FINA 320 - QUIZ 2

You deposited $1,000 in a savings account that pays 8 percent annual interest compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive? (round to the nearest dollar)

$1,126 N = 6 I/Y = 2 PV = 1,000 PMT = 0 FV =-1,126

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? (round to the nearest cent)

$1,348.48 N=5 I/Y =15 PV = 0 PMT = 200 FV= -1,348.48

An investment promises a payoff of $195 two and half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?

$162.75 N=2.5 I/Y = 7.5 PMT = 0 FV=195 PV = -162.75

Your parents plan to spend $20,000 on a car for you upon graduation from college. If you will graduate in three years and your parents can earn 4.125% annually on their investment, how much money must they set aside today for your car?

$17,716 N=3 I/Y =4.125 PMT=0 FV= 20,000 PV = -17,716.

Your uncle has agreed to deposit $3,000 in your brokerage account at the beginning of each of the next five years (t = 0, 1, 2, 3, and 4). You estimate that you can earn 9 percent a year on your investments. How much will you have in your account right after the last deposit is made? (Assume that no money is withdrawn from the account)

$17,954.13 N = 5 I/Y = 9 PV = 0 PMT = 3000 FV = 19,570

Harry decided he was tired of being a poor college student when he visited a local electronics store and experienced its finest theatre system. He determined that he would invest today a portion of the remaining money he earned last summer cleaning animal cages at the veterinary clinic. He plans to invest the money into an international mutual fund for 3.5 years and expects to earn an average annual dollar rate of return of 15%. If Harry wants to have $4,000 in the account at the end of this time, how much must he invest today? (Round your answer to the nearest dollar)

$2,453 FV = 4,000 I/Y = 15 N = 3.5 PMT = 0 PV = 2,452.55

Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $9,000 to invest today and can earn 12% on invested funds. If your parents match the amount of money you have in two years, what is the maximum you can spend on the new car?

$22,579 PV = 9,000 N = 2 PMT = 0 I/Y = 12 FV = 11,289.60 x 2 = $22,579

How much interest can be accumulated in two years on a $1,000 deposit paying annual interest rate of 10%, compounded monthly? (Round to the nearest dollar)

$220 PV = 1,000 N = 2 x 12 = 24 I/Y = 10/12 = 0.83333 PMT = 0 FV = 1,220.39 1,220.39 - 1,000 = 220.39

If a 5-year ordinary annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? (round to the nearest cent)

$263.80 N = 5 I/Y = 10 PV = 1000 FV=0 PMT = -263.80

You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 2.90 percent per year, compounded monthly for the first six months, increasing thereafter to 15 percent compounded monthly. Assuming you transfer the $3,000 balance from our existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year? (round to the nearest cent)

$279.30 N = 6 PV = 3,000 I/Y = 2.9/12 = 0.24167 PMT = 0 FV = 3,043.76 Then, find the balance at the end of 12 months: N = 6 PV = 3043.76 I/Y = 15/12 = 1.25 PMT = 0 FV = 3,279.30 Thus, interest = 3,279.30 - 3,000 = 279.30

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

$3,604.78 PMT = 1,000 N = 5 I/Y = 12 FV = 0 PV = 3,604.78

You have an annuity of equal annual end-of-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars?

$3,899.47

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 8% interest with monthly compounding? (Round to the nearest hundred dollar)

$323,900.00 PMT = 2,500 N = 25 x 12 = 300 I/Y = 8/12 = 0.6667 FV = 0 PV = 323,911

You are given the cash flows listed below at Years 3, 5, and 6, but you aren't sure about the cash flow at Year 4. Assume that the appropriate interest rate for these cash flows is 12% and that the value of all the cash flows in Years 3 to 6, evaluated as if Year 10 is $1,982.47. Determine the value of the cash flow at Year 4. Year 3, Cash Flow $100 Year 4, Cash Flow $? Year 5, Cash Flow $200 Year 6, Cash Flow $425

$375.00 FV Year 10 = 100 x (1 + 12%)^(10 - 3) + X(1 + 12%)^(10 - 4) + 200(1 + 12%)^(10 - 5) + 425(1 + 12%)^(10 - 6) = 1,982.47 = 221.068 + X(1.12)^6 + 352.468 + 668.746

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. The loan has an annual interest rate of 8.5% and requires annual installment payment. If the loan is to be completely paid off by the end of year five, what should be the annual payment? (Round to the nearest dollar)

$380,649 PV = 1,500,000 I/Y = 8.5 N = 5 FV = 0 PMT = 380,649

You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account right after the last deposit is made?

