Download presentation

Presentation is loading. Please wait.

Published byRoss Nicholes Modified over 9 years ago

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

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

3
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
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
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
6 22 Compound Interest Interest is calculated on principal plus previously accumulated interest Compounding can occur annually, semi-annually, quarterly, etc.

7
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
8 Compound Interest Periods Year 1Year 2 10% annually 5% + 5% semiannually 5% + 5% semiannually 4 periods @ 5% semi-annual interest

9
9 Example of Compound Interest Period BeginningInterest Ending Principal at 5% Balance 1 $ 3,000 $ 150 $ 3,150 2 3,150 158 3,308 3 3,308 165 3,473 4 3,473 174 3,647

10
10 Comparing Interest Methods Simple annual interest: $3,000 x.10 x 2 = $ 600 Semiannual compounding: 1 $ 150 2 158 3 165 4 174 Total $ 647

11
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
12 Future Value of Single Amount Known amount of single payment or deposit Future Value + Interest =

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

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

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

16
16 (n) 2% 4% 6% 8% 10% 11.020 1.0401.0601.0801.10 21.0401.082 1.124 1.1661.210 3 1.0611.1251.1911.260 1.331 41.0821.1701.2621.3601.464 51.1041.2171.3381.4701.611 61.1261.2651.4191.5871.772 71.1491.3161.5041.7141.949 81.1721.3691.5941.8512.144 Future Value of $1

17
17 FV = Present Value x FV Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X 1.331 = $ 13,310 Future Value of a Single Amount Example - Using Tables FV = $13,310 $10,000 PV Yr. 1Yr. 2Yr. 3

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

19
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 Discount @ 10% Yr. 1Yr. 2Yr. 3

20
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
21 PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 10%) Present Value of a Single Amount Example - Using Tables FV=$10,000 PV ?? Yr. 1Yr. 2Yr. 3

22
22 Present Value of $1 (n) 2% 4% 6% 8% 10% 1.9804.9615.9434.9259.9090 2.9612.9246.8900.8573.8265 3.9423.8890.8396.7938.7513 4.9238.8548.7921.7350.6830 5.9057.8219.7473.6806.6209

23
23 PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 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
24 Periods Future Value? +Interest Future Value of an Annuity 1 2 3 4 $0 $3,000$3,000$3,000 $3,000

25
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
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 periods @ 10%) Future Value of Annuity Example

27
27 Future Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 12% 1 1.000 1.000 1.000 1.000 1.000 1.000 22.020 2.040 2.060 2.080 2.100 2.120 3 3.060 3.122 3.184 3.246 3.310 3.374 4 4.122 4.246 4.375 4.506 4.641 4.779 55.204 5.416 5.637 5.867 6.105 6.353

28
28 FV = Payment x FV Factor = $ 3,000 x (4 periods @ 10%) = $ 3,000 x 4.641 = $ 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
29 Present Value of an Annuity Periods 12341234 Present Value ? Discount $0 $500 $500 $500 $500

30
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
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 periods @ 10%)

32
32 Present Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 10.980 0.962 0.943 0.926 0.909 21.942 1.886 1.833 1.783 1.735 3 2.884 2.775 2.673 2.577 2.487 4 3.808 3.630 3.465 3.312 3.170 54.713 4.452 4.212 3.992 3.791

33
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 periods @ 10%) = $ 4,000 x 3.170 = $ 12,680

34
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
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
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
37 53 Present Value of an Annuity Table (n) 10% 11% 12% 15% 10.909 0.901 0.893 0.870 21.736 1.713 1.690 1.626 32.487 2.444 2.402 2.283 43.170 3.102 3.037 2.855 5 3.791 3.696 3.605 3.352 PV factor of 3.605 equates to an interest rate of 12%.

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google