College of Business Administration Savannah State University

Finance 3155 Quiz 1 - Spring 200

Dr. William A. Dowling Name _________________________________

Instructions: You are to answer each of the following. Since most of these questions require calculation, make sure that you sufficiently justify your answers in the space provided. Additionally, your justification must be legible and arranged in an orderly fashion.

 

Multiple Choice

Identify the choice that best completes the statement or answers the question.

 

____ 1. An annuity due is a set of

a.

equal, annual payments made at the end of the year

b.

equal, annual payments

c.

equal, annual payments made at the beginning of the year

d.

rising annual payments

 

 

____ 2. Which of the following is the largest if the interest rate is 12 percent annually?

 

1.

$100 compounded for three years

2.

$100 annuity compounded for three years

3.

the present value of $100 received after three years

 

a.

1

b.

2

c.

3

d.

answer cannot be determined

 

 

____ 3. If interest rates rise,

a.

the future value of a dollar declines

b.

the present value of a dollar rises

c.

the present value of an annuity falls

d.

the future value of an annuity falls

 

 

____ 4. The time value of money suggests

a.

that the present is less attractive than the future

b.

individuals prefer a dollar in the present to a dollar in the future

c.

the present value of an annuity is negative

d.

annuities are worth less than lump sums

 

 

____ 5. For investors, an annuity due

a.

is to be preferred to an ordinary annuity

b.

is worth less than an equal lump sum received at the end of the time period

c.

receives payments at the end of the time period

d.

produces unequal payments

 

 

 

Problems

 

6. You borrow $100,000 to buy a house; if the annual interest rate is 6% and the term of the loan is 20 years, what is the monthly payment required to retire the mortgage loan?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. A firm has a $1,000,000 debt (e.g., a bond) outstanding that matures after 10 years. The sinking fund requires the firm to set aside annually an amount so the debt may be retired at maturity. If the firm can earn 10% compounded semi-annually on these funds, how much must it invest annually to meet the sinking fund?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. You are offered two jobs. One initially pays $25,000 annually, and your salary will grow annually at 10%. The other pays $22,000 annually, but your salary will grow at 12%. What is the difference between the two jobs after 10 years?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9. You bought a stock for $30 and after 10 years sold it for $50. It paid an annual dividend of $2. What is the return on this stock?.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. The New Jersey lotto awarded a prize of $560,000 a year for the next 20 years starting today. If the state sold $21,900,000 in lotto tickets, what proportion of the sales will the state distribute if it earns 8% annually on invested funds?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11. An apartment will generate $12,000 a year for 5 years, after which you expect to sell the property for $100,000. What is the maximum you should pay for the property if your cost of money is 10%?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12. A person has an individual retirement account and can deposit $2,000 a year. What will be the difference in the amount in the account if this investor earns 8% instead of 6%?

 

 

 

 

 

 

 

 

 

 

 

13. The Big-Sox currently have 30,000 spectators per game and anticipate annual growth in attendance of 9%. If the Big Stadium holds 65,000 people, how long will it take for the team to reach capacity?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14. If a company paid a dividend of $1 in 2006 and the dividend grows annually by 7 percent, what will be the dividend in 2011?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15. If a new college graduate wants a car costing $15,000, how much must be saved annually if the funds earn 5 percent if the student wishes to purchase the car in four years?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16. An annuity offers $1,000 for 10 years. If you can earn 12 percent annually on your funds, what is the maximum amount you should pay for this annuity?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

17. An employee and employer each contribute $3,000 annually for 20 years to a retirement account that earns 9 percent a year, how much will the employee be able to withdraw from the account for 25 years?


Finance 3155 - Evening Section - Quiz 1 - Chapter 7 - TVM

Answer Section

 

MULTIPLE CHOICE

 

1. ANS: C PTS: 1

 

2. ANS: B PTS: 1

 

3. ANS: C PTS: 1

 

4. ANS: B PTS: 1

 

5. ANS: A PTS: 1

 

PROBLEM

 

6. ANS:

X = $100,000/139.58 = $716.43

 

139.58 is the interest factor for the present value of an annuity at 6% monthly compounding for twenty years. (PV = 100000; N = 240; I = .5; PMT = ?, and FV = 0. PMT = -716.43)

 

PTS: 1

 

7. ANS:

EAR = (1 + .05)2 - 1 = .1025 = 10.25%

 

X(16.1297) = $1,000,000

X = $1,000,000/15.937 = $61,997.30

 

16.1297 is the interest factor for the future value of $1 at 10% semi-annually for 10 years. (PV = 0; N = 10; I = 10; PMT = ?, and FV = 1000000. PMT = -61997.30)

 

PTS: 1

 

8. ANS:

$25,000(1 + .1)10 = $25,000(2.594) = $64,850

 

(PV = -25000; N = 10; I = 10; PMT = 0, and FV = ?. FV = 64843.)