$39,363

You have purchased a savings bond that will pay $10,000 to your newborn child in fifteen years. If the bank discounts this bond at a rate of 3.875% per year, what is today's price (the present value) for this bond?

$5,654

You have the opportunity to buy a perpetuity that pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

$6,666.67 PV = 1000/15% = 6,666.67

What is the present value of receiving $100 monthly for two years, followed by $200 monthly for the next three years, payments? Assuming that the annual interest rate is 13%, compounded monthly. (Round to the nearest dollar)

$6,687 CF 1 = 100 F1 = 2 x 12 = 24 CF 2 = 200 F2 = 3 x 12 = 36 I = 13/12 = 1.08333 NPV = 6,686.61

A wealthy woman just died and left her pet cats the following estate: $50,000 per year for the next fifteen years, with the first cash flow today. At a discount rate of 3.2%, what is the feline estate worth in today's dollars?

$607,180.14

Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30? (round to the nearest dollar)

$7,428 N=30 I/Y=10 PV = -425.678 PMT=0 FV =7428

You plan to save $650 per year for the next 8 years. If your bank offers you an annual interest rate of 10%, how much money (round to the nearest dollar) will you have at the end of year 8? Assume each cash flow is deposited into your account at the end of the year.

$7,433 N = 8 I/Y = 10 PMT = 650 PV = 0 FV = 7,433.33

A real estate investment has the following expected cash flows: Year Cash Flows 1 $10,000 2 25,000 3 50,000 4 35,000

$96,110

Your company just sold a product with the following payment plan: $50,000 today, $25,000 next year, and $10,000 the following year. If your firm places the payments into an account earning 10% per year, how much money will be in the account after collecting the last payment?

$98,000

Mercer Shaved Ice Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent?

1, $1,300 2. 500 3, 700 4, 1,620

Rasputin, Inc., has identified an investment project with the following cash flows. If the discount rate is 8 percent, what is the future value of these cash flows in Year 4? What is the future value at a discount rate of 11 percent? At 24 percent?

1, 900 2, 1,000 3, 1,100 4, 1,200

Assume you invested $1,000 in stocks 10 years ago, and that your account is now worth $2,839.42. Determine the annual rate of return that you have earned on this investment.

11% PV = -1,000 N = 10 FV = 2,838.42 PMT = 0 I/Y = 11

If you can earn 5.25% per year on your investments, how long, exactly, will it take to double your money? (hint: do not use the Rule of 72)

13.55 years I/Y = 5.25 PV = -100 FV = 200 PMT = 0 N = 13.55

You have a balance of $2,000 on your credit card and your monthly minimum payment is $35. The credit card company charges an APR of 18%, compounded monthly. If you just make the minimum payment and do not add additional charges on the card, how long does it take you to pay the balance off? (round to the nearest month)

131 months PV = 2,000 FV = 0 PMT = -35 I/Y = 18/12 = 1.5 N = 131

An investment offers $4,100 per year for 15 years, with the first payment occurring one year from now. If the required return is 10 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

15 years: N = 15 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $31,184.93 40 years: N = 40 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $40,094.11 75 years: N = 75 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $3,162.45 Perpetuity: PVA = $4,100/.10 = $41,000.00 Perpetuity cannot be solved with financial calculator. Note the difference in present values between perpetuity and a 75-year annuity is very small, less than $35.

Marie has a $1,000,000 investment portfolio, and she wishes to spend $87,500 per year as an ordinary annuity. If the investment account earns 6% annually. How long will her portfolio last?

