reference material, course handouts, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14 and standard classroom supplies.

2. 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?
Show Slide #2: Concrete Experience: Time Value of Money Concepts
Facilitator’s Note: (Concrete Experience 5 minutes) Ask the learners the following Questions. Facilitate a discussion on the answers given by the learners.
Facilitator’s Note: (Publish and Process 5 minutes) The critical portion of this part of the ELM process is to force the learners to think.
Introduction:
Is $1 received today worth the same as $1 to be received one year from today? Why or why not?
Learners should be able to come up with at least a few reasons why the $1 received today is worth more than the dollar to be received in the future. There is inflation to consider. There is also interest.
Is $1 received today worth the same as $1 to be received one hundred years from today? Why or why not?
This question brings up the idea of utility. The dollar to be received one 100 years from today has very little value because it’s unlikely any of us will be around to enjoy it.
Inflation, interest, and utility are all reasons why we need to consider what is called the “Time Value of Money”.

3. Terminal Learning Objective
Action: Calculate Present or Future Value of a Variety of Cash Flows Scenarios
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Calculate Future Value
Calculate Present Value
Show Slide #3: Terminal Learning Objective (TLO)
Action: Calculate Present or Future Value of a Variety of Cash Flows Scenarios
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners)
Calculate Future Value
Calculate Present Value
Facilitator’s Note: Throughout this lesson, solicit from learners the challenges they experienced in the current operational environment (OE) and what they did to resolve them. Encourage learners to apply at least 1 of the 8 critical variables: physical environment, political stability of the state, sociological demographics, infrastructure, military capabilities, information, time, and economics.
Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM , Risk Management. Leaders will complete a DD Form 2977 DELIBERATE RISK ASSESSMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation
Risk Assessment Level: Low. Hazard Identification: Electrical Shock, Fire, Slippery Floors, Physical Injure/Strain, Tripping Tight Spaces in Classroom, and Influenza. Hazard controls: Primary Instructor (PI) will ensure: All electrical cords are properly stored under desks, liquid containers have lids on them and all spills are immediately cleaned and mopped and allowed to completely dry before allowing learners/personnel to walk on them. All chairs are ergonomically designed, adjust to individual preference and that all learners are awake and paying attention in class. All cables/cords are properly plugged in, sheathed, and secured along tables, walls, and ceilings. No damaged or frayed cords/cables will be used. PI will brief proper hand washing techniques, the use of hand sanitizer, and evacuation procedures. All trash will be removed daily.
Environmental Statement: Environmental protection is not just the law but the right thing to do. It is a continual process and starts with deliberate planning. Always be alert to ways to protect our environment during training and missions. In doing so, you will contribute to the sustainment of our training resources while protecting people and the environment from harmful effects. Refer to FM Environmental Considerations and GTA ENVIRONMENTAL-RELATED RISK ASSESSMENT.
Evaluation: No formal written examination will be administered; the learners understanding of the material will be evaluated through check on learning questions and practical exercise.
Instructional Lead In: If you received $1 today, the present value would be $1 because present value is what your investment gives you if you were to spend it today. If you received $1 in a year, the present value of the amount would not be $1 because you do not have it in your hand now, in the present. This lesson is designed to assist Financial Managers with understanding and calculating the time value of money – present and future value of cash flows.

