Chapter 5: Time Value Of Money Concepts

Question 1

The value that an amount today will grow to in the future is referrer to as the:
A) future value of a single amount.
B) present value of a single amount.
C) present value of an annuity.
D) future value of an annuity.

Answer 1

A

Question 2

Present and future values of $1 at 3% are presented below:

FV$1 PV$1 FV$1 PVA$1 FVAD$1 PVAD$1

Bill wants to give Maria a $510,000 gift in 5 years. If money is worth 6% compounded semiannually, what is Maria’s gift worth today?

***n=10, i= 3% —> 0.74409

Answer 2

$510,000 x PV$1= $379,486

*PV$1 is 0.74409

Question 3

How much will $7,500 invested at the end of each year grow to in two years, assuming an interest rate of 9% compounded annually?
Note: Use tables, Excel, or a financial calculator. Round your final answer to the nearest whole dollar. (FV of $1, PV of $1, FVA of $1, and PVA of $1).

n=2, i= 9% —> 2.0900

Answer 3

FVA= $7,500 x FVA of $1= $15,675

• FVA of $1 is 2.0900

Question 4

Present and future values of $1 at 3% are presented below:

FV$1 PV$1 FVA$1 PVA$1 FVAD$1 PVAD$1

A firm leases equipment under a long-term finance lease (analogous to an installment purchase) that calls for 12 semiannual payments of 47,641.12. The first payment is due at the inception of the lease. The annual rate on the lease is 6%. What is the value of the leased asset at inception of the lease?

n= 12, i=3% —> 10.25262

Answer 4

PVAD= $47,64.12 x PVAD$1= $488,446

** PVAD$1 is 10.25262

Question 5

Garland Incorporated offers a new employee a single-sum signing bonus at the date of employment, June 1, 2024. Alternatively, the employee can receive $54,000 at the date of employment plus $25,000 each June 1 for four years, beginning in 2027. Assuming the employee’s time value of money is 9% annually, what single amount at the employment date would make the options equally desirable?
Note: Use tables, Excel, or a financial calculator. Round your final answer to the nearest whole dollar. (FV of $1, PV of $1, FVA of $1,PVA of $1, FVAD of $1 and PVAD of $1)

3.53129 & 0.77218

Answer 5

The single-sum equivalent would be $54,000 + the PV of a $25,000 deferred annuity. The PV of the deferred annuity on June 1, 2027, is an annuity due with
n=4 and i= 9%. That is,
($25,000 × 3.53129 from PVAD of $1 table) = $88,282.

To compute the equivalent of that amount at employment date, we take the PV of $88,282 where n=3 and i=9% from PV of $1 table, which is
$88,282 × 0.77218 = $68,170.

Therefore, the single-sum equivalent would be
$54,000 + $68,170 = $122,170.

Question 6

The Strug Company purchased office furniture and equipment for $8,600 and agreed to pay for the purchase by making five annual installment payments beginning one year from today. The installment payments include interest at 8%. What is the required annual installment payment?
Note: Use tables, Excel, or a financial calculator. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1)

3.99271

Answer 6

$8,600 ÷ 3.99271 (Present value of an ordinary annuity of $1 at 8% for 5 years) = $2,154

Question 7

Marquis Company acquired equipment. Marquis paid $160,000 in cash immediately and signed a $640,000 noninterest-bearing note for the remaining balance, which is due in one year. An interest rate of 5% reflects the time value of money for this type of loan agreement. For how much should Marquis value the note payable of $640,000?
Note: Use tables, Excel, or a financial calculator. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1)

0.95238

Answer 7

$609,523 = $640,000 note × 0.95238

*PV of $1 (n = 1, i = 5%) -> 0.95238

Question 8

Danielle wants to know how much to invest today at 5% interest in order to accumulate a sum of $45,000 in four years. Which time value concept would be used to compute this amount?

A) Present value of $1
B) Future value of $1
C) Present value of an ordinary annuity of $1
D) Future value of an annuity due of $1

Answer 8

A

$45,000 × (PV of $1: n = 4, i = 5%) = Amount to Invest

Question 9

How does simple interest differ from compound interest?

