Corporate Finance 4th Edition By Berk – Test Bank

 

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Sample Questions

 

 

Corporate Finance, 4e (Berk / DeMarzo)

Chapter 4   The Time Value of Money

 

4.1   The Timeline

 

Use the figure for the question(s) below.

 

 

1) Which of the following statements regarding timelines is FALSE?

1.   A) Timelines are an important first step in organizing and then solving a financial problem.

2.   B) We refer to a series of cash flows lasting several periods as a stream of cash flows.

3.   C) Not every stream of cash flows can be represented on a timeline.

4.   D) A timeline is a linear representation of the timing of the (expected) cash flows.

Answer:  C

Diff: 1

Section:  4.1 The Timeline

Skill:  Conceptual

 

2) Which of the following statements regarding the timeline is FALSE?

1.   A) Date 1 is one year from now.

2.   B) The $5000 below date 1 is the payment you will receive at the end of the first year.

3.   C) The $5000 below date 2 is the payment you will receive at the beginning of the second year.

4.   D) Date 0 represents today.

Answer:  C

Diff: 2

Section:  4.1 The Timeline

Skill:  Definition

 

3) Which of the following statements regarding the timeline is FALSE?

1.   A) Date 1 is the end of the first year.

2.   B) Date 0 is the beginning of the first year.

3.   C) The space between date 0 and date 1 represents the time period between two specific dates.

4.   D) You will find the timeline most useful in tracking cash flows if you interpret each point on the timeline as a period or interval of time.

Answer:  D

Diff: 2

Section:  4.1 The Timeline

Skill:  Definition

 

4) Which of the following statements regarding the timeline is TRUE?

1.   A) Date 1 is the beginning of the first year.

2.   B) Date 2 is the beginning of the second year.

3.   C) Date 1 is the beginning of the second year.

4.   D) Date 0 is the end of the first year.

Answer:  C

Diff: 2

Section:  4.1 The Timeline

Skill:  Conceptual

 

Use the information for the question(s) below.

 

Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur.  In exchange for the family business, Joe has been offered an immediate payment of $100,000.  Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years.  The current market rate of interest for Joe is 6%.

 

5) Draw a timeline detailing Joe’s cash flows from the sale of the family business.

Answer:

Diff: 2

Section:  4.1 The Timeline

Skill:  Conceptual

 

6) You have been offered the following investment opportunity, if you pay $2500 today, you will receive $1000 at the end of each of the next three years.  Draw a timeline detailing this investment opportunity.

Answer:

Diff: 1

Section:  4.1 The Timeline

Skill:  Conceptual

 

Use the table for the question(s) below.

 

Year	A	B
0	-$150	-$225
1	40	175
2	80	125
3	100	-50

 

7) Draw a timeline detailing the cash flows from investment “A.”

Answer:

Diff: 1

Section:  4.1 The Timeline

Skill:  Conceptual

 

8) Draw a timeline detailing the cash flows from investment “B.”

Answer:

Diff: 1

Section:  4.1 The Timeline

Skill:  Conceptual

 

Use the information for the question(s) below.

 

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child’s college education.  Currently, college tuition, books, fees, and other costs, average $12,500 per year.  On average, tuition and other costs have historically increased at a rate of 4% per year.

 

9) Assume that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest.  Draw a timeline that details the amount of money she will need to have in the future four each of her four years of her undergraduate education.

Answer:

18	19	20	21
25,322.71	$25,322.71(1.)1	$25,322.71(1.04)2	$25,322.71(1.04)3

 

Note that the tuition for the first year is calculated as: $12,500(1.04)18 = $25,322.71

Diff: 2

Section:  4.1 The Timeline

Skill:  Conceptual

 

10) Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child’s college education.  They decide to make deposits into an educational savings account on each of their daughter’s birthdays, starting with her first birthday.  Assume that the educational savings account will return a constant 7%.  The parents deposit $2000 on their daughter’s first birthday and plan to increase the size of their deposits by 5% each year.  Draw a timeline that details the amount that would be available for the daughter’s college expenses on her 18th birthday.

