missouriffa.org time value of money/e… · web viewabs.04.01.02.a. identify financial concepts...

EP6

Agriculture Management, Economics, & SalesTime Value of Money

Unit: Economic Principles in Agribusiness

Lesson Title: Time Value of Money

Standards ABS.01.01.01.a. Recognize principles of capitalism as related to AFNR businesses.ABS.04.01.03.a. Explain the importance of return on investment for an agribusiness enterprise.ABS.04.01.02.a. Identify financial concepts associated with production and profit.CS.02.04.01.c. Demonstrate critical and creative thinking skills while completing a task.CS.03.01.01.a. Use basic technical and business writing skills.CS.09.01.01.a. Calculate the effect of compound interest on AFNR investments.

Missouri Personal Finance MM.5. Summarize how inflation affects spending and savings decisions.Missouri Personal Finance SI.3. Examine reasons for saving and investing.Missouri Personal Finance SI.6. Analyze factors affecting the rate of return on investments (Rule of 72, simple interest, compound interest).

CCSS.Math.Content.HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.CCSS.Math.Content.HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.CCSS.Math.Content.HSA-SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.CCSS.ELA-Literacy.SL.11-12.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used.CCSS.ELA-Literacy.W.11-12.2 Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

Student Learning Objectives

Slide 2 in EP6 Time Value of Money Lesson ObjectiveAfter completing the lesson on time value of money, students will demonstrate their ability to apply the concept in real-world situations by obtaining a minimum score of 80% on a Time Value of Money Blog.

Enabling ObjectivesAs a result of this lesson, the student will…

1. Define time value of money.2. Define and calculate the future value of a dollar.3. Define and calculate the future value of a dollar per period.4. Define and calculate sinking fund factors.5. Define and calculate the present value of a dollar.6. Define and calculate the present value of a dollar per period.7. Define and calculate amortization.8. Correlate the connection between time value of money and inflation

Time: Approximately 200 minutes

List of ResourcesBacon K., Boren N., Kirkwood V., Birkenholz R., Plain R., Rohrbach N. (1988).

Agriculture Management and Economics Instructor Guide. Columbia, MO: Instructional Materials Laboratory.

Bacon K., Boren N., Kirkwood V., Birkenholz R., Plain R., Rohrbach N. (1988). Agriculture Management and Economics Student Reference Guide. Columbia, MO: Instructional Materials Laboratory.

Hondros Learning. (2006). Statistics, modeling & finance. Westerville, OH: Retrieved from: www.HONDROSLEARNING.COM.

Sterling, M.J. (2008). Business Math for Dummies. Hoboken, NJ: Wiley Publishing, Inc.

Sepand jazzi. (2012). Time Value of Money. Retrieved from http://www.youtube.com/watch?v=rT4UH3I4CEw.

Mulligan, K. (2012). Time Value of Money, Inflation, and Opportunity Costs. Retrieved from http://www.moolanomy.com/5842/time-value-of-money-inflation-and-opportunity-cost-kmulligan/.

Ko, E. (n.d.). The Wealth Accumulator. Retrieved from http://wealth.enochko.com/2008/04/inflation-compounding-and-time-value-of.html.

Economic Principles in Agriculture EP6 Time Value of Money

https://bluprd0711.outlook.com/owa/redir.aspx?C=pZloX8CEWkOUfHJYZofhYXFGBUYbNNAIH_N8ORNEQ2_HJxyK1IpXyPl8rs4XTuoajESJ8FCpL8U.&URL=http%3A%2F%2Fwww.HONDROSLEARNING.COM

Bankman. (n.d.). High Yield Savings Accounts. Retrieved from http://highyieldsavingsaccounts.net/time-value-of-money/.

List of Tools, Equipment, and SuppliesEP6 PowerPoint PresentationEP6 Activity Sheet and Evaluation PacketNote card or small sheet of paper for review activityNote to teachers for problem solving – using scientific calculatorsTime Value Tools Excel Document

Key TermsSlide 3 in EP6 Time Value of Money

The following terms are presented in this lesson (shown in bold italics):Time value of moneyPresent valueFuture valueInterest CompoundingDiscounting Ordinary AnnuityAnnuity Due


Interest Approach: Use an interest approach that will prepare the students for the lesson. Teachers often develop approaches for their unique class and student situations. A possible approach is included here.

Slide 4 in EP6 Time Value of MoneyWhat is this thing – Time Value of Money? Ask students upon first impression of seeing “Time Value of Money” what they think it means, entails, describes, etc.

Then pose a question to students, “If you won 1 million dollars in the lottery and had two choices – to take the money today or wait a year to take the money – which would you choose?

Facilitate a discussion on students’ thoughts and ideas, asking “why” questions. Then show this video: http://www.youtube.com/watch?v=rT4UH3I4CEw


http://www.youtube.com/watch?v=rT4UH3I4CEw

Summary of Content and Teaching StrategiesObjective 1: Define time value of money.