4. Time Value of Money Concepts:
Money received Today:
Money received in the Future:
Can be invested Today to earn interest
Can be spent Today at Today’s prices
Has not yet begun to earn interest
Can be spent in the Future at inflated prices
Show Slide #4: Calculate Future Value
Learning Step/Activity #1: Calculate Future Value
Method of Instruction: DSL-Discussion (small or large group discussion)
Facilitator to Student Ratio: 2:25
Time of Instruction: 40 Minutes
Media: PowerPoint, Printed Reference Material
Facilitator’s Note: All handouts and learner materials for this lesson are located in Tab 23.
Facilitator's Note: Before facilitating this lesson, ask the learners which of the 21st Century Soldier (Learner) Competency do they think pertain to this lesson? Facilitate a discussion on the answers given and at the end of the lesson revisit it and see if the learners still believe their choice are the same. For this lesson these competencies should be talked about.
1. Character and accountability
6. Communication and engagement (oral, written, and negotiation)
7. Critical thinking and problem solving
9. Tactical and technical competence (full spectrum capable)
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Time Value of Money Concepts:
It should be fairly evident that Money received Today:
Can be invested Today to earn interest. The money can begin earning interest for us as soon as we receive it.
It can also be spent Today at Today’s prices.
On the other hand, Money received in the Future:
Has not yet begun to earn interest. We can’t put it to use earning interest until we receive it.
Can be spent in the Future at inflated prices. The dollar that buys a large coffee today may only buy a small coffee in the future as inflation causes buying power to shrink.

5. Principal * Annual Interest Rate * Time in Years
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
Show Slide #5: Simple Interest
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Simple interest means that interest is earned on the principal only. The simple interest formula is: Principal * Annual Interest Rate * Time in Years
Using this formula, if we invest $1 today at 10% interest for 3 years: Interest = $1 * .10 * 3 = $.30. Our $1 grows to $1.30 over 3 years.

6. 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
Show Slide #6: Compound Interest or Future Value
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Compound interest, also called Future Value, is a more realistic and more powerful concept. It is more realistic because when the money is invested for more than one year, some compounding is assumed. We are assuming Annual compounding in all of our examples.
Interest earned on Principal and Interest. Compounding means that interest is earned on Principal and Interest.
If we invest $1 today at 10% Interest for 3 years, compounded annually, we see that once the interest is earned, it is added to the balance and also earns interest in the next period.
Facilitator’s Note: (Advance slide).
In year one our dollar earns $.10 in interest and grows to $1.10.
In year two our $1.10 earns $.11 in interest and grows to $ This relationship can be expressed as:
Principal * (1 + Annual Interest Rate)Time in Years
$1*(1+.10)3 = $1.33
In year three our $1.21 earns $.12 in interest and grows to $ This is three cents more than we would have made with simple interest.
This relationship can be expressed as:
The formula saves us from having to make a separate calculation for each year.
Principal
* 10% (1 year)
= Interest
New Balance
$1.00
* .10
= $.10
$1.10
= $.11
$1.21
= $.12
$1.33
Principal
* 10% (1 year)
= Interest
New Balance
$1.00
* .10
= $.10
$1.10
= $.11
$1.21
= $.12
$1.33
Principal
* 10% (1 year)
= Interest
New Balance
$1.00
* .10
= $.10
$1.10
= $.11
$1.21
= $.12
$1.33

7. Effect of Interest Rate and Time
Show Slide #7: Effect of Interest Rate and Time
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The X-Axis represents Time in Years
a. As time increases, Future Value of $1 Increases
b. After 2 years at 10% our dollar is worth $1.21, and after 8 years at 10% it is worth $2.14.
After 2 years at 10% …..and after 8 years at 10%
X-Axis = Time in Years
As Time increases, Future Value of $1 Increases

8. Effect of Interest Rate and Time (Cont.)
A higher interest rate causes the future value to increase more in the same 8 years.
Show Slide #8: Effect of Interest Rate and Time
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Again, the X-Axis represents Time in Years. Here we show the future value of $1 at three interest rates: 5%, 10% and 15%.
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. At 5%, the dollar grows to only $1.48 in 8 years. At 10%, it grows to $2.14, and at 15% it grows to $3.06.
X-Axis = Time in Years
As interest rate increases, Future Value of $1 Increases

9. The Future Value Table
Show Slide #9: The Future Value Table
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The future value table is useful because it allows us to calculate present value without memorizing the formula. It contains pre-calculated factors for each interest rate and number of years.
2. It takes the focus off of memorizing the formula and instead emphasizes the key variables: number of years and interest rates. We have already seen how significantly these two variables affect the outcome.
3. The column headings represent interest rates while the rows represent number of periods. Using our previous example, $1 at 10% for 8 years, we first find the interest rate of 10% at the top of the chart. Then we move down 8 rows to find the factor that represents 10% for 8 years. We can see that it is If we multiply that times our principal amount of $1, we get $2.14.
a. What would be the factor for 12%, 5 years? (1.762)
b. For 4%, 4 years? (1.170)
The Value of $1 at 10% interest after 8 years is $2.14
The Factors are pre-calculated on the FV Table.