Answer:

Diff: 2

Section:  4.1 The Timeline

Skill:  Analytical

 

 

4.2   The Three Rules of Time Travel

 

1) Which of the following statements is FALSE?

1.   A) The process of moving a value or cash flow forward in time is known as compounding.

2.   B) The effect of earning interest on interest is known as compound interest.

3.   C) It is only possible to compare or combine values at the same point in time.

4.   D) A dollar in the future is worth more than a dollar today.

Answer:  D

Explanation:  D) A dollar in the future is worth less than a dollar today.

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Conceptual

2) Which of the following statements is FALSE?

1.   A) Finding the present value and compounding are the same.

2.   B) A dollar today and a dollar in one year are not equivalent.

3.   C) If you want to compare or combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units or move them to the same point in time.

4.   D) The equivalent value of two cash flows at two different points in time is sometimes referred to as the time value of money.

Answer:  A

Explanation:  A) Finding the present value and discounting are the same.

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Conceptual

 

3) At an annual interest rate of 7%, the future value of $5000 in five years is closest to:

1.   A) $3565

2.   B) $6750

3.   C) $7015

4.   D) $7035

Answer:  C

Explanation:  C) FV = PV(1 + i)N = 5000(1.07)5 = 7012.76

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

4) At an annual interest rate of 7%, the present value of $5000 received in five years is closest to:

1.   A) $3565

2.   B) $6750

3.   C) $7015

4.   D) $7035

Answer:  A

Explanation:  A) PV = FV/(1 + i)N = 5000(/1.07)5 = 3564.93

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

Use the following information to answer the question(s) below.

 

Consider the following four alternatives:

1.   $132 received in two years.

2.   $160 received in five years.

3.   $200 received in eight years.

4.   $220 received in ten years.

 

5) The ranking of the four alternatives from most valuable to least valuable if the interest rate is 7% per year would be:

1.   A) 1, 2, 3, 4

2.   B) 4, 3, 2, 1

3.   C) 3, 4, 2, 1

4.   D) 3, 1, 2, 4

Answer:  D

Explanation:  D)

Alternative	Year	Amount	PV	Rank
1	2	132	115.2939	2
2	5	160	114.0778	3
3	8	200	116.4018	1
4	10	220	111.8368	4

Diff: 2

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

6) The ranking of the four alternatives from most valuable to least valuable if the interest rate is 6% per year would be:

1.   A) 1, 2, 3, 4

2.   B) 1, 3, 2, 4

3.   C) 4, 3, 1, 2

4.   D) 3, 4, 2, 1

Answer:  D

Explanation:  C)

Alternative	Year	Amount	PV	Rank
1	2	132	117.4795	4
2	5	160	119.5613	3
3	8	200	125.4825	1
4	10	220	122.8469	2

Diff: 2

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

Use the following information to answer the question(s) below.

 

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83.

 

7) The amount of money that your great aunt Matilda originally put in the account is closest to:

1.   A) $600

2.   B) $800

3.   C) $1000

4.   D) $1200

Answer:  C

Explanation:  C) PV = FV/(1 + i)N = 5033.83(/1.08)21 = 1000

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

8) The amount of money that would be in the account if you left the money there until your 65th birthday is closest to:

1.   A) $29,556

2.   B) $148,780

3.   C) $168,824

4.   D) $748,932

Answer:  B

Explanation:  B) FV = PV(1 + i)N = 5033.83(1.08)(65 – 21) = $148,779.85

Diff: 2

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

9) Which of the following statements is FALSE?

1.   A) The process of moving a value or cash flow backward in time is known as discounting.

2.   B) FV =

3.   C) The process of moving a value or cash flow forward in time is known as compounding.

4.   D) The value of a cash flow that is moved forward in time is known as its future value.

Answer:  B

Explanation:  B) FV = C(1 + r)n

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Conceptual

 

10) Consider the following time line:

If the current market rate of interest is 8%, then the present value of this timeline is closest to:

1.   A) $1000

2.   B) $857

3.   C) $860

4.   D) $926

Answer:  B

Explanation:  B) PV = FV/(1 + r)n = 1000/(1.08)2 = 857.34 or approximately $857

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

11) Consider the following timeline:

