FINANCE CH 4
Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has been offered an immediate payment of $100,000. Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years. The current market rate of interest for Joe is 6%. In terms of present value (PV), how much will Joe receive for selling the family business?
$254,641
) 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 ________. A) $61,303 B) $30,652 C) $42,912 D) $67,433
A
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? A) $603.94 B) $301.97 C) $724.73 D) $966.30
A
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 B) $160 C) $175 D) $190
A
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
A
How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000? A) 4.25 years B) 3.25 years C) 5.25 years D) 6.25 years
A
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. B) Investment X has a lower growth rate than Investment Y. C) The answer cannot be determined without knowing the interest rate for both investments. D) With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value.
A
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 B) $19,918 C) $23,237 D) $26,557
A
Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% 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 ________. A) $37,086.78 B) $22,252.07 C) $44,504.14 D) $51,921.49
A
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 ________. A) $110,793 B) $55,397 C) $77,555 D) $132,952
A
Which of the following formulas is INCORRECT? A) PV of a growing annuity = C × B) PV of an annuity = C × C) PV of a growing perpetuity = D) PV of a perpetuity =
A
Which of the following statements regarding growing perpetuities is FALSE? A) We assume that r < g for a growing perpetuity. B) PV of a growing perpetuity = C) To find the value of a growing perpetuity one cash flow at a time would take forever. D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.
A
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. B) The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. C) The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. D) No comparison can be madewe need to know the cash flows to calculate the present value.
A
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. B) The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B. C) The present value of cash flows in Investment A is equal to the present value of cash flows in Investment B. D) No comparison can be made—we need to know the cash flows to calculate the present value.
A
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 B) $500,000 C) $250,000 D) This problem cannot be solved
A
is a stream of N equal cash flows paid at regular intervals
ANNUITY
) 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? A) $158.13 B) $316.25 C) $379.50 D) $506.00
B
) 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 ________. A) $24,479 B) $40,799 C) $48,959 D) $57,119
B
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? A) $14,630 B) $18,287 C) $25,602 D) $29,259
B
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? A) 5.8% B) 6.8% C) 7.8% D) 9.8%
B
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? A) $94.40 million B) $118.00 million C) $165.20 million D) $188.80 million
B
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 ________. A) $722,766 B) $1,445,531 C) $1,011,872 D) $1,590,084
B
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 ________. A) $32,181 B) $53,635 C) $64,362 D) $75,089
B
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 ________. A) $80,232 B) $160,463 C) $112,324 D) $176,509
B
Which of the following statements regarding annuities is FALSE? A) PV of an annuity = C × B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.
B
You are interested in purchasing a new automobile that costs $33,000. The dealership offers you a special financing rate of (0.75% per month) for 60 months. Assuming that you do not make a down payment on the auto and you take the dealer's financing deal, then your monthly car payments would be closest to ________. A) $548 B) $685 C) $959 D) $1096
B
) If the current rate of interest is 8%, then the present value (PV) of an investment that pays $1200 per year and lasts 24 years is closest to ________. A) $7581 B) $15,162 C) $12,635 D) $17,689
C
) 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? A) $1420; $110,739 B) $2271; $166,109 C) $2839; $184,565 D) $3123; $221,478
C
) 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? A) $10,062.20 B) $20,124.40 C) $16,770.33 D) $23,478.46
C
A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year? A) $600 B) $960 C) $1200 D) $720
C
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%? A) $2695 B) $4312 C) $5390 D) $3234
C
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) $58,334 B) $93,334 C) $116,667 D) $70,000
C
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) $85.60 B) $171.20 C) $142.67 D) $199.74
C
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? A) $39,614 B) $63,382 C) $79,228 D) $95,074
C
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? A) 4.3 years B) 6.3 years C) 5.3 years D) 7.3 years
C
An annuity pays $47 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 8%? A) $1563.88 B) $3127.76 C) $3649.06 D) $2606.47
D
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? A) $100,000.00 B) $160,000.00 C) $200,000.00 D) $240,000.00
C
Which of the following statements regarding perpetuities is FALSE? A) To find the value of a perpetuity by discounting one cash flow at a time would take forever. B) A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever. C) PV of a perpetuity = D) One example of a perpetuity is the British government bond called a consol.
C
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 ________. A) 5.0% B) 7.1% C) 6.0% D) 8.2%
C
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 ________. A) $2554 B) $4470 C) $3193 D) $5109
C
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? A) $15,888.95 B) $18,537.11 C) $21,185.26 D) $13,240.79
D
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%? A) $1456 B) $19,867 C) $21,320 D) There is no solution to this problem
D
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 years' time. What is the present value (PV) of this donation, given that the interest rate is 11%? A) $3,840,628.87 B) $5,376,880.42 C) $6,913,131.97 D) $7,681,257.74
D
An annuity pays $13 per year for 53 years. What is the future value (FV) of this annuity at the end of that 53 years given that the discount rate is 9%? A) $8258.91 B) $16,517.82 C) $19,270.79 D) $13,764.85
D
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? A) $125,000.00 B) $200,000.00 C) $300,000.00 D) $250,000.00
D
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%? A) -$3189.80 B) -$5907.57 C) 5907.57 D) $3189.80
D
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 year's time? A) 37% B) 44% C) 43% D) 40%
D
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%? A) $2500 B) $4000 C) $3000 D) $5000
D
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) $7291.00 B) $14,582.00 C) $17,012.34 D) $12,151.67
D
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?
Every cash flow contains two pieces of information—the nominal value and the time stamp. If we decide to eliminate the zero cash flows from the timeline and concentrate only on the nonzero ones, we will be distorting the time stamp of some nonzero cash flows. Hence, we need to show the timeline in full, including all cash flows zero as well as nonzero.
) Trial and error is the only way to compute the internal rate of return (IRR) when interest is calculated over five or more periods. T OR F
FALSE
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? Answer: This is a two-step problem.
FIRST YEAR=25,322.71 FOUR YEARS=$97,110.01
Cash flows from an annuity occur every year in the future. T OR F
False
is a stream of N growing cash flows, paid at regular intervals
GROWING ANNUITY
is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.
GROWING PERPETUITY
is a stream of equal cash flows that occur at regular intervals and lasts forever
PERPETUITY
A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV). T OR F
TRUE
The internal rate of return (IRR) is the interest rate that sets the net present value (NPV) of the cash flows equal to zero. T OR F
TRUE
The present value (PV) of a stream of cash flows is just the sum of the present values of each individual cash flow. T OR F
TRUE
How do the growth perpetuity results differ with negative and positive growths of similar magnitude assuming everything else remains unchanged
The denominator in the formula for growth perpetuity plays in important role on the results for negative and positive growths of similar magnitude. A positive growth results in a smaller denominator thereby increasing the present value (PV). Contrarily, a negative growth results in a larger denominator giving a smaller present value (PV
Can we apply the growing perpetuity equation for negative growth as well?
Yes, it is perfectly in order to apply the growth perpetuity for negative growth
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. B) Since a perpetuity generates cash flows every period infinitely, initial cash outflow must be discounted to calculate the present value. C) Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow using the present value and the interest rate. D) Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV.
a
An annuity is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 9%? A) $5776 B) $9626 C) $11,551 D) $13,476
b
Which of the following is true about perpetuities? 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
d