10. Demonstration a Problem
If I invest $50,000 today at 8%, what will it be worth in 10 years?
A. Step 1: Identify the key variables:
Cash flow
Interest rate
Time in years
B. Step 2: Build a timeline
C. Step 3: Multiply cash flow by FV factor from the Table
Show Slide #10: Demonstration a Problem
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
If I invest $50,000 today at 8%, what will it be worth in 10 years?
There are three basic steps to follow in any time value of money problem:
Steps 1: Identify the key variables. The key variables are:
1. Cash flow
2. Interest rate
3. and Time in years
B. Step 2: Build a timeline. We will show this in just a moment. The timeline will help us visualize the cash flows and will help us to choose the correct factor from the table.
C. Step 3: Multiply cash flow by FV factor from the Table.

11. 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%
3. Time in Years = 10
Show Slide #11: Identify Key Variables
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The key variables are: cash flows, interest rate, and time in years.
Cash Flows. The cash flows are:
$50,000 to be paid now. (Cash Payments are negative numbers) and some unknown amount to be received ten years in the future. (Cash Receipts are positive numbers.)
Interest Rate = 8%
3. Time in Years = 10

12. Unknown amount to be received in 10 years
Build a Timeline $ K ?
$50,000 to be invested now
Unknown amount to be received in 10 years
Show Slide #12: Build a Timeline
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The timeline, using a bar graph, gives us a visual representation of the cash flows. The $50,000 to be invested now is represented by a negative.
$50K $ K
X-Axis = Time in Years

13. Multiply by the FV Factor
Show Slide #13: Multiply by the FV Factor
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The Factor of $1 at 8% interest for 10 years is
$50,000 * = $107,950. This means that our $50,000 invested at 10% will grow to $107,950 at the end of 8 years.
The Factor of $1 at 8% interest for 10 years is 2.159
$50,000 * = $107,950

14. Using the Formula
The formula proves that the answer from the table is correct:
$50,000 * ( )10 = $107,946
The difference of $4 is caused by rounding in the table.
Show Slide #14: Using the Formula
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The formula proves that the answer from the table is correct:
$50,000 * ( )10 = $107,946
The difference of $4 is caused by rounding in the table.

15. Proof
Year
Principal
* 8 %
= Interest
New Balance 1
$50,000
* .08
= $4,000
$54,000 2
$54.000
= $4,320
$58,320 3
= $4,666
$62,986 4
= $5,039
$68,024 5
= $5,442
$73,466 6
= $5,877
$79,343 7
= $6,347
$85,690 8
= $6,855
$92,545 9
= $7,404
$99,949 10
= $7,996
$107,945
Show Slide #15: Proof
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
This table shows that the year-by-year calculations also agree with the amount calculated using the future value table. Again, the $5 difference is due to rounding error in the Future Value table, and is not significant.

16. LSA #1 Check on Learning
Q1. How does compound interest differ from simple interest? Q2. How does number of years affect the future value of an investment?
A1. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return.
Show Slide #16 LSA #1: Check on Learning
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
Q1. How does compound interest differ from simple interest?
1A. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return.
2Q. How does number of years affect the future value of an investment?
2A. The more years that the investment is earning and compounding interest, the higher the future value will be.
A2. The more years that the investment is earning and compounding interest, the higher the future value will be.

