Question 1

A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV).

Accepted Answer

A) True 
 B)False  True

Question 2

Can we apply the growing perpetuity equation for negative growth as well?

Accepted Answer

Yes, it is perfectly in order to apply the growth perpetuity for negative growth. A negative growth gives two negatives in the denominator making it larger than a positive growth thus reducing the valuation compared to a positive growth of similar magnitude.

Question 3

Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be $42,000 one year from now and you also 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 9%. The present value (PV) (at age 30) of your retirement savings is closest to ________.

Accepted Answer

A)  $61,303 
B)  $30,652 
C)  $42,912 
D)  $67,433 
A)  $61,303 
B)  $30,652 
C)  $42,912 
D)  $67,433 A

Question 4

The present value (PV) of a stream of cash flows is just the sum of the present values of each individual cash flow.

Accepted Answer

A) True 
 B)False

Question 5

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.
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 what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education?

Accepted Answer

This is a two-step problem.
Step 1: Dete

Question 6

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?

Accepted Answer

A)  $16,598 
B)  $19,918 
C)  $23,237 
D)  $26,557 
A)  $16,598 
B)  $19,918 
C)  $23,237 
D)  $26,557

Question 7

Ally wishes to leave a provision in her will that $7000 will be paid annually in perpetuity to a local charity. How much must she provide in her will for this perpetuity if the interest rate is 6%?

Accepted Answer

A)  $58,334 
B)  $93,334 
C)  $116,667 
D)  $70,000 
A)  $58,334 
B)  $93,334 
C)  $116,667 
D)  $70,000

Question 8

A lottery winner will receive $6 million at the end of each of the next twelve years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 8.6% per year?

Accepted Answer

A)  $94.40 million 
B)  $118.00 million 
C)  $165.20 million 
D)  $188.80 million 
A)  $94.40 million 
B)  $118.00 million 
C)  $165.20 million 
D)  $188.80 million

Question 9

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

Accepted Answer

A)  $242 
B)  $581 
C)  $484 
D)  $774 
A)  $242 
B)  $581 
C)  $484 
D)  $774

Question 10

Which of the following is true about perpetuities?

Accepted Answer

A)  All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher. 
B)  All else equal, the present value of a perpetuity is higher when the interest rate is lower. 
C)  If two perpetuities have the same present value and the same interest rate, they must have the same cash flows. 
D)  All of the above are true statements. 
A)  All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher. 
B)  All else equal, the present value of a perpetuity is higher when the interest rate is lower. 
C)  If two perpetuities have the same present value and the same interest rate, they must have the same cash flows. 
D)  All of the above are true statements.

Question 11

You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months) at   (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.

Accepted Answer

A)  $2554 
B)  $4470 
C)  $3193 
D)  $5109 
A)  $2554 
B)  $4470 
C)  $3193 
D)  $5109

Question 12

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 5% per year.)

Accepted Answer

A)  $145 
B)  $160 
C)  $175 
D)  $190 
A)  $145 
B)  $160 
C)  $175 
D)  $190

Question 13

Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be $40,000 one year from now and you also 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 10%. The future value (FV) at retirement (age 65) of your savings is closest to ________.

Accepted Answer

A)  $722,766 
B)  $1,445,531 
C)  $1,011,872 
D)  $1,590,084 
A)  $722,766 
B)  $1,445,531 
C)  $1,011,872 
D)  $1,590,084

Question 14

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent?

Accepted Answer

A)  $14,630 
B)  $18,287 
C)  $25,602 
D)  $29,259 
A)  $14,630 
B)  $18,287 
C)  $25,602 
D)  $29,259

Question 15

Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity?

Accepted Answer

A)  $125,000.00 
B)  $200,000.00 
C)  $300,000.00 
D)  $250,000.00 
A)  $125,000.00 
B)  $200,000.00 
C)  $300,000.00 
D)  $250,000.00

Question 16

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

Accepted Answer

Every cash flow contains two pieces of i

Question 17

A business promises to pay the investor of $6000 today for a payment of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time. What is the present value of this business opportunity if the interest rate is 6% per year?

Accepted Answer

A)  $603.94 
B)  $301.97 
C)  $724.73 
D)  $966.30 
A)  $603.94 
B)  $301.97 
C)  $724.73 
D)  $966.30

Question 18

An annuity pays $10 per year for 98 years. What is the present value (PV) of this annuity given that the discount rate is 7%?

Accepted Answer

A)  $85.60 
B)  $171.20 
C)  $142.67 
D)  $199.74 
A)  $85.60 
B)  $171.20 
C)  $142.67 
D)  $199.74

Question 19

A bank offers a home buyer a 20-year loan at 8% per year. If the home buyer borrows $130,000 from the bank, how much must be repaid every year?

Accepted Answer

A)  $15,888.95 
B)  $18,537.11 
C)  $21,185.26 
D)  $13,240.79 
A)  $15,888.95 
B)  $18,537.11 
C)  $21,185.26 
D)  $13,240.79

Question 20

Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments?

Accepted Answer

A)  Investment X has a higher present value. 
B)  Investment Y has a higher present value. 
C)  Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both. 
D)  No comparison can be made-we need to know the interest rate to calculate the present value. 
A)  Investment X has a higher present value. 
B)  Investment Y has a higher present value. 
C)  Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both. 
D)  No comparison can be made-we need to know the interest rate to calculate the present value.

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

A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV).

Can we apply the growing perpetuity equation for negative growth as well?

The present value (PV) of a stream of cash flows is just the sum of the present values of each individual cash flow.

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?

Ally wishes to leave a provision in her will that $7000 will be paid annually in perpetuity to a local charity. How much must she provide in her will for this perpetuity if the interest rate is 6%?

A lottery winner will receive $6 million at the end of each of the next twelve years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 8.6% per year?

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

Which of the following is true about perpetuities?

You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months) at (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.

Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity?

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

A business promises to pay the investor of $6000 today for a payment of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time. What is the present value of this business opportunity if the interest rate is 6% per year?

An annuity pays $10 per year for 98 years. What is the present value (PV) of this annuity given that the discount rate is 7%?

A bank offers a home buyer a 20-year loan at 8% per year. If the home buyer borrows $130,000 from the bank, how much must be repaid every year?

Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments?

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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