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

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Question 1

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An investment pays you $30,000 at the end of this year, and $15,000 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 5% per year?

A) $39,614
B) $63,382
C) $79,228
D) $95,074

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Question 2

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Dan buys a property for $210,000. He is offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment Dan must make?

A) $18,653.76
B) $22,384.51
C) $26,115.26
D) $29,846.02

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Question 3

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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.)

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%?

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

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 ________.

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 6%, then the future value (FV) of this stream of cash flows is closest to ________.

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest?

Which of the following formulas is INCORRECT?

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

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

If the current rate of interest is 7%, then the future value (FV) of an investment that pays $1200 per year and lasts 18 years is closest to ________.

How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000?

You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

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%?

Which of the following is true about perpetuities?

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%?

You are saving money to buy a car. If you save $310 per month starting one month from now at an interest rate of 6%, how much will you be able to spend on the car after saving for 4 years?

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?

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 ________.