17. LSA #1 Check on Learning (Cont.)
Q3. What is the first step in solving a future value problem? Q4. How are cash payments represented in the timeline?
A3. The first step is to identify the variables: cash flows, number of years, interest rate
Show Slide #17 LSA #1: Check on Learning (Cont.)
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
Q3. What is the first step in solving a future value problem?
A3. The first step is to identify the variables: cash flows, number of years, interest rate
Q4. How are cash payments represented in the timeline?
A4. Cash payments (or investments) are outflows of cash and are represented as negative numbers.
** Facilitator’s Note: LSA Summary will be given at the end of this lesson.
A4. Cash payments (or investments) are outflows of cash and are represented as negative numbers.

18. 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-
b. How much must be invested today to achieve $1 in the Future?
Show Slide #18: Calculate Present Value
Learning Step/Activity #2: Calculate Present Value
Method of Instruction: DSL-Discussion (small or large group discussion)
Facilitator to Student Ratio: 2:25
Time of Instruction: 40 Minutes
Media: PowerPoint, Printed Reference Material
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Future Value vs. Present Value:
1. Future Value answers the question:
To what value will $1 grow in the Future?
2. Present Value answers the question:
What is the value Today of $1 to be received in the Future?
-or-
b. How much must be invested today to achieve $1 in the Future?

19. Future Value vs. Present Value
Show Slide #19: Future Value vs. Present Value
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
1. The value of a dollar received today will increase in the future.
2. 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
A dollar to be received in the future is worth less than a dollar received today

20. 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!
Show Slide #20: Present Value Concepts
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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!
Facilitator’s Note: (Advance slide).
The Discount Rate represents Interest or Inflation:
Assume a Rate of 10%
What is the cost expression for this relationship?
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

21. Present Value Concepts
Discount Rate represents interest or inflation
Assume a rate of 10%
What is the cost expression for this relationship?
* (1+ .10) = $1.00
$Investment = $1/(1.10)
$Investment = $.91
$ Investment Today + Interest = $1.00
-or-
$ Investment + ($ Investment * .10) = $1.00
$ Investment * (1+ .10) = $1.00
$ Investment = $1/(1.10)
$ Investment Today + Interest = $1.00
-or-
$ Investment + ($ Investment * .10) = $1.00
$ Investment * (1+ .10) = $1.00
$ Investment = $1/(1.10)
$ Investment = $.91
$ Investment Today + Interest = $1.00
-or-
$ Investment + ($Investment * .10) = $1.00
$ Investment * (1+ .10) = $1.00
$ Investment Today + Interest = $1.00
-or-
$ Investment + ($Investment * .10) = $1.00nt *
Show Slide #21: Present Value Concepts
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Q. What is the cost expression for this relationship? We want the investment we make today, plus the interest we earn on the investment to equal $1.00
$ Investment Today + Interest = $1.00
Since interest is equal to investment principal times rate, this can translate to:
$ Investment + ($Investment * .10) = $1.00
Facilitator’s Note: (Advance slide).
Once we have the equation set up, it is just a matter of doing the math. Factor out “investment” and you have:
$ Investment * (1+ .10) = $1.00
Divide both sides of the equation by 1.10, which is the same as 1+.10
$ Investment = $1/(1.10)
The division calculation yields:
$ Investment = $.91
This means that our investment Today to achieve $1 one year from Today must be $.91 (91 cents).

22. Proof Plug $.91 in to the original equation:
$.91 + ($.91 * .10) = $1.00
$ = $1.00
This relationship is fairly simple for one period, but what about multiple periods?
Show Slide #22: Proof
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
To prove the calculation, plug $.91 in to the original equation:
$.91 + ($.91 * .10) = $1.00
$ = $1.00
This relationship is fairly simple for one period, but what about multiple periods?