A) Simple interest includes interest earned on the initial investment only.
B) Simple interest is for a longer time interval.
C) Simple interest is for a shorter time interval.
D) Simple interest includes interest earned on the initial investment plus interest earned on previous interest.

Answer 9

A

$45,000 × (PV of $1: n = 4, / = 5%) = Amount to Invest

Question 10

An executive borrows $50,000 from the company today and promises to repay $57,881 three years from now. What is the interest rate implied in the agreement?
Note: FV of $1, PV of $1,
FVA of $1, PVA of $1, FVAD of $1 and PVAD of $.

A) 3%
B) 6%
C) 5%
D) 4%

0.86384

Answer 10

C

The interest rate is the rate that will provide a present value of $50,000 when determining the present value of the $57,881 to be received in three years:

$50,000 (present value) = $57,881 × PV factor*

• Present value of $1: n = 3, i = ?

Rearranging algebraically, we find that the present value factor is 0.86384.
When you consult the present value table, PV of $1, you search row three
(n = 3) for this value and find it in the 5% column. So the interest rate is 5%.

Question 11

Loan A has the same original principal, interest rate, and payment amount as Loan B. However, Loan A is structured as an annuity due, while Loan B is structured as an ordinary annuity. The present value of Loan A will be:

A) higher than Loan B.
B) Indeterminate with respect to Loan B.
C) lower than Loan B.
D) the same as Loan B.

Answer 11

A

Since payments from an annuity due are received sooner, its value is higher than if the payments are received later.

Question 12

Mattison is trying to decide how much an investment of $10,000 today will grow to be in the future. Which of the following will she not need to help calculate that amount?

A) Number of compounding periods
B) Present value factor
C) Interest rate
C) Future value factor

Answer 12

B

Question 13

A series of equal periodic payments in which the first payment is made on the beginning date of the contract is:

A) an ordinary annuity.
B) an annuity due.
C) a deferred annuity.
D) a delayed annuity.

Answer 13

B

In an ordinary annuity, cash flows occur at the end of each period. In an annuity due, cash flows occur at the beginning of each period.

Question 14

Present and future values of $1 at 3% are presented below:
FV $1, PV $1, FVA $1, PVA $1, FVAD $1, PVAD $1

Suppose you would like to have $130,000 5-years from now. How much must you invest today in an account that earns 6% compounded semiannually?

0.74409

Answer 14

$96,732

PV = $130,000 × 0.74409* = $96,732
*PV of $1: n =10; i = 3%

Question 15

An investor purchases a 8-year, $1,000 par value bond that pays semiannual interest of $16. If the semiannual market rate of interest is 8%, what is the current market value of the bond?
Note: FV of $1, PV of $1, FVA of $1,
PVA of $1, FVAD of $1 and PVAD of $1)

8.8514, 0.2919

Answer 15

$434

$16 x 8.8514*= $142
$1k x 0.2919**= $292

$145+$292= 434

• PVA of $1: n=16 and i= 8%
  ** PV of $1: n=16 and i= 8%

Question 16

CC: Jacob Lee invested $600 in a savings account paying 8% interest compounded twice a year. What will be his investment balance at the end of the year? Round to the nearest dollar.

A) $680
B) $649
C) $624
D) $600

Answer 16

B

Initial deposit balance: $600
After 6 mo.: 4% x $600= 24; $624 balance
End of year: 4% x $624= $25; $649 balance

*8% annual rate is 4% semi-annual rate

Question 17

CC: Oliver Kim invests $5,000 in an investment account earning 8% interest compounding annually. How much will he have in his account in four years? Round to the nearest dollar.

A) $5,412
B) $6,242
C) $5,937
D) $6,802

1.36049

Answer 17

D

FV= PV x FV Factor
FV= $5,000 x 1.36049
FV= $6,802

Question 18

CC: The Versa Tile Company purchased a delivery truck on February 1, 2024. The agreement required Versa Tile to pay the purchase price of $44,000 on February 1, 2025. Assuming an 8% rate of interest, to calculate the price of the truck Versa Tile would multiply $44,000 by the:

a. Future value of an ordinary annuity of $1
b. Present value of $1
c. Present value of an ordinary annuity of $1
d. Future value of $1

Answer 18

B

The calculation is for the present value today of the $44,000 to be paid one year from now.

