FIN CH 4 - EXAM 1

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $40,000 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 10%. The future value (FV) at retirement (age 65) of your savings is closest to ________.

$1,445,531

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 ________.

$100,000

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

$11,699

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 ________.

$110,793

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%?

$116,667

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?

$118.00 million

You are offered an investment opportunity that costs you $28,000, has a net present value (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 ________.

$12,000

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

$1200

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.)

$145

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 9%. The parents deposit $2400 on their daughter's first birthday and plan to increase the size of their deposits by 7% 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 ________.

$160,463

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

$1723

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?

$18,653.76

If the current market rate of interest is 10%, then the present value (PV) of this stream of cash flows is closest to ________.

$20,227

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?

$250,000.00

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?

$2839; $184,565

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?

$316.25

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%?

$3189.80

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

$484

What is the present value (PV) of an investment that will pay $500 in one year's time, and $500 every year after that, when the interest rate is 10%?

$5000

Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% 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 ________.

$53,635

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%?

$5390

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?

$603.94

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $42,000 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 9%. The present value (PV) (at age 30) of your retirement savings is closest to ________.

$61,303

An investment pays you $30,000 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 5% per year?

$79,228

You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. If the bond is currently selling for $496.97, then the internal rate of return (IRR) for investing in this bond is closest to ________.

6.0%

Which of the following is true about perpetuities? (TWO)

All of the above are true statements. (TWO)

Cash flows from an annuity occur every year in the future

FALSE (EVERY YEAR)

Trial and error is the only way to compute the internal rate of return (IRR) when interest is calculated over five or more periods.

FALSE (TRIAL)

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?

Investment X has a higher growth rate than Investment Y.

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

Investment Y has a higher present value.

Which of the following statements regarding perpetuities is FALSE?

PV of a perpetuity = r/C

Which of the following is true about perpetuities?

Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate.

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

TRUE (GROWING PERP)

The internal rate of return (IRR) is the interest rate that sets the net present value (NPV) of the cash flows equal to zero.

TRUE (IRR)

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

TRUE (PV)

Which of the following statements regarding annuities is FALSE?

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

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?

The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B.

A perpetuity will pay $1000per 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%?

There is no solution to this problem

Which of the following statements regarding growing perpetuities is FALSE?

We assume that r < g for a growing perpetuity.