23. Present Value Concepts
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
$ 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 * (1 + Rate) #Years = $ Future Value
$ Investment = $ Future Value / (1 + Rate) #Years
-or-
$ Investment * (1+.10) 3 = $1.00
Show Slide #23: Present Value Concepts
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
How much must be invested today to achieve $1.00 three years from today?
What is the cost expression for this relationship? We know that:
$ Investment * (1 + Rate) #Years = $ Future Value
The exponent for “number of years” accounts for the compounding over the multiple periods. Since we want to know the Investment needed to achieve $1 in the future, we divide both sides of the equation by (1 + Rate) #Years
This yields the cost expression:
$ Investment = $ Future Value / (1 + Rate) #Years
So, the investment needed to achieve $1 is : $ 1/(1 + Rate) #Years
Facilitator’s Note: (Advance slide).
Now we plug our information into the formula. The future value is $ The interest or discount rate is 10%. The number of years is 3.
$ Investment * (1+.10) 3 = $1.00
The result of the calculation is:
$ Investment = $1.00 / (1+.10) 3
$ Investment = $.75
This means that if we invest 75 cents today at 10%, we will have one dollar at the end of three years.

24. Present Value Concepts
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
Show Slide #24: Present Value Concepts
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The Investment amount is known as the Present Value. This means that the value Today of the dollar to be received at the end of three years is $.75.
The Present Value relationship is expressed in the formula:
Future Cash Flow * 1/(1 + Rate) #Years
-or-
$1 * 1/(1.10)3 = $.75

25. Proof There is also a table shortcut for Present Value $.75 * .10
Principal
* 10% (1 year)
= Interest
New Balance
$.75
* .10
= $.075
$.83
= $.083
$.91
= $.091
$1.00
There is also a table shortcut for Present Value
Show Slide #25: Proof
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
This chart proves that 75 cents invested at 10% will grow to $1.00 at the end of three years. At the end of one year, it grows to $.83, at the end of two years, to $.91, and at the end of three years, grows to $1.00
Thankfully we don’t need to memorize the formula for Present Value. There is a table shortcut for Present value just as there is for future value.

26. The Present Value Table
Show Slide #26: The Present Value Table
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The present value table is set up in the same way as the future value table, with percentages across the top and years down the left hand side. Notice that, while the factors in the future value table are all greater than 1, because they represent growth, the factors in the present value table are all less than one. The value of $1 to be received in the future will always be less than $1.
The factor for 10% and three years is .751.
$1.00 * .751 = $.75
This corresponds to our calculation that the Present Value of $1 at 10% to be received in 3 years is $.75
The Present Value of $1 at 10% to be received in 3 years is $.75

27. Effect of Interest Rate and Time
Show Slide #27: Effect of Interest Rate and Time
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Here we see the effect of time on Present Value.
The X-Axis represents Time in Years. As Time increases, Present Value of $1 Decreases. That is, the farther out into the future that the payment is to be received, the less value it has today.
$1 to be received in 2 years at 10% …..and in 8 years at 10%
X-Axis = Time in Years
As Time increases, Present Value of $1 Decreases

28. Effect of Interest Rate and Time (Cont.)
A higher discount rate causes the present value to decrease more in the same 8 years.
Show Slide #28: Effect of Interest Rate and Time (Cont.)
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
A higher discount rate causes the present value to decrease more in the same 8 years. At 5% the $1 to be received in 8 years is worth $.68. At 10%, it is only worth $.47, and at 15% it is worth a mere $.33.
This makes sense when we consider that the discount rate is something like an inflation rate. If the inflation rate is high, the buying power of our future dollars decreases very rapidly.
X-Axis = Time in Years
As Time increases, Present Value of $1 Decreases

29. Demonstration a Problem
What is the Present Value of a $60,000 cash flow to be received 6 years from today assuming 12% discount rate?
A. Step 1: Identify the key variables
Cash flow
Discount rate
Time in years
Step 2: Build a timeline
C. Step 3: Multiply cash flow by the Factor from the PV Table.
Show Slide #29: Demonstration a Problem
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
What is the Present Value of a $60,000 cash flow to be received 6 years from today assuming 12% discount rate?
The steps are the same as for calculating future value.
Step 1: Identify the key variables, which are the same as in the Future Value calculation:
Cash flow
Discount rate
Time in years
Step 2: Build a timeline. We will represent cash outflows as negative numbers, and cash inflows as positive numbers.
Step 3: Multiply cash flow by the Factor from the PV Table.