 

$22,000(1 + .12)10 = $22,000(3.106) = $68,332

 

(PV = -22000; N = 12; I = 10; PMT = 0, and FV = ?. FV = 68328.)

 

68328 - 64850 = 3478

 

PTS: 1

 

9. ANS:

What interest rate forces the equality: $30 = $2(PVIFA ?I, 10N) + $50(PVIF ?I, 10N)?

 

(PV = -30; N = 10; I = ?; PMT = 2, and FV = 50. I = 10.71.)

 

PTS: 1

 

10. ANS:

This problem illustrates the present value of an annuity due. The present value of the promised payments is $560,000(9.818)(1.08) = $5,937,930.

 

9.818 is the interest factor for the present value of the ordinary annuity at 8% for 20 years, and the 1.08 converts the interest factor into the interest factor for an annuity due.

 

The state will distribute 27.1 percent of the ticket sales:

$5,937,930/$21,900,000 = 27.1%.

 

PTS: 1

 

11. ANS:

This is another valuation problem set as a real estate investment. The maximum price you should pay is the present value of the estimated cash flow and sale price:

$12,000(3.791) + $100,000(0.621) = $107,592.

 

The annual cash flows are insufficient to justify buying the property. (PV = ?; N = 5; I = 10; PMT = 12000, and FV = 100,000. PV = -107582.)

 

PTS: 1

 

12. ANS:

At 6%: $2,000(36.785) = $73,570

 

36.785 is the interest factor for the future value of an annuity of $1 at 6% for twenty years. (PV = 0; N = 20; I = 6; PMT = -2000, and FV = ? FV = 73572.)

 

At 8%: $2,000(45.762) = $91,524

 

45.762 is the interest factor for the future value of an annuity of $1 at 8% for twenty years. (PV = 0; N = 20; I = 8; PMT = -2000, and FV = ? FV = 91524.)

 

The additional interest is $91,524 $73,570 = $17,954.

 

PTS: 1

 

13. ANS:

30,000(1 + .09)t = 65,000

(1 + .09)t = 65,000/30,000 = 2.167

t is 9 years.

 

Look up 2.167 in the future value of $1 table at 9% and determine that n is approximately 9 years. (PV = -30000; N = ?; I = 9; PMT = 0, and FV = 65000. N = 8.97.)

 

PTS: 1

 

14. ANS:

This is another example of future value:

 

$100(1 + .07)5 = X

 

The interest factor for the future value of a dollar at 7 percent for 5 years is 1.403. Hence

$100(1.403) = $1.40

 

(PV = -100; N = 5; I = 7; PMT = 0; FV = ?; FV = 1.4026.)

 

PTS: 1

 

15. ANS:

This is an example of the future value of an annuity. The question is, what amount (X) times the interest factor for the future sum of an ordinary annuity of $1.00 for 4 years at 5 percent (interest factor = 4.310) equals $10,000?

X(4.310) = $15,000

X = $15,000/4.310 = $3,480

 

The graduate will have to save $3,480 annually to have accumulated the $15,000. (PV = 0; N = 4; I = 5; FV = 15000; PMT = ?; PMT = 3480.18.)

 

PTS: 1

 

16. ANS:

This problem is similar to #21 but is applied to an individual's investment. The present value of the annuity is

PVA = $1,000(5.650) = $5,650.

 

5.650 is the interest factor for the present value of an ordinary annuity at 12 percent for 10 years. The investor should pay no more than $5,650 for this investment. (PMT = 1000; N = 10; FV = 0; I = 12; PV = ? PV = -5650.22.)

 

PTS: 1

 

17. ANS:

This problem illustrates the basics of pension plans. The amount accumulated:

 

$3,000(51.160) = $153,480

 

(PV = 0; I = 9; PMT = -3000; N = 20; FV = ?; FV = 153480)

 

The annual withdrawals:

$153,480/IFPVA = 153,480/9.823 = $15624.55

 

Investing only $3,000 a year for 20 years, permits the individual to withdraw over $15,600 a year for 25 years. (PV = -153480; I = 9; N = 25; FV = 0; PMT = ?; PMT = 31250.52

 

PTS: 1