Calculate Present or Future Value of Cash Flows Intermediate Cost Analysis and Management Show Slide #1: Calculate Present or Future Value of Cash Flows Facilitator’s Note: Administrative Data: 1 Hr Large Group Instruction 1 Hr Practical Exercise Safety Requirement: No food or drink is allowed near or around electrical equipment (CPU, file servers, printers, projectors, etc.) due to possible electrical shock or damage to equipment.  Exercise care in personal movement in and through such areas.  Avoid all electrical cords and associated wiring.  In event of electrical storm, you will be instructed to power down equipment. Everyone is responsible for safety. A thorough risk assessment must be completed prior to every mission or operation. Risk Assessment: 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 students/personnel to walk on them. All chairs are ergonomically designed, adjust to individual preference and that all students 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. Leader actions: Detailed in-brief covering all aspects of safety to include daily classroom inspections, spills cleaned immediately, emergency exit plans, leader checks, hygiene procedures, and weekly safety briefings. Probability of Occurrence: Unlikely Severity Potential of Injury: Marginal 2.3

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: Time Value of Money Concepts Facilitator's Note: State the Motivator: Is $1 received today worth the same as $1 to be received one year from today? Why or why not? Students 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”.

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, spreadsheet tools, and awareness of Operational Environment (OE) 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 Show Slide #3: Terminal Learning Objective Facilitator’s Note: Read TLO 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, spreadsheet tools, and awareness of Operational Environment (OE) 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 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 3-34.5 Environmental Considerations and GTA 05-08-002 ENVIRONMENTAL-RELATED RISK ASSESSMENT. In a training environment, leaders must perform a risk assessment in accordance with FM 5-19, Composite Risk Management. Leaders will complete a DA Form 7566 COMPOSITE RISK MANAGEMENT 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). Note: During MOPP training, leaders must ensure personnel are monitored for potential heat injury. Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the MOPP work/rest cycles and water replacement guidelines IAW FM 3-11.4, NBC Protection, FM 3-11.5, CBRN Decontamination. Evaluation: You will be given a graded 15 question exam, which will cover this task. A passing score on the exam is 80%.

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: Time Value of Money Concepts Facilitator’s Note: Activity Step 1 Explain future value (compound interest) 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.

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: Activity Step 1 Explain future value (compound interest) 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

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 = $.11 $1.21 = $.12 $1.33 Show Slide #6: Compound Interest or Future Value Facilitator’s Note: Activity Step 1 Explain future value (compound interest) 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.

Compound Interest or Future Value (Cont.) 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 = $.11 $1.21 = $.12 $1.33 Show Slide #7: Compound Interest or Future Value (Cont.) Facilitator’s Note: Activity Step 1 Explain future value (compound interest) In year one our dollar earns $.10 in interest and grows to $1.10.

Compound Interest or Future Value (Cont.) 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 = $.11 $1.21 = $.12 $1.33 Show Slide #8: Compound Interest or Future Value (Cont.) Facilitator’s Note: Activity Step 1 Explain future value (compound interest) In year two our $1.10 earns $.11 in interest and grows to $1.21. This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+.10)3 = $1.33

Compound Interest or Future Value (Cont.) 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 = $.11 $1.21 = $.12 $1.33 Show Slide #9: Compound Interest or Future Value (Cont.) Facilitator’s Note: Activity Step 1 Explain future value (compound interest) In year three our $1.21 earns $.12 in interest and grows to $1.33. This is three cents more than we would have made with simple interest.

Compound Interest or Future Value (Cont.) 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 = $.11 $1.21 = $.12 $1.33 Show Slide #10: Compound Interest or Future Value (Cont.) Facilitator’s Note: Activity Step 1 Explain future value (compound interest) This relationship can be expressed as: Principal * (1 + Annual Interest Rate)Time in Years $1*(1+.10)3 = $1.33 The formula saves us from having to make a separate calculation for each year.

Effect of Interest Rate and Time Show Slide #11: Effect of Interest Rate and Time Facilitator’s Note: Activity Step 1 Explain future value (compound interest) The X-Axis represents Time in Years As time increases, Future Value of $1 Increases 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

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 #12: Effect of Interest Rate and Time (Cont.) Facilitator’s Note: Activity Step 1 Explain future value (compound interest) 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

The Future Value Table Show Slide #13: The Future Value Table Facilitator’s Note: Activity Step 1 Explain future value (compound interest) 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. 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. 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 2.144. If we multiply that times our principal amount of $1, we get $2.14. What would be the factor for 12%, 5 years? (1.762) 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.