30. Identify Key Variables
1. Cash Flow
$60,000 to be received in the Future
Is equal to some unknown amount Today
2. Discount Rate = 12%
3. Time in Years = 6
Show Slide #30: Effect of Interest Rate and Time
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
1. Cash Flow
$60,000 to be received in the Future
Is equal to some unknown amount Today
2. Discount Rate = 12%
3. Time in Years = 6

31. $60,000 to be received in 6 years
Build a Timeline $ K
$60K
$60,000 to be received in 6 years
Unknown
Present Value ?
Show Slide #31: Build a Timeline
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The represents the fact that the $60,000 to be received in the future is worth some unknown amount to us today. This amount is the Present value.
X-Axis = Time in Years

32. Multiply by the PV Factor
Show Slide #32: Multiply by the PV Factor
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Using the table, we find the factor for 12% and 6 years. The Factor of $1 at 12% discount for 6 years is
$60,000 * = $30,420
What does this mean?
The learners should be able to verbalize that this the amount that must be invested today at 12% to achieve $60,000 in six years. Or, that the value Today of $60,000 to be received in the future is $30,420. Or, that in six years, with 12% inflation, $60,000 will buy what $30,420 buys today.
The Factor of $1 at 12% discount for 6 years is 0.507
$60,000 * = $30,420

33. Using the Formula
The formula proves that the answer from the table is correct:
$60,000 * 1/( )6 = $30,398
The difference of $22 is caused by rounding in the table
Show Slide #33: Using the Formula
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The formula proves that the answer from the table is correct:
$60,000 * 1/( )6 = $30,398
The difference of $22 is caused by rounding in the table.

34. Proof
Year
Principal
* 8 %
= Interest
New Balance 1
30,420
* .12
= $3,650
$34,070 2
34,070
= $4,088
$38,159 3
38,159
= $4,579
$42,738 4
42,738
= $5,129
$47,866 5
47,866
= $5,744
$53,610 6
53,610
= $6,433
$60,044
Show Slide #34: Proof
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
We can also prove this by going through the six-year compounding process. Again, the difference is due to rounding in the table.

35. LSA #2 Check on Learning
Q1. What does Present Value represent? Q2. How does the Present Value table differ from the Future Value table?
A1. Present value represents the value Today of a dollar to be received in the future. Another way of describing it is that it is the investment required today to grow to $1.00 in the future.
Show Slide #35 LSA #2 Check on Learning
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
Q1. What does Present Value represent?
A1. Present value represents the value Today of a dollar to be received in the future. Another way of describing it is that it is the investment required today to grow to $1.00 in the future.
Q2. How does the Present Value table differ from the Future Value table?
A2. The factors in the Present Value table are all less than 1, because the value of a dollar to be received in the future is always less than one. The factors in the Future Value table are all greater than one, because the dollar will grow in the future.
A2. The factors in the Present Value table are all less than 1, because the value of a dollar to be received in the future is always less than one. The factors in the Future Value table are all greater than one, because the dollar will grow in the future.

36. LSA #2 Check on Learning (Cont.)
Q1. How does time affect the present value of a cash flow? Q2. How does the discount rate affect the present value of a cash flow?
A1. The farther into the future that the cash flow is to be receive, the less its present value.
Show Slide #36 LSA #2 Check on Learning (Cont.)
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
Q3. How does time affect the present value of a cash flow?
A3. The farther into the future that the cash flow is to be receive, the less its present value.
Q4. How does the discount rate affect the present value of a cash flow?
A4. The higher the discount rate, the less the present value of the cash flow.
** Facilitator’s Note: LSA Summary will be given at the end of this lesson.
A2. The higher the discount rate, the less the present value of the cash flow.