19.86 years

Your credit card has a balance of $3,000. The bank requires a minimum monthly payment of $64.90 and states that it will take 100 months to pay off the balance if you only make minimum payment every month and do NOT make additional charges on the card. What is the annual interest rate charges by your credit card?

21.60% PV = 3,000 PMT = -64.90 N = 100 FV = 0 I/Y = 1.80 1.80 x 12 = 21.69%

When you were born, your grandparents opened a savings account on your behalf and deposited $1,000. Neither additional deposit nor withdrawal has ever been made since. The account pays an annual interest rate of 5%. The account balance today is $3,920.1. How old are you now (round to the nearest year)?

28 years old PV = 1,000 FV = -3,920.q I/Y = 5 PMT = 0 N = 28

You currently have $67,000 in an interest-earning account. From this account, you wish to make twenty year-end payments of $5,000 each. What annual rate of return must you make on this account to meet your objective?

4.16%

Two rival football fans have made the following wager: if one fan's college football team wins the conference title outright, the other fan will donate $1,000 to the winning school. Both schools have had relatively unsuccessful teams, but are improving each season. If the two fans must put up their potential donation today and the discount rate is 8% for the funds, what is the required upfront deposit if both expect a team to win the conference title in five years? Ten years? Twenty years?

5 years: N = 5 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $680.58 10 years: N = 10 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $463.19 20 years: N = 20 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $214.55

The Stack has just written and recorded the single greatest rock song ever made. The boys in the band believe that the royalties from this song will pay the band a handsome $200,000 every year forever. The record studio is also convinced that the song will be a smash hit and the royalty estimate is accurate. The record studio wants to pay the band up front and not make any more payments for the song. What should the record studio offer the band if it uses a 5% discount rate, a 7.5% discount rate, or a 10% discount rate?

5%: PV of perpetuity = pmt/r = 200000/5% = $4,000,000 7.5%: PV of perpetuity = pmt/r = 200000/7.5% = $2,666,667 10%: PV of perpetuity = pmt/r = 200000/10% = $2,000,000

Approximately how long will it take to double your money if you get a 5.5%, 7.5%, or 9.5% annual return on your investment? Verify the approximate doubling period with the time value of money equation.

5.5: N = ? I/Y = 5.5 PV = 100 PMT = 0 FV = -200 N = 12.95 7.5: N = ? I/Y = 7.5 PV = 100 PMT = 0 FV = -200 N = 9.58 9.5: N = ? I/Y = 9.5 PV = 100 PMT = 0 FV = -200 N = 7.64

Your grandfather placed $5,000 in a trust fund for you. In 12 years the fund will be worth $10,000. What is the rate of return on the trust fund? (round to the nearest one hundredth of 1%)

5.95% PV = -5000 FV = 10,000 PMT = 0 N = 12 I/Y = 5.946

Buying your own home is often mentioned as "the best investment you can make." In 1930, the average home sale price was $3,845. By 1990, the average home sale price had risen to $123,000. What was the average annual rate of return of investing in house over this time period?

5.95% per year N = 60 PV= -3845, FV=123,000 PMT=0 I/Y= 5.95

Kelvin has $2,500 but needs $5,000 to purchase a new golf cart. If he can invest his money at a rate of 12% per year, approximately how many years will it take the money in Kelvin's account to grow to $5,000? Use the Rule of 72 to determine your answer.

6 years 72/12 = 6

After winning the lottery, you state that you are indifferent between receiving twenty $500,000 end of the year payments (first payment one year from today) and receiving a lump sum payment of $5,734,961 today. What interest rate are you using in your decision making process such that you are indifferent between the two choices?

6%

Kant Miss Company is promising its investors that it will double their money every three years. Is this promise too good to be true? What annual rate is Kant Miss promising? If you invest $250 now and Kant Miss is able to deliver on its promise, how long will it take your investment to reach $32,000? Use the Rule of 72.