LSA #1 Check on Learning Q1. How does compound interest differ from simple interest? A1. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q2. How does number of years affect the future value of an investment? A2. The more years that the investment is earning and compounding interest, the higher the future value will be. Show Slide #14: LSA #1 Check on Learning Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q1. How does compound interest differ from simple interest? A1. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q2. How does number of years affect the future value of an investment? A2. The more years that the investment is earning and compounding interest, the higher the future value will be.

LSA #1 Check on Learning (Cont.) Q3. How does compound interest differ from simple interest? A3. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q4. How does number of years affect the future value of an investment? A4. The more years that the investment is earning and compounding interest, the higher the future value will be. Show Slide #15: LSA #1 Check on Learning (Cont.) Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q3. How does compound interest differ from simple interest? A3. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q4. How does number of years affect the future value of an investment? A4. The more years that the investment is earning and compounding interest, the higher the future value will be.

LSA #1 Check on Learning (Cont.) Q5. How does compound interest differ from simple interest? A5. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q6. How does number of years affect the future value of an investment? A6. The more years that the investment is earning and compounding interest, the higher the future value will be. Show Slide #16: LSA #1 Check on Learning (Cont.) Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q5. How does compound interest differ from simple interest? A5. Compound interest means that interest is earned on both principal and interest. Compound interest will yield a higher return. Q6. How does number of years affect the future value of an investment? A6. The more years that the investment is earning and compounding interest, the higher the future value will be.

Demonstration Problem If I invest $50,000 today at 8%, what will it be worth in 10 years? Steps: Identify the key variables Cash flow Interest rate Time in years Build a timeline Multiply cash flow by FV factor from the Table Show Slide #17: Demonstration Problem Facilitator’s Note: Activity step 2: demonstration problem 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: Cash flow Interest rate And Time in years 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. Step 3: 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 Show Slide #18: Identify Key Variables Facilitator’s Note: Activity step 2: demonstration problem 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% Time in Years = 10

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 #19: Build a Timeline Facilitator’s Note: Activity step 2: demonstration problem 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

Multiply by the FV Factor Show Slide #20: Multiply by the FV Factor Facilitator’s Note: Activity step 2: demonstration problem The Factor of $1 at 8% interest for 10 years is 2.159 $50,000 * 2.159 = $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 * 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 Show Slide #21: Using the Formula Facilitator’s Note: Activity step 2: demonstration problem 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

Proof Year Principal * 8 % = Interest New Balance 1 $50,000 * .08 = $4,000 $54,000 2 = $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 #22: Proof Facilitator’s Note: Activity step 2: demonstration problem 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.

LSA #1 Check on Learning (Cont.) Q7. What is the first step in solving a future value problem? A7. The first step is to identify the variables: cash flows, number of years, interest rate. Q8. How are cash payments represented in the timeline? A8. Cash payments (or investments) are outflows of cash and are represented as negative numbers. Show Slide #23: LSA #1 Check on Learning (Cont.) Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q7. What is the first step in solving a future value problem? A7. The first step is to identify the variables: cash flows, number of years, interest rate. Q8. How are cash payments represented in the timeline? A8. Cash payments (or investments) are outflows of cash and are represented as negative numbers.

LSA #1 Check on Learning (Cont.) Q9. What is the first step in solving a future value problem? A9. The first step is to identify the variables: cash flows, number of years, interest rate Q10. How are cash payments represented in the timeline? A10. Cash payments (or investments) are outflows of cash and are represented as negative numbers. Show Slide #24: LSA #1 Check on Learning (Cont.) Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q9. What is the first step in solving a future value problem? A9. The first step is to identify the variables: cash flows, number of years, interest rate Q10. How are cash payments represented in the timeline? A10. Cash payments (or investments) are outflows of cash and are represented as negative numbers.

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? Show Slide #25: Future Value vs. Present Value Facilitator’s Note: Activity step 3: Explain 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 (Cont.) Show Slide #26: Future Value vs. Present Value (Cont.) Facilitator’s Note: Activity step 3: Explain present value Future Value vs. Present Value 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. 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

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 #27: Present Value Concepts Facilitator’s Note: Activity step 3: Explain present value 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! Assume a Rate of 10% The Discount Rate represents Interest or Inflation

Present Value Concepts (Cont.) 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 Show Slide #28: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value Discount Rate represents interest or inflation Assume a rate of 10% What is the cost expression for this relationship? (Students will have the blank slide)

Present Value Concepts (Cont.) 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 Show Slide #29: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value 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

Present Value Concepts (Cont.) 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 Show Slide #30: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value 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

Present Value Concepts (Cont.) 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 Show Slide #31: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value Divide both sides of the equation by 1.10, which is the same as 1+.10 $Investment = $1/(1.10)

Present Value Concepts (Cont.) 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 Show Slide #32: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value The division calculation yields: $Investment = $.91 This means that our investment Today to achieve $1 one year from Today must be $.91 (91 cents)

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? Show Slide #33: Proof Facilitator’s Note: Activity step 3: Explain present value To prove the calculation, 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?

