Question 1

Which of the following is true about perpetuities?

Accepted Answer

A)  Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate. 
B)  Since a perpetuity generates cash flows every period infinitely, initial cash outflow must be discounted to calculate the present value. 
C)  Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow using the present value and the interest rate. 
D)  Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV. 
A)  Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate. 
B)  Since a perpetuity generates cash flows every period infinitely, initial cash outflow must be discounted to calculate the present value. 
C)  Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow using the present value and the interest rate. 
D)  Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV.

Question 2

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 7% per year forever. If the appropriate interest rate is 3%, then the value of this mining operation is closest to ________.

Accepted Answer

A)  $100,000 
B)  $500,000 
C)  $250,000 
D)  This problem cannot be solved. 
A)  $100,000 
B)  $500,000 
C)  $250,000 
D)  This problem cannot be solved.

Question 3

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 $12,000 per year. On average, tuition and other costs have historically increased at a rate of 5% per year. Assuming that college costs continue to increase an average of 5% per year and that all her college savings are invested in an account paying 8% 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 ________.

Accepted Answer

A)  $110,793 
B)  $55,397 
C)  $77,555 
D)  $132,952 
A)  $110,793 
B)  $55,397 
C)  $77,555 
D)  $132,952

Question 4

An annuity pays $47 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 8%?

Accepted Answer

A)  $1563.88 
B)  $3127.76 
C)  $3649.06 
D)  $2606.47 
A)  $1563.88 
B)  $3127.76 
C)  $3649.06 
D)  $2606.47

Question 5

Define the following terms:
(a) perpetuity
(b) annuity
(c) growing perpetuity
(d) growing annuity

Accepted Answer

(a) A perpetuity is a stream of equal ca

Question 6

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?

Accepted Answer

A)  -$3189.80 
B)  -$5907.57 
C)  5907.57 
D)  $3189.80 
A)  -$3189.80 
B)  -$5907.57 
C)  5907.57 
D)  $3189.80

Question 7

You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. Investment A has a discount rate of 4%, and Investment B has a discount rate of 5%. Which of the following is true?

Accepted Answer

A)  The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B. 
B)  The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. 
C)  The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. 
D)  No comparison can be made-we need to know the cash flows to calculate the present value. 
A)  The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B. 
B)  The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. 
C)  The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. 
D)  No comparison can be made-we need to know the cash flows to calculate the present value.

Question 8

Consider the following timeline detailing a stream of cash flows:   If the current market rate of interest is 8%, then the future value (FV) of this stream of cash flows is closest to ________.

Accepted Answer

A)  $11,699 
B)  $5850 
C)  $14,039 
D)  $18,718 
A)  $11,699 
B)  $5850 
C)  $14,039 
D)  $18,718

Question 9

An annuity pays $13 per year for 53 years. What is the future value (FV) of this annuity at the end of that 53 years given that the discount rate is 9%?

Accepted Answer

A)  $8258.91 
B)  $16,517.82 
C)  $19,270.79 
D)  $13,764.85 
A)  $8258.91 
B)  $16,517.82 
C)  $19,270.79 
D)  $13,764.85

Question 10

A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year?

Accepted Answer

A)  $600 
B)  $960 
C)  $1200 
D)  $720 
A)  $600 
B)  $960 
C)  $1200 
D)  $720

Question 11

If $8000 is invested in a certain business at the start of the year, the investor will receive $2400 at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 6% per year?

Accepted Answer

A)  $158.13 
B)  $316.25 
C)  $379.50 
D)  $506.00 
A)  $158.13 
B)  $316.25 
C)  $379.50 
D)  $506.00

Question 12

Which of the following statements regarding annuities is FALSE?

Accepted Answer

A)  PV of an annuity = C ×  
  
B)  The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. 
C)  An annuity is a stream of N equal cash flows paid at regular intervals. 
D)  Most car loans, mortgages, and some bonds are annuities. 
A)  PV of an annuity = C ×  
  
B)  The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. 
C)  An annuity is a stream of N equal cash flows paid at regular intervals. 
D)  Most car loans, mortgages, and some bonds are annuities.