If the current market rate of interest is 10%, then the future value of this timeline is closest to:

1.   A) $666

2.   B) $500

3.   C) $605

4.   D) $650

Answer:  A

Explanation:  A) FV = PV(1 + r)n = 500(1.10)3 = 665.50 which is approximately $666

Diff: 1

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

12) Consider the following timeline:

If the current market rate of interest is 7%, then the future value of this timeline as of year 3 is closest to:

1.   A) $1720

2.   B) $1500

3.   C) $1404

4.   D) $1717

Answer:  A

Explanation:  A) FV = PV(1 + r)n

 

FV = 500(1.07)3 + 500(1.07)2 + 500(1.07)1 = $1719.97 or approximately $1720

Diff: 3

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

13) Consider the following timeline:

If the current market rate of interest is 9%, then the present value of this timeline as of year 0 is closest to:

1.   A) $492

2.   B) $637

3.   C) $600

4.   D) $400

Answer:  A

Explanation:  A) PV = FV(1 + r)n

 

100/(1.09)1 = 91.74

200/(1.09)2 = 168.34

300/(1.09)3 = 231.66

 

Sum = 491.74 which is approximately $492

Diff: 3

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

14) Consider the following timeline:

If the current market rate of interest is 8%, then the value of the cash flows as of year 1 is closest to:

1.   A) $0

2.   B) $1003

3.   C) $540

4.   D) $77

Answer:  D

Explanation:  D) Two part problem:

 

FV = PV(1 + r)n = 500(1.08)1 = $540

PV = FV/(1 + r)n = -500/(1.08)1 = -$463

 

So the answer is $540 + -$463 = $77

Diff: 2

Section:  4.2 The Three Rules of Time Travel

Skill:  Analytical

 

 

4.3   Valuing a Stream of Cash Flows

 

1) Consider the following timeline detailing a stream of cash flows:

If the current market rate of interest is 8%, then the present value of this stream of cash flows is closest to:

1.   A) $22,871

2.   B) $21,211

3.   C) $24,074

4.   D) $26,000

Answer:  B

Explanation:  B) PV = 5000/(1.07)1 + 6000/(1.07)2 + 7000/(1.07)3 + 8000/(1.07)4 = $21,210.72

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

2) Which of the following statements is FALSE?

1.   A) FV =

2.   B) PV =

3.   C) FV = Cn× (1 + r)n

4.   D) Most investment opportunities have multiple cash flows that occur at different points in time.

Answer:  A

Diff: 1

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Conceptual

 

 

3) Consider the following timeline detailing a stream of cash flows:

If the current market rate of interest is 8%, then the future value of this stream of cash flows is closest to:

1.   A) $11,699

2.   B) $10,832

3.   C) $12,635

4.   D) $10,339

Answer:  A

Explanation:  A) FV = 1000(1.08)4 + 2000(1.08)3 + 3000(1.08)2 + 4000(1.08)1 = $11,699

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

4) Consider the following timeline detailing a stream of cash flows:

If the current market rate of interest is 10%, then the present value of this stream of cash flows is closest to:

1.   A) $674

2.   B) $600

3.   C) $460

4.   D) $287

Answer:  C

Explanation:  C) PV = 100/(1.10)1 + 100/(1.10)2 + 200/(1.10)3 + 200/(1.10)4 = $460

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

 

 

5) Consider the following timeline detailing a stream of cash flows:

If the current market rate of interest is 6%, then the future value of this stream of cash flows is closest to:

1.   A) $1723

2.   B) $1500

3.   C) $1626

4.   D) $1288

Answer:  A

Explanation:  A) FV = 100(1.06)5 + 200(1.06)4 + 300(1.06)3 + 400(1.06)2 + 500(1.06)1 = $1723

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

Use the following timeline to answer the question(s) below.