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 -or- $Investment * (1+.10) 3 = $1.00 $Investment = $1.00 / (1+.10) 3 $Investment = $.75 Show Slide #34: Present Value Concepts Facilitator’s Note: Activity step 3: Explain present value 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

Present Value Concepts (Cont.) 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 Show Slide #35: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value Now we plug our information into the formula. The future value is $1.00. The interest or discount rate is 10%. The number of years is 3. $Investment * (1+.10) 3 = $1.00

Present Value Concepts (Cont.) 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 Show Slide #36: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value 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.

Present Value Concepts (Cont.) 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 #37: Present Value Concepts (Cont.) Facilitator’s Note: Activity step 3: Explain present value 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

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 Show Slide #38: Proof Facilitator’s Note: Activity step 3: Explain present value 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.

The Present Value Table Show Slide #39: The Present Value Table Facilitator’s Note: Activity step 3: Explain present value 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

Effect of Interest Rate and Time Show Slide #40: Effect of Interest Rate and Time Facilitator’s Note: Activity step 3: Explain present value 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

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 #41: Effect of Interest Rate and Time (Cont.) Facilitator’s Note: Activity step 3: Explain present value 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

LSA #1 Check on Learning (Cont.) Q11. What does Present Value represent? A11. 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 Q12. How does the Present Value table differ from the Future Value table? A12. 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. Show Slide #42: LSA #1 Check on Learning (Cont.) Facilitator’s Note: Conduct Check on Learning. Facilitate the answers given. Q11. What does Present Value represent? A11. 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 Q12. How does the Present Value table differ from the Future Value table? A12. 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.

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: Identify the key variables Cash flow Discount rate Time in years Build a timeline Multiply cash flow by the Factor from the PV Table Show Slide #43: Demonstration Problem Facilitator’s Note: Activity Step 4: Demonstration problem 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

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 Show Slide #44: Identify Key Variables Facilitator’s Note: Activity Step 4: Demonstration problem Cash Flow $60,000 to be received in the Future Is equal to some unknown amount Today Discount Rate = 12% Time in Years = 6

$60,000 to be received in 6 years Build a Timeline $K $60K $60,000 to be received in 6 years Unknown Present Value Discounted at 12% ? Show Slide #45: Build a Timeline Facilitator’s Note: Activity Step 4: Demonstration problem 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

Multiply by the PV Factor Show Slide #46: Multiply by the PV Factor Facilitator’s Note: Activity Step 4: Demonstration problem Using the table, we find the factor for 12% and 6 years. The Factor of $1 at 12% discount for 6 years is 0.507. $60,000 * 0.507 = $30,420 What does this mean? [The students 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 * 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 Show Slide #47: Using the Formula Facilitator’s Note: Activity Step 4: Demonstration problem 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. The rounding error is not significant. $22/$30420 is less than 1/10 of 1%

Proof Year Principal * 12 % = 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 #48: Proof Facilitator’s Note: Activity Step 4: Demonstration problem We can also prove this by going through the six-year compounding process. Again, the difference is due to rounding in the table. 44/60000 = less than 1/10 of 1%

Conduct Practical Exercise Show Slide #49: Conduct Practical Exercise Facilitator’s Note: Practical Exercise: Have students complete PE AJBIC102.1 and conduct a check on learning. When satisfied, have students move on AJBIC102.2. Address any questions or areas of concern until students can successfully complete the exercise.

Time Value of Money Worksheet Enter key variables in the blank white cells to generate the graph shown below Show Slide #50: Time Value of Money Worksheet Facilitator’s Note: Activity Step 5 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. © Dale R. Geiger 2011

Time Value of Money Worksheet (Cont.) The spreadsheet tool also calculates Present Value Show Slide #51: Time Value of Money Worksheet (Cont.) Facilitator’s Note: Activity Step 5 Demonstrate Time Value of Money Worksheet The spreadsheet tool also calculates Present Value © Dale R. Geiger 2011

Conduct Practical Exercise Show Slide #52: Conduct Practical Exercise Facilitator’s Note: Practical Exercise

TLO Summary 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, spreadsheet tools, and awareness of Operational Environment (OE) 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 Show Slide #53: TLO Summary Facilitator’s Note: Restate the TLO 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, spreadsheet tools, and awareness of Operational Environment (OE) 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 “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.