72/3 = 24. Based on the Rule of 72, the annual rate must be 24% to double the money every three years. From $250 to $32,000, the investment increases by 128 times. In other words, the initial investment has doubled itself 7 times. If money is doubled every 3 years, then it would take approximately 21 years. More specifically, to increase from $250 to $32,000, it is an increase of 128 times, or 32,000=250(1+100%)7 In other words, the money needs to be doubled 7 times, or from 250 to 500 (1 times, or 3 years) from 500 to 1,000 (2 times, or 6 years) from 1,000 to 2,000 (3 times, or 9 years) from 2,000 to 4,000 (4 times, or 12 years) from 4,000 to 8,000 (5 times, or 15 years) from 8,000 to 16,000 (6 times, or 18 years) from 16,000 to 32,000 (7 times, or 21 years).

South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying? (round to the nearest one hundredth of 1%)

8.00% N = 5 I/Y= 8 PV = 10,000 PMT = -2,504.56 FV = 0

Which of the following statements is most correct? a. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. b. To increase present consumption beyond present income normally requires either the payment of interest or else an opportunity cost of interest forgone. c. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value. d. Disregarding risk, if the present value of a sum is equal to its future value, then the interest rate must be zero e. All of the statements above are correct.

All of the statements above are correct.

Which of the following will result in a future value of greater than $100?

All the future values are greater than $100

The present value of annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due? (Round to the nearest dollar).

An increase of $61 614(1 + 10%) = 675.4 675.4 - 614 = 61.4

Marie is 65 years old and ready to retire. She has a $1 million nest egg and wishes to spend $90,000 per year as an ordinary annuity. If her investment portfolio earns 6% annually, at what age will she run out of money? (Longevity risk)

Around 84 years old PV = $1,000,000 PMT = -90,000 I/Y = 6 FV = 0 N = 18.85 65 + 19 = 84

The band from the previous problem agrees to the one-time payment at a 5% discount rate, but it wants to figure the royalty payments from the beginning of the year, not the end of the year. How much more will the band receive with annuity due payments on the royal checks?

By shifting it to perpetuity due, the present value will increase to $4 million x (1+5%) = $4.2 million.

Which of the following actions will INCREASE the present value of an investment?

Decrease the interest rate.

Which of the following will increase the present value of annuity, other things equal?

Decreasing the interest rate

To determine the present value of a future amount, one should ________ the future cash flows.

Discount

Given a set future value, which of the following will contribute to a lower present value?

Higher discount rate

Two mutual fund managers, Martha and David, have been discussing whose fund is the top performer. Martha states that investors bought shares in her mutual fund ten years ago for $21 and those shares are now worth $65. David states that investors bought shares in his mutual fund for only $3 six years ago and they are now worth $7.30 which mutual fund manager had the higher growth rate for the management period?

Martha: N = 10 I/Y = ? PV = -21 PMT = 0 FV = 65 I/Y = 11.96 David: N = 6 I/Y = ? PV = -3 PMT = 0 FV = 7.30 I/Y = 15.98 David generated a better rate of return.

Cooley Landscaping Company needs to borrow $30,000 for a new front-end dirt loader. The bank is willing to loan the funds at 8.5% interest with annual payments at the end of the year for the next ten years. The loan is fully amortized, i.e., the loan will be fully paid off at the end of year ten. What is the annual payment on this loan for Cooley Landscaping?

N = 10 I/Y = 8.5 PV = 30,000 PMT = ? FV = 0 PMT = $4,572.23

Your coin collection contains fifty 1952 silver dollars. If your parents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2067, assuming they appreciate at 4% annual rate?

N = 115 I/Y = 4 PV = -50 PMT = 0 FV = ? FV = $4,547.83

Upstate Bank is offering long-term certificates of deposit with a face value of $100,000 (future value). Bank customers can buy these CDs today for $67,000 and will receive the $100,000 in fifteen years. What interest rate is the bank paying on these CDs?

N = 15 I/Y = ? PV = -67,000 PMT = 0 FV = 100,000 I/Y = 2.706

Standard Insurance is developing a long-life insurance policy for people who outlive their retirement nest egg. The policy will pay out $250,000 on your eighty-fifth birthday. You must buy the policy on your sixty-fifth birthday. The insurance company can earn 7% on the purchase price of your policy. What is the minimum purchase price the insurance company should charge for this policy?