 

0                      1                      2                     3        

$600               $1200           $1800

 

6) At an annual interest rate of 7%, the future value of this timeline in year 3 is closest to:

1.   A) $3295

2.   B) $3600

3.   C) $3770

4.   D) $4035

Answer:  C

Explanation:  C) FV = PV(1 + i)N = $600(1.07)2 + 1200(1.07)1 + 1800 = 3770.94

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

 

7) At an annual interest rate of 7%, the present value of this timeline in year 0 is closest to:

1.   A) $3080

2.   B) $3600

3.   C) $3770

4.   D) $4035

Answer:  A

Explanation:  A) PV = FV/(1 + i)N = $600/(1.07)1 + 1200/(1.07)2 + 1800/(1.07)3 = 3078.21

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

 

 

8) At an annual interest rate of 7%, the future value of this timeline in year 2 is closest to:

1.   A) $3080

2.   B) $3525

3.   C) $3770

4.   D) $4035

Answer:  B

Explanation:  B) FV year 2 = $600(1.07)1 + 1200 + 1800/(1.07)1 = 3524.24

Diff: 3

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

9) Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual payments at the end of the next three years of $1,000,000 each. The bank has offered to allow Taggart Transcontinental to skip making the next two payments in lieu of making one large payment at the end of the loan’s term in three years. If the interest rate on the loan is 6%, then the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to:

1.   A) $2,673,000

2.   B) $3,000,000

3.   C) $3,184,000

4.   D) $3,375,000

Answer:  C

Explanation:  C) FV = PV(1 + i)N = $1,000,000(1.06)2 + 1,000,000(1.06)1 + 1,000,000 = 3,183,600

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

 

Use the information for the question(s) below.

 

Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur.  In exchange for the family business, Joe has been offered an immediate payment of $100,000.  Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years.  The current market rate of interest for Joe is 6%.

 

10) In terms of present value, how much will Joe receive for selling the family business?

Answer:  PV = $100,000 + $50,000/(1.06)1 + $50,000/(1.06)2 + $75,000/(1.06)3 = $254,641

Diff: 2

Section:  4.3 Valuing a Stream of Cash Flows

Skill:  Analytical

 

 

4.4   Calculating the Net Present Value

 

Use the following information to answer the question(s) below.

 

Nielson Motors is considering an opportunity that requires an investment of $1,000,000 today and will provide $250,000 one year from now, $450,000 two years from now, and $650,000 three years from now.

 

1) If the appropriate interest rate is 10%, then the NPV of this opportunity is closest to:

1.   A) ($88,000)

2.   B) $88,000

3.   C) $300,000

4.   D) $1,300,000

Answer:  B

Explanation:  B) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17

Diff: 2

Section:  4.4 Calculating the Net Present Value

Skill:  Analytical

2) If the appropriate interest rate is 10%, then Nielson Motors should:

1.   A) invest in this opportunity since the NPV is positive.

2.   B) not invest in this opportunity since the NPV is positive.

3.   C) invest in this opportunity since the NPV is negative.

4.   D) not invest in this opportunity since the NPV is negative.

Answer:  A

Explanation:  A) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17

Invest since positive NPV

Diff: 2

Section:  4.4 Calculating the Net Present Value

Skill:  Analytical

 

3) If the appropriate interest rate is 15%, then Nielson Motors should:

1.   A) invest in this opportunity since the NPV is positive.

2.   B) not invest in this opportunity since the NPV is positive.

3.   C) invest in this opportunity since the NPV is negative.

4.   D) not invest in this opportunity since the NPV is negative.

Answer:  D

Explanation:  D) NPV = -1,000,000 + 250,000/(1.15)1 + 450,000/(1.15)2 + 650,000/(1.15)3 = -14,958.49

Do Not Invest since negative NPV

Diff: 2

Section:  4.4 Calculating the Net Present Value

Skill:  Analytical

 

 

4) Kampgrounds Inc. is considering purchasing a parcel of wilderness land near a popular historic site. Although this land will cost Kampgrounds $400,000 today, by renting out wilderness campsites on this land, Kampgrounds expects to make $35,000 at the end of every year indefinitely. If the appropriate discount rate is 8%, then the NPV of this new wilderness campsite is closest to:

