Chapter (4) Time value of Money

What Is the Time Value of Money?

The purchasing power of a particular amount of money differs from the purchasing power of that
same amount in the future.
What is the difference between future value and present value?

Present Value Future Value

Describes how much a future sum of money what a sum of money invested today will become
is worth today. over time, at a rate of interest
Define and differentiate among the three basic patterns of cash flow →
(1) a single amount, (2) an annuity, and (3) a mixed stream.

Single amount Annuity Mixed stream

A lump sum amount either held A level periodic stream of cash A stream of unequal periodic
currently or expected at some flow (equal dollar amount). cash flows that reflect no
future date. particular pattern.
What is the difference between Discounting and Compounding ?

Discounting Compounding
Method is to compute the present value of future money. Method is used to know the future value of present money

How to Calculate Present Value and Future Value ?

Type Present Value Future Value

Single amount

Ordinary
(deferred)
→ Money paid
at the End.
Annuity

Due →
Money paid at
the beginning.

You have to Prepare the following schedule You have to Prepare the following schedule

Mixed stream

Important Note Annuity due is always greater than ordinary annuity.

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 Questions Part

True or False
1) Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the
timing of cash flows does not have any significant economic consequences.
Answer: FALSE

2) Time-value of money is based on the belief that a dollar that will be received at some future date is worth more
than a dollar today.
Answer: FALSE

3) Future value is the value of a future amount at the present time, found by applying compound interest over a
specified period of time.
Answer: FALSE

4) For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer
the period of time, the greater the future value.
Answer: TRUE

5) The greater the interest rate and the longer the period of time, the higher the present value.
Answer: FALSE

6) Everything else being equal, the higher the interest rate, the higher the future value.
Answer: TRUE

7) Future value increases with increases in the interest rate or the period of time funds are left on deposit.
Answer: TRUE

8) Everything else being equal, the higher the discount rate, the higher the present value.
Answer: FALSE

9) Everything else being equal, the longer the period of time, the lower the present value.
Answer: TRUE

10) An annuity due is an amount that occurs at the beginning of each period.
Answer: TRUE

11) An ordinary annuity is an annuity in which cash flows occurs at the beginning of each period.
Answer: FALSE

12) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary
annuity for interest rates greater than zero.
Answer: TRUE

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 MCQs
1) When the amount earned on a deposit has become part of the principal at the end of a specified time period
the concept is called
A) discount interest.
B) compound interest.
C) primary interest.
D) future value.
Answer: B
2) The future value of $100 received today and deposited at 6 percent for four years is
A) $126.
B) $ 79.
C) $124.
D) $116.
Answer: A
3) The future value of $200 received today and deposited at 8 percent for three years is
A) $248.
B) $252.
C) $158.
D) $200.
Answer: B
4) The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is
A) $236.
B) $699.
C) $ 42.
D) $ 75.
Answer: C
5) The amount of money that would have to be invested today at a given interest rate over a specified period in
order to equal a future amount is called
A) future value.
B) present value.
C) future value of an annuity.
D) present value of an annuity.
Answer: B
6) The present value of $200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is
A) $ 50.
B) $200.
C) $518.
D) $ 77.
Answer: D
7) The future value of a dollar ________ as the interest rate increases and ________ the farther in the future an
initial deposit is to be received.
A) decreases; decreases
B) decreases; increases
C) increases; increases
D) increases; decreases
Answer: C
8) The annual rate of return is variously referred to as the
A) discount rate.
B) opportunity cost.
C) cost of capital.
D) all of the above.
Answer: D

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10) Indicate which of the following is true about annuities.
A) An ordinary annuity is an equal payment paid or received at the beginning of each period.
B) An annuity due is a payment or received at the beginning of each period that increases by an equal amount each period.
C) An annuity due is an equal payment paid or received at the beginning of each period.
D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount
each period.
Answer: C
12) An annuity with an infinite life is called a(n)
A) perpetuity.
B) prima.
C) indefinite.
D) deep discount.
Answer: A
15) Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the
end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have
at the end of the twentieth year?
A) $19,292
B) $14,938
C) $40,000
D) $144,104
Answer: D
17) In comparing an ordinary annuity and an annuity due, which of the following is true?
A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity.
B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due.
C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since
one less payment is received with an annuity due.
D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due.
Answer: A
18) The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next
10 years is
A) $28,974.
B) $31,292.
C) $14,494.
D) $13,420.
Answer: B
20) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is
A) $11,808.
B) $11,464.
C) $ 8,530.
D) $10,000.
Answer: B
22) The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4
percent, is
A) $288.
B) $1,896.
C) $1,750.
D) $1,558.
Answer: D
23) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost
of 11 percent, is
A) $ 1,020.
B) $27,869.
C) $18,800.
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D) $12,093.
Answer: D
24) Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is
the present value of her royalty income if the opportunity cost is 12 percent?
A) $120,000
B) $ 67,800
C) $ 38,640
D) None of the above.
Answer: B
25) To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight
years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th
year?
A) $16,000
B) $17,920
C) $24,600
D) $27,552
Answer: D
26) James plans to fund his individual retirement account, beginning today, with 20 annual deposits of $2,000,
which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his
deposits, the amount in the account upon retirement will be
A) $19,636.
B) $91,524.
C) $98,846.
D) $21,207.
Answer: C
30) Find the future value at the end of year 3 of the following stream of cash flows received at the end of each
year, assuming the firm can earn 17 percent on its investments.

A) $20,724
B) $20,127
C) $23,550
D) $23,350
Answer: B
35) Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 25
percent.

A) $27,168
B) $35,200
C) $34,000
D) $32,500
Answer: A