N = 20 I/Y = 7 PV = ? PMT = 0 FV = -250,000 PV = $64,604.75

Imprudential, Inc., has an unfunded pension liability of $650 million that must be paid in 20 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.5%, what is the present value of this liability?

N = 20 I/Y = 8.5 PV = ? PMT = 0 FV = -650,000,000 PV = $127,150,652.40

The State of Confusion wants to change the current retirement policy for state employees. To do so, however, the state must pay the current pension fund members the present value of their promised future payments. There are 240,000 current employees in the state pension fund. The average employee is twenty-two years away from retirement, and the average promised future retirement benefit is $400,000 per employee. If the state has a discount rate of 5% on all its funds, how much money will the state have to pay to the employees before it can start a new pension plan?

N = 22 I/Y = 5 PV = ? PMT = 0 FV = -96,000,000,000 PV = $32,820,000

County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for twenty-five years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume it is an ordinary annuity and the price is the same as present value.

N = 25 I/Y = 6 PV = ? PMT = -500 FV = 0 PV = $6,391.68

A local government is about to run a lottery, but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next twenty-five years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?

N = 25 I/Y = ? PV = 2,000,000 PMT = -150,000 FV = 0 I/Y = 5.56

Marty received an offer for an injury settlement of $10,000 payable in three years. He wants to know what the present value of the injury settlements is if his opportunity cost is 5% (The opportunity cost is the interest rate in this problem.)

N = 3 I/Y = 5 PV = ? PMT = 0 FV = -10,000 PV = $8,638.38

Sam Hinds, a local dentist, is going to remodel the dental reception area and add two new workstations. He has contacted A-Dec, and the new equipment and cabinetry will cost $18,000. A-Dec will finance the equipment purchase at 7.5% over a six-year period. What will Hinds have to pay in annual payments for this equipment?

N = 6 I/Y = 7.5 PV = 18,000 PMT = ? FV = 0 PMT = $3,834.81

A smooth used-car salesman who smiles considerably is offering you a great deal on a "preowned" car. He says, "For only six annual payments of $2,500, this beautiful 2008 Honda Civic can be yours." If you can borrow money at 8%, what is the price of this car?

N = 6 I/Y = 8 PV = ? PMT = -2,500 FV = 0 PV = $11,557.20

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 1995, Christie's auctioned the William de Kooning painting Untitled. The highest bid of $2.2 million was rejected by the owner, who had purchased the painting at the height of the art market in 1989 for $3.52 million. Had the seller accepted the bid, what would his annual rate of return have been?

N = 6 I/Y = ? PV = -3,520,000 PMT = 0 FV = 2,200,000 I/Y = 7.53

You expect to receive $10,000 at graduation in 2 years. You plan on investing it at 12% until you have $120,000. How long will you wait from now?

N = ? I/Y = 12 PV = -10,000 PMT = 0 FV = 120,000 N = 21.93 From now, you'll wait 2 + 21.93 = 23.93 years

You're trying to save to buy a new $120,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.5% annual interest on its accounts. How long will it be before you have enough to buy the car?

N = ? I/Y = 5.5 PV = 40,000 PMT = 0 FV = -120,000 N = 20.52

Your grandfather will sell you a piece of beachfront property for $72,500. He says the price is firm whenever you can pay him cash. You know your finances will allow you to save only $5,000 a year and you can make 8% on your investment. If you invest faithfully every year at the end of the year, how long will it take you to accumulate the necessary $72,500 future cash for the beachfront property?

N = ? I/Y = 8 PV = 0 PMT = -5,000 FV = 72,500 N = 10

A home improvement firm has quoted a price of $9,800 to fix up John's backyard. Five years ago John put $7,500 into a home improvement account that has earned an average of 5.25% per year. Does John have enough money in his account to pay for the backyard fix-up?

No. John has only $9687 in his home improvement account.

Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your cost of capital is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.)