Question 19

CC: Turp and Tyne Distillery is considering investing in a two-year project. The company’s required rate of return is 10%. The project is expected to create cash flows, net of taxes, of $240,000 in the first year, and $300,000 in the second year. The distillery should invest in the project if the project’s cost is less than or equal to:

a. $540,000
b. $490,860
c. $465,960
d. $446,040

0.909, 0.826

Answer 19

C

PV = FV x PV $1 factor
$218,160 ($240,000 × 0.909)
+ 247,800 ($300,000 × 0.826)
=$465,960

Question 20

CC: The Stinch Fertilizer Corporation wants to accumulate $8,000,000 for plant expansion. The funds are needed on January 1, 2029. Stinch intends to make five equal annual deposits in a fund that will earn interest at 7% compounded annually. The first deposit is to be made on January 1, 2024.
What is the amount of the required annual deposit?

а. $1,300,813
b. $1,391,304
c. $1,951,220
d. $1,704,000

n=5 i= 7%—> 6.15

Answer 20

A

FV = ANN × FV Ann Due Factor $8,000,000 = ANN × 6.15
ANN = 8,000,0000/6.15 = $1,300,813

Question 21

CC: I. R. Wright plans to make quarterly deposits of $200 for five years into a savings account. The first deposit will be made immediately. The savings account pays interest at an annual rate of 8%, compounded quarterly. How much will Wright have accumulated in the savings account at the end of the five-year period? Round to the nearest dollar.

a. $2,672
b. $4,000
c. $4,957
d. $5,237

24.7833

Answer 21

C

FV= ANN x FV Ann Due Factor
= $200 × 24.7833* = $4,957

*Future value of an annuity due for 20 periods at 2%

Question 22

CC: U. B. Wong plans to make quarterly deposits of $200 for five years into a savings account. The deposits will be made at the end of each quarter. The savings account pays interest at an annual rate of 8%, compounded quarterly. How much will Wong have accumulated in the savings account at the end of the five-year period? Round to the nearest dollar.

a. $2,672
b. $4,000
c. $5,237
d. $4,859

24.2974

Answer 22

D

FV = ANN x FV Ordinary Ann Factor
= $200 × 24.2974*= $4,859

*Future value of an ordinary annuity for 20 periods at 2%

Question 23

CC: Justin Investor wants to calculate how much money he needs to deposit today into a savings account that earns 4% in order to be able to withdraw $6,000 at the end of each of the next 5 years. He should use which time value concept?

A) Present value of $1 for 5 periods.
B) Future value of an annuity due of $1 for 5 periods.
C) Present value of an ordinary annuity of $1 for 5 periods.
D) Future value of $1 for 5 periods.

Answer 23

C

The calculation is how much needs to be deposited today, the present value, so that equal amounts can be withdrawn over the next six years at the end of the year (ordinary annuity).

Question 24

CC: The Knotworth Gedding Consulting Company purchased a machine for $15,000 down and $500 a month payable at the end of each of the next 36 months. How would the company calculate the cash price of the machine, assuming the annual interest rate is known?

a. $15,000 plus the present value of $18,000 ($500 × 36)
b. $15,000 plus the present value of an annuity due of $500 for 36 periods
c. $33,000
d. $15,000 plus the present value of an ordinary annuity of $500 for 36 periods

Answer 24

D

The cash price is equal to the present value of the future cash outflows. This includes the $15,000 today plus the value today (present value) of the $500 payments made at the end of each month (ordinary annuity).

Question 25

CC: What would you pay for an investment that pays you $10,000 at the end of each year for the next ten years and then returns a maturity value of $50,000 after ten years? Assume that the relevant interest rate for this type of investment is 6%.

7.36009 and 0.55839

Answer 25

$10,000 (annuity amount) x 7.36009
= PVA $73,600.9
$50,000 (lump-sum) x 0.55839
= PV $27,919.5
Price you pay: PVA + PV= $101,520.4