1.   A) -$50,000

2.   B) -$37,500

3.   C) $37,500

4.   D) $50,000

Answer:  C

Explanation:  C) NPV = -400,000 + $35,000/.08 = 37,500

Diff: 1

Section:  4.4 Calculating the Net Present Value

Skill:  Analytical

5) Wyatt oil is considering drilling a new self sustaining oil well at a cost of $1,000,000. This well will produce $100,000 worth of oil during the first year, but as oil is removed from the well the amount of oil produced will decline by 2%, per year forever. If the Wyatt oil’s appropriate interest rate is 8%, then the NPV of this oil well is closest to:

1.   A) -$250,000

2.   B) $0

3.   C) $250,000

4.   D) $1,000,000

Answer:  B

Explanation:  B) NPV = -1,000,000 + $100,000/(.08 – (-.02)) = $0

Diff: 2

Section:  4.4 Calculating the Net Present Value

Skill:  Analytical

 

 

4.5   Perpetuities and Annuities

 

1) Which of the following statements regarding perpetuities is FALSE?

1.   A) To find the value of a perpetuity one cash flow at a time would take forever.

2.   B) A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever.

3.   C) PV of a perpetuity =

4.   D) One example of a perpetuity is the British government bond called a consol.

Answer:  C

Explanation:  C) PV of a perpetuity =

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Conceptual

 

2) Which of the following statements regarding annuities is FALSE?

1.   A) PV of an annuity = C ×

2.   B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.

3.   C) An annuity is a stream of N equal cash flows paid at regular intervals.

4.   D) Most car loans, mortgages, and some bonds are annuities.

Answer:  B

Explanation:  B) A perpetuity never ends.

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Conceptual

3) Which of the following statements regarding growing perpetuities is FALSE?

1.   A) We assume that r < g for a growing perpetuity.

2.   B) PV of a growing perpetuity =

3.   C) To find the value of a growing perpetuity one cash flow at a time would take forever.

4.   D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

Answer:  A

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

4) Which of the following statements regarding growing annuities is FALSE?

1.   A) A growing annuity is a stream of N growing cash flows, paid at regular intervals.

2.   B) We assume that g < r when using the growing annuity formula.

3.   C) PV of a growing annuity = C ×

4.   D) A growing annuity is like a growing perpetuity that never comes to an end.

Answer:  D

Explanation:  D) An annuity does end.

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Conceptual

 

5) Which of the following statements is FALSE?

1.   A) The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments.

2.   B) Most car loans, mortgages, and some bonds are annuities.

3.   C) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

4.   D) An annuity is a stream of N equal cash flows paid at irregular intervals.

Answer:  D

Explanation:  D) Annuities are paid at regular intervals.

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Conceptual

6) Which of the following formulas is INCORRECT?

1.   A) PV of a growing annuity = C ×

2.   B) PV of an annuity = C ×

3.   C) PV of a growing perpetuity =

4.   D) PV of a perpetuity =

Answer:  A

Explanation:  A) PV of a growing annuity = C ×

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Conceptual

 

 

Use the information for the question(s) below.

 

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child’s college education.  Currently, college tuition, books, fees, and other costs, average $12,500 per year.  On average, tuition and other costs have historically increased at a rate of 4% per year.

 

7) Assuming that costs continue to increase an average of 4% per year, tuition and other costs for one year for this student in 18 years when she enters college will be closest to:

1.   A) $12,500

2.   B) $21,500

3.   C) $320,568

4.   D) $25,323

Answer:  D

Explanation:  D) FV = PV(1 + i)N = $12,500(1.04)18 = $25,322.71

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

8) Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:

1.   A) $97,110

2.   B) $107,532

3.   C) $101,291

4.   D) $50,000

Answer:  A

Explanation:  A) This is a two step problem.

Step #1 determine the cost of the first year of college.

 

FV = PV(1 + i)N = $12,500(1.04)18 = $25,322.71

 

Step #2 figure out the value for four years of college.

