Chapter IVTutorial

Time Value of Money

Important Abbreviations

• N (number of periods)

• I/Y (interest per year)

• PV (present value)

• PMT (payment)

• FV (future value)

Overview Present/Future Value

• FV = PV * (1+i)ⁿ

• PV = FV * 1/(1+i) ⁿ

• PV = $100

• n = 2, i = 0.05

• FV = 100 * 1.05 * 1.05 = 110.25

• Page 201 has some key definitions, formulas, and equations

Problem 4-5

You have $1,500 to invest at 7% compounded annually

• How much you will have accumulated over

a) 3 years b) 6 years c) 9 years

• Calculate amount of interest earned in first 3 years, years 3-6 and years 6-9

• Moodle OR Appendix A in Book for Financial Table

Problem 4-5 Solution

Problem 4-7

• Time value

• You can deposit $10,000 into an account paying 9% annual today or in 10 years from today

• How much better will you be at the end of 40 years if you decide to make the deposit today rather than 10 years from today?

Problem 4-7 Solution

A. Investing today

• FV = PV * (1 + 0.09)^40

• FV = $10,000 * (31.409)

• FV = $314,090

A. Investing in 10 years

• FV = PV * (1 + 0.09)^30

• FV = $10,000 * (13.268)

• FV = $132,680

• You would be better off by $181,410 ($314,090 -

$132,680)

Problem 4-9

• Single payment loan repayment

• A person borrows $200 with annual interest 14%

• What will be due if the loan is repaid after:

• a) 1 year

• b) 4 years

• c) 8 years

Problem 4-9 solution

• a) FV = $200 * (1.14)^1 = $228

• b) FV = $200 * (1.14)^4 = $200 * (1.689) = $337.80

• c) FV = $200 * (1.14)^8 = $200 * (2.853) = $570.60

*Problem 4-15

• Time value and discount rates

• You won a lottery that pays $1,000,000 in 10 years

• What is the least you would be willing to sell it for if you can earn return:

• a) 6% b) 9% c) 12%

• What if the payment will be received in 15 years?

• Discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum

Problem 4-18

• Calculate the future value of the annuity

• assuming that it is

• a) An ordinary annuity

• b) An annuity due

• Compare your findings. Given all things equal which type of annuity is preferable? Why?

Problem 4-18 (cont.)Case Amount of

AnnuityInterest

RateDeposit Period (years)

A $2,500 8% 10

B $500 12% 6

C $30,000 20% 5

Problem 4-22

• Value of a retirement annuity

• For a single payment today you can obtain

• $12,000 at the end of each year for the next 25 years

• You can currently earn 9% on comparable investment

• What is the most you would pay for this annuity?

Problem 4-22 Solution

• Present value of annuity

Exercise 4-3

• Gabrielle won $2.5 million

• Receive $1.3 million now

• Get paid $100,000 at the end of each of the next 25 years

• Gabrielle can earn 5% annually on her investment

• Which option should she take?

Exercise 4-3 Solution

• PVA = $1,300,000

• Compare with present value annuity of 25x $100,000 with 5% discount

• PVIFA = 14.094

• PVB = 100,000 * 14.094 = $1,409,400

• PVB > PVA

• Gabrielle should take the $100,000 yearly payments

Questions?