Time Value of Money

1. Time Value of Money Unit 2: Economic Principles in Agribusiness Lesson: EP6

2. Objectives Lesson Objective: • After 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 Objectives: • Define time value of money. • Define and calculate the future value of a dollar. • Define and calculate the future value of a dollar per period. • Define and calculate sinking fund factors. • Define and calculate the present value of a dollar. • Define and calculate the present value of a dollar per period. • Define and calculate amortization. • Correlate the connection between time value of money and inflation.

3. Key Terms • Time value of money • Present value • Future value • Interest • Compounding • Discounting • Ordinary Annuity • Annuity Due

4. http://www.youtube.com/watch?v=rT4UH3I4CEw Time value of money

5. What is Time Value of Money? • 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 • Interest is the cost of borrowing money or the income earned by investing money.

6. Six Functions of the Dollar • Future valueof a $1 • Future value of a $1 per period • Sinking fund factor • Present value of a $1 • Present value of a $1 per period • Amortization

7. 1. 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 to calculate interest for the next period • FV = future value • PV = present value • i = interest • n = number of compounding periods per year • t = number of years

8. Calculating Future Value of a Dollar • An investor deposits $100 into a bank savings account • Initial investment or present value (PV) • Bank pays 5%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 1because it is annual and the time (t) is 2years • Investment’s future value is $110.25 • ($105 x $1.05 = $110.25)

9. Rule of 72 • Used to determine how long it takes for money to double at any giveninterestrate • 72 = number of years for sum to doublecompounding rate • $10,000 invested at 6% interest • 72/6 = 12 • 12 years to double to $20,000

10. 2. 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 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

11. 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 • 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 • Another $100 is deposited • Brings total to $315.25 for the three years

12. 3. 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 • A desired or target amount is accumulated at the end of the investment term

13. 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 years • i = 5%, or .05 interest • n = 12 (monthly) • t = 4 years • Pmt = $ ? Monthly deposit required

14. 4. 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

15. Calculating Present Value of the Dollar • A promissory note for $1000 is due in two years • A typical return on deposits is currently 4% annually • PV = 1000 x = $924.56

16. 5. 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

17. Calculating Present Value of an Annuity • 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? • PMT = $ 10,000 per period • i = 7%, or .07 interest • n = 1 (annual) • t = 20 years • PV = ? Present Value

18. 6. 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

19. Calculating Amortization • 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 years • PMT = $ ? Monthly payment

20. Conclusion • The 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.

21. Exit Card • What did you learn today about time value of money? • What questions do you still have about time value of moneyor calculating the six functions of a dollar?