 

PV of a growing annuity due = C × (1 + r)

= $25,322.71 × (1 + .07) = $97,110.01

Diff: 3

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

9) The British government has a consol bond outstanding that pays ₤100 in interest each year.  Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment one year from now, then the value of the consol bond is closest to:

1.   A) ₤1000

2.   B) ₤1100

3.   C) ₤2100

4.   D) ₤2000

Answer:  D

Explanation:  D) PVP = C/r = 100/.05 = 2000

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

10) The British government has a consol bond outstanding that pays ₤100 in interest each year.  Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment immediately upon purchasing the consol bond, then the value of the consol bond is closest to:

1.   A) ₤2000

2.   B) ₤2100

3.   C) ₤1000

4.   D) ₤1100

Answer:  B

Explanation:  B) PVP = C/r = 100/.05 = 2000 + 100 immediate interest payment = ₤2100

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

11) If the current rate of interest is 8%, then the present value of an investment that pays $1000 per year and lasts 20 years is closest to:

1.   A) $18,519

2.   B) $45,761

3.   C) $9818

4.   D) $20,000

Answer:  C

Explanation:  C) PV = C/r (1 – (1 + r)-N) = 1000/.08 (1 – (1 + 0.08)-20)

PV = $9818

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

12) If the current rate of interest is 8%, then the future value 20 years from now of an investment that pays $1000 per year and lasts 20 years is closest to:

1.   A) $45,762

2.   B) $36,725

3.   C) $9818

4.   D) $93,219

Answer:  A

Explanation:  A) FV = C/r((1 + r)N – 1) = 1000/0.08((1 + 0.08)20 – 1)

FV = $45,762

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

13) Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child’s college education.  They decide to make deposits into an educational savings account on each of their daughter’s birthdays, starting with her first birthday.  Assume that the educational savings account will return a constant 7%.  The parents deposit $2000 on their daughter’s first birthday and plan to increase the size of their deposits by 5% each year.  Assuming that the parents have already made the deposit for their daughter’s 18th birthday, then the amount available for the daughter’s college expenses on her 18th birthday is closest to:

1.   A) $42,825

2.   B) $97,331

3.   C) $67,998

4.   D) $103,063

Answer:  B

Explanation:  B) FV of a growing annuity

$2000 ×  (1.07)18 = $97,331

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

14) Since your first birthday, your grandparents have been depositing $1000 into a savings account on every one of your birthdays.  The account pays 4% interest annually.  Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to:

1.   A) $25,645

2.   B) $36,465

3.   C) $12,659

4.   D) $18,000

Answer:  A

Explanation:  A) FV = C/r((1 + r)N – 1) = 1000/0.04((1 + 0.04)18 – 1)

FV = $25,645

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

15) Consider a growing perpetuity that will pay $100 in one year.  Each year after that, you will receive a payment on the anniversary of the last payment that is 6% larger than the last payment.  This pattern of payments will continue forever.  If the interest rate is 11%, then the value of this perpetuity is closest to:

1.   A) $1667

2.   B) $588

3.   C) $2000

4.   D) $909

Answer:  C

Explanation:  C) PV growing Perpetuity = C/r – g = 100/(.11 – .06) = $2000

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

16) You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year.  As the ore closest to the surface is removed it will become more difficult to extract the ore.  Therefore, the value of the ore that you mine will decline at a rate of 8% per year forever.  If the appropriate interest rate is 6%, then the value of this mining operation is closest to:

1.   A) $71,429

2.   B) $500,000

3.   C) $166,667

4.   D) This problem cannot be solved.

Answer:  A

Explanation:  A) PVP = C/r – g = 10,000/(.06 – (-.08)) = 10,000/.14 = $71,429

Diff: 3

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

Use the information for the question(s) below.

 

Assume that you are 30 years old today, and that you are planning on retirement at age 65.  Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work.  To save for your retirement, you plan on making annual contributions to a retirement account.  Your first contribution will be made on your 31st birthday and will be 8% of this year’s salary.  Likewise, you expect to deposit 8% of your salary each year until you reach age 65.  Assume that the rate of interest is 7%.