Teaching Strategies Related Content1. Based upon our discussion and the

video we just watched, let’s define time value of money.

Slide 5 in EP6 Time Value of Money

2. Introduce six functions of the dollar.


What is time value of money? The idea that a dollar today is worth

more than a dollar a year from now No matter how much money is

invested, there is an opportunity cost involved – biggest opportunity cost is interest – the cost of borrowing money or the income earned by investing money

Six functions of the dollar1. Future value of a $12. Future value of a $1 per period3. Sinking fund factor4. Present value of a $15. Present value of a $1 per period6. Amortization

Present value What something is worth today $50 savings bond that matures 12 years

in the future may be purchased today for $25 – a lower price for the bond is paid because it will be earning interest, which is added to its initial cost to raise its value to $50 at maturity

Objective 2: Define and calculate the future value of a dollar. Teaching Strategies Related Content

1. Facilitate a discussion on how students would define the future value of a dollar.


Future value of a dollar What the value of $1 invested today

will be if the money is allowed to grow over a period of time

All monies earned (interest) must be reinvested

Compounding – Process of calculating future value; Interest earned during one period is added to principal in order


in EP6 Time Value of Money

2. Practice calculating future value of a dollar on EP6.1.


3. Practice calculating future value of a dollar on EP6.1.

to calculate interest for the next period

FV =PV x ¿

Calculating future value of the dollar An investor deposits $100 into a bank

savings account – initial investment or present value (PV); bank pays 5% annual interest – interest rate (i) – after one year, the investment will have a future value (FV) of $105 ($100 x $1.05 = $105); the compounding period (n) is one because it is annual and the time (t) is two years – investment’s future value is $110.25 ($105 x $1.05 = $110.25)

Rule of 72 Used to determine how long it takes for

money to double at any given interest rate

72/compounding rate = number of years it takes for the sum of money to double

$10,000 invested at 6% interest – 72/6 = 12 – takes 12 years to double to $20,000

Objective 3: Define and calculate the future value of a dollar per period.

Teaching Strategies Related Content1. The second function of the dollar is

future value of a dollar per period.


Future value of a dollar per period What the value of $1 invested on a

periodic basis (weekly, monthly, yearly, etc.) will grow to if investment is allowed to grow over time

All interest must be reinvested or compounded

Also known as an annuity – Annuity


in EP6 Time Value of Money

2. Practice calculating future value of an annuity on EP6.1.

Due – Payment or deposits made at beginning of period; Ordinary Annuity – Payments made at end of each period

Similar to future value of the dollar except – rather than placing a single payment into an account at the beginning of the term, payments are deposited on a regular basis at the end of each turn; ordinary annuity

Lease payments received on an asset with the cash flow residual deposited at end of each year

Calculating future value of an annuity After paying all expenses on a facility,

an investor will have $100 at the end of each year to deposit into a savings account – represents periodic payment (PMT)

Bank pays 5% interest – interest rate (i)

After the first year, the investment will have a value of $100 since the money was deposited in the account at the end of the first year

At the end of year two, the total amount grows to $205 – the first $100 deposit has now earned $5 plus the additional $100 deposited at the end of the second year

Amount will grow at 5% for the next year and equal $215.25 at the end of that time – at which another $100 is deposited – brings total to $315.25 for the three years

Objective 4: Define and calculate sinking fund factors. Teaching Strategies Related Content

1. The third function of a dollar is sinking fund factors


Sinking Fund Factors Show amount of regular payments that

must be invested over a period of time At a specified interest rate With reinvestment of all monies earned


2. Practice calculating sinking fund factors on EP6.1.


So a desired or target amount is accumulated at the end of the investment term

Calculating sinking fund factors Joyce would like to buy a car following

her college graduation after 4 more years of school. She estimates the car will cost $10,000 when she graduates. If her savings account pays a 5% annual rate of interest, compounded monthly, how much does she need to deposit monthly to have $10,000 when she graduates in 4 years?

FV = $ 10,000 Future Value 4 yearsi = 5%, or .05 interestn = 12 (monthly)t = 4 yearsPmt = $ ? Monthly deposit required

Objective 5: Define and calculate the present value of a dollar.

Teaching Strategies Related Content1. Facilitate a discussion on students’

ideas on the definition of the present value of a dollar.


2. Practice calculating the present value of a dollar on EP6.1.


Present value of a dollar How much must be invested today for

the investment to grow to $1 at the end of a specified time period

All monies earned must be reinvested Value of something in the future is

known; what it is worth today must be determined

Discounting – process of calculating present value of something that will be received in the future; opposite of compounding

PV =FV x 1(1+i)nt

Calculating present value of a dollar A promissory note for $1000 is due in

two years. A typical return on deposits is currently 4% annually


PV = 1000 x 1

(1+.04)1∗2

$924.56

Objective 6: Define and calculate the present value of a dollar per period. Teaching Strategies Related Content

1. The next function of the dollar is the present value of a dollar per period. This is also known as present value of an annuity.


