1 Chapter 11 Time Value of Money Adapted from Financial Accounting 4e by Porter and Norton

2 18 Time Value of Money  Prefer payment now vs. in future due to interest factor  Applicable to both personal and business decisions

3 Simple Interest I = P x R x T Principal amount Dollar amount of interest per year Time in years Interest rate as a percentage

4 20 Example of Simple Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years Calculate interest on the note.

5 21 Example of Simple Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years Calculate interest on the note. Px R x T $ 3,000 x.10 x 2 = $ 600

6 22 Compound Interest Interest is calculated on principal plus previously accumulated interest Compounding can occur annually, semi-annually, quarterly, etc.

7 Example of Compound Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years semiannual compounding of interest Calculate interest on note.

8 Compound Interest Periods Year 1Year 2 10% annually 5% + 5% semiannually 5% + 5% semiannually 4 5% semi-annual interest

9 Example of Compound Interest Period BeginningInterest Ending Principal at 5% Balance 1 $ 3,000 $ 150 $ 3, , , , , , ,647

10 Comparing Interest Methods Simple annual interest: $3,000 x.10 x 2 = $ 600 Semiannual compounding: 1 $ Total $ 647

11 Compound Interest Computations Present value of an annuity Future value of an annuity Present value of a single amount Future value of a single amount

12 Future Value of Single Amount Known amount of single payment or deposit Future Value + Interest =

13 Future Value of a Single Amount Example If you invest $10,000 10% compound interest, what will it be worth 3 years from now? invest $10,000 Future Value? + 10% per year Yr. 1Yr. 2Yr. 3

14 Future Value of a Single Amount Example - Using Formulas n FV = p (1 + i) 3 = $10,000 (1.10) = $13,310

15 FV = Present Value x FV Factor = $ 10,000 X (3 10%) Future Value of a Single Amount Example - Using Tables FV?? $10,000 PV Yr. 1Yr. 2Yr. 3

16 (n) 2% 4% 6% 8% 10% Future Value of $1

17 FV = Present Value x FV Factor = $ 10,000 X (3 10%) = $ 10,000 X = $ 13,310 Future Value of a Single Amount Example - Using Tables FV = $13,310 $10,000 PV Yr. 1Yr. 2Yr. 3

18 34 Present Value of Single Amount Discount Known amount of single payment in future Present Value

19 Present Value of a Single Amount Example If you will receive $10,000 in three years, what is it worth today (assuming you could invest at 10% compound interest)? Present Value? $ 10,000 10% Yr. 1Yr. 2Yr. 3

20 Present Value of a Single Amount Example - Using Formulas -n PV = payment x (1 + i) -3 = $10,000 x (1.10) = $7,513

21 PV = Future Value x PV Factor = $ 10,000 X (3 10%) Present Value of a Single Amount Example - Using Tables FV=$10,000 PV ?? Yr. 1Yr. 2Yr. 3

22 Present Value of $1 (n) 2% 4% 6% 8% 10%

23 PV = Future Value x PV Factor = $ 10,000 X (3 10%) = $ 10,000 X.7513 = $ 7,513 Present Value of a Single Amount Example - Using Tables FV=$10,000 PV = $7,513 Yr. 1Yr. 2Yr. 3

24 Periods Future Value? +Interest Future Value of an Annuity $0 $3,000$3,000$3,000 $3,000

25 If we invest $3,000 each year for four years at 10% compound interest, what will it be worth 4 years from now? Future Value of Annuity Example $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV ??

26 $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV ?? FV = Payment x FV Factor = $ 3,000 x (4 10%) Future Value of Annuity Example

27 Future Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 12%

28 FV = Payment x FV Factor = $ 3,000 x (4 10%) = $ 3,000 x = $ 13,923 $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV = $13,923 Future Value of Annuity Example

29 Present Value of an Annuity Periods Present Value ? Discount $0 $500 $500 $500 $500

30 Present Value of an Annuity Example What is the value today of receiving $4,000 at the end of the next 4 years, assuming you can invest at 10% compound annual interest? PV ?? Yr. 1Yr. 2 Yr. 3 Yr. 4 $0 $4,000 $4,000 $4,000 $4,000

31 Present Value of an Annuity Example Yr. 1Yr. 2 Yr. 3 Yr. 4 PV ?? $0 $4,000 $4,000 $4,000 $4,000 PV = Payment x PV Factor = $ 500 x (4 10%)

32 Present Value of Annuity of $1 (n) 2% 4% 6% 8% 10%

33 Present Value of an Annuity Example Yr. 1Yr. 2 Yr. 3 Yr. 4 P.V. = $12,680 $0 $4,000$4,000 $4,000 $4,000 PV = Payment x PV Factor = $ 4,000 x (4 10%) = $ 4,000 x = $ 12,680

34 Solving for Unknowns Assume that you have just purchased a new car for $14,420. Your bank has offered you a 5-year loan, with annual payments of $4,000 due at the end of each year. What is the interest rate being charged on the loan?

35 Solving for Unknowns Yr. 1Yr. 2 Yr. 3 Yr. 4 Yr. 5 discount discount discount discount discount PV = $14,420 PV = Payment x PV factor PV factor = PV / Payment rearrange equation to solve for unknown

36 Solving for Unknowns Yr. 1Yr. 2 Yr. 3 Yr. 4 Yr. 5 discount discount discount discount discount PV = $14,420 PV factor = PV / Payment = $14,420 / $4,000 = 3.605

37 53 Present Value of an Annuity Table (n) 10% 11% 12% 15% PV factor of equates to an interest rate of 12%.