FInance Ch 4

4) 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

$116,667 (7000/.06)

3) 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 (10,000/(.09-.05))

9) 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 childʹs 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

(a) perpetuity

A perpetuity is a stream of equal cash flows that occur at regular intervals and lasts forever.

12) 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 ________.

A) $100,000 (10,000/(.1))

1) 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.)

A) $145 (2900x.05)

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?

A) $16,598

3) 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

10) 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 yearʹs 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 ________.

A) $61,303

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

A) 4.25 years

2) 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?

A) Investment X has a higher growth rate than Investment Y.

8) Which of the following is true about perpetuities?

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

2) 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?

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

11) 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 yearʹs 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 ________.

B) $1,445,531

8) 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 childʹs college education. They decide to make deposits into an educational savings account on each of their daughterʹs birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughterʹs 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 daughterʹs 18th birthday, then the amount available for the daughterʹs college expenses on her 18th birthday is closest to ________.

B) $160,463

4) 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?

B) $18,287

7) 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?

B) 6.8%

11) You are interested in purchasing a new automobile that costs $33,000 . The dealership offers you a special financing rate of 9% APR (0.75% per month) for 60 months. Assuming that you do not make a down payment on the auto and you take the dealerʹs financing deal, then your monthly car payments would be closest to ________.

B) 685

3) Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Year Investment X Investment Y 1 $5,000 $11,000 2 $7,000 $9,000 3 $9,000 $7,000 4 $11,000 $5,000

B) Investment Y has a higher present value

6) Which of the following statements regarding growing perpetuities is FALSE?

B) PV of a growing perpetuity = C / r - g

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

C) $1200 20,000x.06

4) 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?

C) $200,000 (4,000/(.09-.07))

5) 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%?

C) $5390 (900/.11) (8181.82/(1.11)^4)

12) 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 12% APR (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.

C) 3193

9) Faisal has $12,000 in his savings account and can save an additional $3600 per year. If interest rates are 12%, how long will it take his savings to grow to $47,000 ?

C) 5.3 years

13) 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 ________.

C) 6%

7) Which of the following statements regarding perpetuities is FALSE?

C) PV of a perpetuity = r/C

5) 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?

D) $13,240.79

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

D) $5000 (500/.1)

5) 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 yearsʹ time. What is the present value (PV) of this donation, given that the interest rate is 11%

D) $7,681,257.74

10) What is the internal rate of return (IRR) of an investment that requires an initial investment of $11,000 today and pays $15,400 in one yearʹs time?

D) 40%

9) Which of the following is true about perpetuities?

D) All the above are true statements

6) 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%?

D) There is no solution to this problem.

1) Cash flows from an annuity occur every year in the future.

False

2) 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

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

True

1) 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

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

True