 

17) The present value (at age 30) of your retirement savings is closest to:

1.   A) $87,000

2.   B) $108,000

3.   C) $46,600

4.   D) $75,230

Answer:  A

Explanation:  A) First deposit = .08 × $45,000 = $3600

 

$3600 ×  = $87,003

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

18) The future value at retirement (age 65) of your savings is closest to:

1.   A) $497,530

2.   B) $928,895

3.   C) $1,263,236

4.   D) $108,000

Answer:  B

Explanation:  B) First deposit = .08 × $45,000 = $3600

 

$3600 ×  (1.07)35 = $928,895 or

 

PVA (growing) = $3600 ×  = $87,003

 

FV = PV(1 + i)N = $87,003(1.07)35 = $928,895

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

19) You work for a pharmaceutical company that has developed a new drug.  The patent on the drug will last for 17 years.  You expect that the drug will produce cash flows of $10 million in its first year and that this amount will grow at a rate of 4% per year for the next 17 years.  Once the patent expires, other pharmaceutical companies will be able to produce generic equivalents of your drug and competition will drive any future profits to zero.  If the interest rate is 12% per year, then the present value of producing this drug is closest to:

1.   A) $71 million

2.   B) $90 million

3.   C) $170 million

4.   D) $105 million

Answer:  B

Explanation:  B) $10 ×  = $89.53 million

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

20) Your son is about to start kindergarten in a private school.  Currently, the tuition is $12,000 per year, payable at the start of the school year.  You expect annual tuition increases to average 6% per year over the next 13 years.  Assuming that you son remains in this private school through high school and that your current interest rate is 7%, then the present value of your son’s private school education is closest to:

1.   A) $332,300

2.   B) $137,900

3.   C) $155,800

4.   D) $156,000

Answer:  B

Explanation:  B) $12,000 ×  = $137,893

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

21) Your son is about to start kindergarten in a private school.  Currently, the tuition is $12,000 per year, payable at the start of the school year.  You expect annual tuition increases to average 6% per year over the next 13 years.  Assuming that your son remains in this private school through high school and that your current interest rate is 6%, then the present value of your son’s private school education is closest to:

1.   A) $106,230

2.   B) $156,000

3.   C) $137,900

4.   D) This problem cannot be solved.

Answer:  B

Explanation:  B) This is a bit of a trick question.  The PV of a growing annuity formula is undefined since r = g.  But since r = g, the growth in the payments is exactly offset by the current interest rate.  Therefore the answer is 12,000 × 13 = $156,000.  You could also individually discount each of the 13 payments and arrive at the same answer.

Diff: 3

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

22) If the appropriate interest rate is 8%, then present value of $500 paid at the end of each of the next 40 years is closest to:

1.   A) $23

2.   B) $5962

3.   C) $6439

4.   D) $20,0000

Answer:  B

Explanation:  B) PVA = PMT[1/i – 1/(i(1 + i)n)] = 500[1/.08 – 1/(.08(1.08)40)] = 5962.31

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

23) If the appropriate interest rate is 8%, then present value of $500 paid at the beginning of each of the next 40 years is closest to:

1.   A) $23

2.   B) $5962

3.   C) $6439

4.   D) $20,000

Answer:  C

Explanation:  C) PVAdue = PMT[1/i – 1/(i(1 + i)n)](1 + i) = 500[1/.08 – 1/(.08(1.08)40)](1.08) = 6439.29

Diff: 1

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

 

24) Dagny Taggart is a graduating college senior and she is considering the costs of going to medical school. Beginning next fall, Dagny expects medical school tuition to run $45,000 for the first year and she estimates that tuition will increase by 6% each year. If Dagny is able to invest her money in an account paying 8% interest per year, then the present value to Dagny of four years of medical school tuition is closest to:

1.   A) $149,045

2.   B) $155,930

3.   C) $162,095

4.   D) $180,000

Answer:  C

Explanation:  C) PVAgrew = PMT

= 45,000  = $162,093.03

Diff: 2

Section:  4.5 Perpetuities and Annuities

Skill:  Analytical

 

25) You are offered an investment opportunity that costs you $28,000, has an NPV of $2278, lasts for three years, has interest rate of 10%, and produces the following cash flows:

The missing cash flow from year 2 is closest to:

1.   A) $12,500

2.   B) $12,000

3.   C) $13,000

4.   D) $10,000

Answer:  B

Explanation:  B) NPV = PV benefits – PV of costs