37. LSA # 1-2 Summary What are your questions?
In modern finance, time-value-of-money concepts play a central role in decision support and planning. In this lesson we, defined, explained, and illustrated the following terms and concepts with example calculations:
Present value (PV) is what the future cash flow is worth today.
Future value (FV) is the value, in non discounted currency units that actually flows in or out at the future time. A $100 cash inflow that will arrive two years from now could, for example, have a present value today of about $95, while its future value is by definition $100.
Show Slide #37: LSA #1-2 Summary:
Facilitator’s Note: In modern finance, time-value-of-money concepts play a central role in decision support and planning. In this lesson we, defined, explained, and illustrated the following terms and concepts with example calculations:
Present value (PV) is what the future cash flow is worth today.
Future value (FV) is the value, in non discounted currency units that actually flows in or out at the future time. A $100 cash inflow that will arrive two years from now could, for example, have a present value today of about $95, while its future value is by definition $100.
What are your questions?
What are your questions?

38. Practical Exercise Time Value of Money Worksheet
Show Slide #38: Deploy the Practical Exercise (PE): Time Value of Money Worksheet (Excel Spreadsheet)
Facilitator’s Note: Direct learners to read 7.1 and have them review the material; them ask them to complete PE Use Walk through Method of Instructions.
Facilitator’s Note: (Have learners access Excel Spreadsheet on their workstations).
The Time Value of Money implies that monetary value can change through time. Money received today can either be invested today to earn interest or can be spent today at today’s prices.
Money received in the future has not begun to earn interest and can be spent in the future at inflated prices.
Key Terminology:
Discount Rate: Represents an interest or inflation rate.
Cash Flow: Inflow or Outflow of cash.
Annuity: Consistent, periodic cash flows.
Number of Periods: Usually years. Also referred to as number of discount periods.
To get started, please continue by clicking on one of the tabs below. You will be asked to enter information into the blank white cells. Calculations are embedded in the worksheet. All other cells are locked.
Help is available by pointing to the Question Mark “?” boxes throughout the worksheet.

39. Time Value of Money Worksheet
Enter key variables in the blank white cells to generate the graph shown below
Show Slide #39: Time Value of Money Worksheet (Excel Spreadsheet)
Facilitator’s Note: (Use Walk Through Method of Instructions and facilitate discussion using the slide).
Demonstrate Time Value of Money Worksheet
Enter key variables in the blank white cells to generate the graph shown below. The key variables are the cash flows, the interest rate, and the number of years.

40. The spreadsheet tool also calculates Present Value
Time Value of Money Worksheet (Cont.)
The spreadsheet tool also calculates Present Value
Show Slide #40: Time Value of Money Worksheet (Excel Spreadsheet)
Facilitator’s Note: (Use Walk Through Method of Instructions and facilitate discussion using the slide).
Demonstrate Time Value of Money Worksheet
The spreadsheet tool also calculates Present Value.

41. TLO Check on Learning
Divide the learners into two groups, have each group as a group write down one question from this lesson, give about two minutes. Once the groups have their question written, pass it to another group to answer it. Facilitate a discussion on each question.
Show Slide #41: TLO Check on Learning
Facilitator’s Note: Divide the learners into two groups, have each group as a group write down one question from this lesson, give about two minutes. Once the groups have their question written, pass it to another group to answer it. Facilitate a discussion on each question.

42. TLO Summary
Action: Calculate Present or Future Value of a Variety of Cash Flows Scenarios
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Calculate Future Value
Calculate Present Value
Show Slide #42: TLO Summary
Facilitator’s Note: Restate the TLO
Action: Calculate Present or Future Value of a Variety of Cash Flows Scenarios
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners)
Calculate Future Value
Calculate Present Value
“Or”
Facilitator's at this time, have one learner from each group to explain the most important take away to them from this lesson. Facilitate a discussion on each answer.
Facilitator’s Note: During this lesson, we covered the following Learning Step Activities:
What are your questions?

43. Practical Exercise Show Slide #43: Deploy the Practical Exercise (PE)
Facilitator’s Note: Conduct the Run-phase Method of Instructions. This is your opportunity to demonstrate what you have learned about accounting. You will have 10 minutes to complete the practical exercise (PE). Do your best to complete the PE in the allotted time. We will conduct an review of the PE as a group.