Question 13

A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. Which of the following is closest to the interest rate being offered by the dealer?

Accepted Answer

A)  5.8% 
B)  6.8% 
C)  7.8% 
D)  9.8% 
A)  5.8% 
B)  6.8% 
C)  7.8% 
D)  9.8%

Question 14

A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%?

Accepted Answer

A)  $2695 
B)  $4312 
C)  $5390 
D)  $3234 
A)  $2695 
B)  $4312 
C)  $5390 
D)  $3234

Question 15

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%.
In terms of present value (PV), how much will Joe receive for selling the family business?

Accepted Answer

PV = $100,000 + $50,

Question 16

A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased. What is the future value (FV) of this perpetuity, given that the interest rate is 3%?

Accepted Answer

A)  $1456 
B)  $19,867 
C)  $21,320 
D)  There is no solution to this problem. 
A)  $1456 
B)  $19,867 
C)  $21,320 
D)  There is no solution to this problem.

Question 17

A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 11%?

Accepted Answer

A)  $3,840,628.87 
B)  $5,376,880.42 
C)  $6,913,131.97 
D)  $7,681,257.74 
A)  $3,840,628.87 
B)  $5,376,880.42 
C)  $6,913,131.97 
D)  $7,681,257.74

Question 18

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true?

Accepted Answer

A)  Investment X has a higher growth rate than Investment Y. 
B)  Investment X has a lower growth rate than Investment Y. 
C)  The answer cannot be determined without knowing the interest rate for both investments. 
D)  With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value. 
A)  Investment X has a higher growth rate than Investment Y. 
B)  Investment X has a lower growth rate than Investment Y. 
C)  The answer cannot be determined without knowing the interest rate for both investments. 
D)  With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value.

Question 19

How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged?

Accepted Answer

The denominator in the formula for growt

Question 20

Which of the following statements regarding growing perpetuities is FALSE?

Accepted Answer

A)  We assume that r < g for a growing perpetuity. 
B)  PV of a growing perpetuity =   
C)  To find the value of a growing perpetuity one cash flow at a time would take forever. 
D)  A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever. 
A)  We assume that r < g for a growing perpetuity. 
B)  PV of a growing perpetuity =   
C)  To find the value of a growing perpetuity one cash flow at a time would take forever. 
D)  A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.

Exam 4: Time Value of Money: Valuing Cash Flow Streams

Which of the following is true about perpetuities?

An annuity pays $47 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 8%?

Define the following terms: (a) perpetuity (b) annuity (c) growing perpetuity (d) growing annuity

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?

You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. Investment A has a discount rate of 4%, and Investment B has a discount rate of 5%. Which of the following is true?

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%, then the future value (FV) of this stream of cash flows is closest to ________.

An annuity pays $13 per year for 53 years. What is the future value (FV) of this annuity at the end of that 53 years given that the discount rate is 9%?

A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year?

If $8000 is invested in a certain business at the start of the year, the investor will receive $2400 at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 6% per year?

Which of the following statements regarding annuities is FALSE?

A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. Which of the following is closest to the interest rate being offered by the dealer?

A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%?

A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased. What is the future value (FV) of this perpetuity, given that the interest rate is 3%?

A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 11%?

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true?

How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged?

Which of the following statements regarding growing perpetuities is FALSE?

Corporate Finance and the Financial Manager

Introduction to Financial Statement Analysis

Time Value of Money: an Introduction

Interest Rates

Bonds

Stock Valuation

Investment Decision Rules

Fundamentals of Capital Budgeting

Stock Valuation: a Second Look

Risk and Return in Capital Markets

Systematic Risk and the Equity Risk Premium

The Cost of Capital

Raising Equity Capital

Debt Financing

Capital Structure

Payout Policy

Financial Modeling and Pro Forma Analysis

Working Capital Management

Short-Term Financial Planning

Option Applications and Corporate Finance

Mergers and Acquisitions

International Corporate Finance

Leasing

Insurance and Risk Management

Corporate Governance

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