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

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Question 1

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

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Question 2

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

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Question 3

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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:

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $4 000 per year. If he can get a five-year loan with an interest rate of 7.5%, what is the maximum price he can pay for the car?

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?

An investment pays you $20 000 at the end of this year, and $10 000 at the end of each of the four following years. What is the present value (PV) of this investment, given that the interest rate is 4% per year?

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?

What is the internal rate of return (IRR) of an investment that requires an initial investment of $10 000 today and pays $14 000 in three years' time?

A bank offers a home buyer a 30-year mortgage at 7% per year. If the home buyer borrows $225 000 from the bank, how much must be repaid every year?

Ally wishes to leave a provision in her will that $2 000 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%?

You just took out a mortgage for $285 600. Your monthly payments are $1 279.29, you are being charged a rate of 0.29% on the outstanding balance per month, and you expect to pay everything back in 30 years. 5 years from now you will have the opportunity to renegotiate your mortgage, what will be the balance you owe at that time?

Which of the following statements regarding annuities is FALSE?

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

If the current rate of interest is 8%, then the future value (FV) of an investment that pays $1 000 per year and lasts 20 years is closest to:

A rich donor gives a hospital $100 000 one year from today. Each year after that, the hospital will receive a payment 5% 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 9%?

A homeowner in Queensland has the opportunity to install a solar water heater in her home for a cost of $3 000. 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 8.5% per year.)

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

Assuming that university costs continue to increase at an average of 4% per year and that all her university 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?

Which of the following is true about perpetuities?

You are saving money to buy a car. If you save $300 per month starting one month from now at an interest rate of 4%, how much will you be able to spend on the car after saving for 4 years?