2. Practice calculating the present value of an annuity on EP6.1.


Present value of a dollar per period How much money, in a single payment,

must be invested today and compounded into the future to equal a series of periodic payments in the future

The value of a stream of payments to be received each year for several years

Also known as an annuity

Calculating present value of an annuity

PV = PMT❑

[(1+ in )

nt

−1](1+ i

n )nt

∗( in )

Jill’s parents will receive $10,000 per year in annual installments from an annuity for the next 20 years. If the fund provides a minimum annual return of 7% on the investments, what is the present value of the annuity based on the minimum return?

Solve for Present Value: PMT = $ 10,000 per period i = 7%, or .07 interest n = 1 (annual) t = 20 years PV = ? Present Value

.

Objective 7: Define and calculate amortization.

Teaching Strategies Related Content


1. The final function of a dollar is amortization. Does anyone know what amortization is?


2. Practice calculating amortization on EP6.1.


Amortization A decrease in a loan balance through

equal periodic payments Principal and interest paid with each

payment With equal payments, there is a larger

amount of interest cost and smaller amount being applied to principal during the early stages of the loan – as number of payments increase, amount of interest decreases, and amount going towards principal increases

Interest is only paid on actual amount still owed

Based on fixed-rate, term loans Does not apply for variable-rate term or

variable term loans

Calculating amortization

PMT=PV ( i

n )1−(1+ i

n )−nt

Jennifer plans to buy her first car and will need to borrow $5000. If she can get a 5 year, equal amortized monthly payment loan with a 6% fixed interest rate, what will her monthly payments be?

P = $ 5,000 loan (Principal)i = 6%, or .06 (interest)n = 12 (monthly)t = 5 yearsPMT = $ ? Monthly payment

Objective 8: Correlate the connection between time value of money and inflation.

Teaching Strategies Related Content1. Recall the definition of time value of

money – money today is worth more than money tomorrow.


2. Give students sample scenarios that involve them deciding if they will take a certain amount of money today or more money one, two, or three years from now. During discussion bring in factors like investment returns, interest rates, etc.

3. Have students identify how they would label the option they did not choose (recall from EP4) – opportunity costs.

4. Inflation must also be considered when talking about time value of money. Let’s see how these relate:

5. Have students read two of the following articles:

http://www.moolanomy.com/ 5842/time-value-of-money-inflation-and-opportunity-cost-kmulligan/

http://wealth.enochko.com/ 2008/04/inflation-compounding-and-time-value-of.html

http:// highyieldsavingsaccounts.net/time-value-of-money/

(More articles may be available for students at CNN Money, Yahoo Money, MSN Money, etc.)

6. While reading, students should note 10 bits of advice they pulled from the articles. Using this advice, create an 8 ½ x11” poster representing the relationship between time value of money and inflation.

7. Present these to the class when finished and hang final products on a bulletin board to make a collage of time value of money/inflation information.

Review/Summary


http://highyieldsavingsaccounts.net/time-value-of-money/



http://wealth.enochko.com/2008/04/inflation-compounding-and-time-value-of.html



http://www.moolanomy.com/5842/time-value-of-money-inflation-and-opportunity-cost-kmulligan/



in EP6 Time Value of MoneyThe time value of money is affected by time. Investments involving short time periods (less than one year) can be compared without using the concept of time value of money. Comparison between two investments should use present values. An investment must be feasible as well as profitable.

Review: Practice math calculations using EP6.3, EP6.4, EP6.5, EP6.6, EP6.7, and EP6.8. Complete some as a class, some with partners, and some individually. EP6.2 is a cheat sheet for teachers/students with six functions of the dollar formulas.

Exit cards: Students will answer the following questions on a note card or small slip of paper and hand to teacher as they exit:

What did you learn today about time value of money? What questions do you still have about time value of money or calculating the six

functions of a dollar?

Application

Extended Activities

Use the FarmDoc Fast Tools time value of money calculator to calculate the time value of money of the sample problems used throughout the lesson. In addition, explore the various other time value of money calculators available online.

Invite a local businessperson from an investment firm to talk to the class about investments and his/her relationship to time value of money. He/she could also preview retirement planning, risk management, etc. This could serve as a preview to topics covered in the agribusiness planning and analysis and agribusiness management units.

Examine student record books and have them identify areas where money is currently invested, but could be invested in other places. Have each student consider if he/she has money in a savings account, how much interest it is making, if it would be more profitable in the long run to invest the money into their Supervised Agricultural Experience Program or another investment entity. Share conclusions and thoughts with the teacher during the next SAE visit.

EvaluationTime Value of Money Blog Evaluation EP6.9

Alternate - Paper-pencil Quiz Evaluation EP6.10

Answers to Evaluation


Evaluation EP6.9Answers will vary. Use scoring guide on EP6.9 to assess student work.

Alternate Evaluation EP6.10See EP6.10 KEY.


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