None of the above Use the BGN mode: I/Y = 7 PV = 100 PMT = -10 FV = 0 N=15.7

You have just made your first $2,000 contribution to your individual retirement account. Assuming you earn a 9% rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing?

Start now: N = 45 I/Y = 9 PV = 2,000 PMT = 0 FV = ? FV = $96,654.57 10 Years: N = 35 I/Y = 9 PV = 2,000 PMT = 0 FV = ? FV = $40,827.94

Which of the following is not an example of annuity cash flows?

The grocery bill that changes every week

Reginal is about to lease an apartment for the year. The landlord wants him to make the lease payments at the start of the month. The twelve monthly payments are $1,300 per month. The landlord says he will allow Reginal to prepay the rent for the entire year with a discount. The one-time annual payment due at the beginning of the lease is $14,778. What is the implied monthly discount rate for the rent? If Reginal is earning 1.5% on his savings monthly, should he pay by month or make the single annual payment?

The month rent is due at the beginning of each month. Thus, it is an annuity due. The one-time annual payment is the present value of the annuity due. We can use the financial calculator to find the implied monthly discount rate. It is important to use the BEG mode in the calculator because the lease is an annuity due. N = 12 I/Y = ? PV = 14,778 PMT = -1300 FV = 0 I/Y = 1

Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year. He offers to sell to you all but the next 20 cash flows (the first to be received one year from today) for $500. In other words, he keeps the first 20 cash flows of his perpetuity and you get all of the rest. Is this a good price for you if the appropriate discount rate is 6%?

Yes, because the present value of the remaining cash flows is $519.68 and you are buying them for only $500. PV = 100/6% = 1,666.667 PMT = 100 I/Y = 6 N = 20 FV = 0 PV = 1,146.992 1,666.667 - 1,146.992 = 519.68

A lottery ticket states that you will receive $250 every year for the next ten years. a. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an ordinary annuity? b. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an annuity due? c. What is the difference between the ordinary annuity and annuity due in parts (a) and (b)?

a. N = 10 I/Y = 6 PV = 0 PMT = 250 FV = 0 PV = 1,840 b. The present value of annuity due = PV of ordinary annuity*(1+r) = 1,840 x 1.06 = $1,950.40 c. 1,950.40 - 1,840 = 110.40

Your dreams of becoming rich have just come true. You have won the State of Tranquility's lottery. The state offers you two payment plans for the $5,000,000 advertised jackpot. You can take the annual payments of $250,000 for the next twenty years or $2,867,480 today. a. If your investment rate over the next twenty years is 8%, which payoff will you choose? b. If your investment rate over the next twenty years is 5%, which payoff will you choose? c. At what investment rate will the annuity stream of $250,000 be the same as the lump-sum payment of $2,867,480?

a. N = 20 I/Y = 8 PV = ? PMT = 250,000 FV = 0 PV = 2,454,537 At 8%, the present value of installment payments is $2,454,537 million, less than the lump sum of $2,867,480. Take the lump sum. b. N = 20 I/Y = 5 PV = ? PMT = 250,000 FV = 0 PV = 3,115,553 At 5%, the present value of installment payments is $3,115,553 million, greater than the lump sum of $2,867,480. Take the installment payments. c. N = 20 I/Y = ? PV = -2,867,480 PMT = 250,000 FV = 0 I/Y = 6 At 6%, the two options are equivalent.

Jack and Jill are saving for a rainy day and decide to put $50 away in their local bank every year for the next twenty-five years. The local Up-the-Hill Bank will pay them 7% on their account. a. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of twenty-five years? b. Unfortunately, Jack was hurt in an accident after only ten years of savings. The medical bill has come to $700. Is there enough in the rainy-day fund to cover it?

a. N = 25 I/Y = 7 PV = 0 PMT = -50 FV = ? FV = $3,162.45 b. N = 10 I/Y = 7 PV = 0 PMT = -50 FV = ? FV = $690.82 Not enough $ to cover medical bill.

The main variables of the TVM equation are

present value, future value, time, interest rate, and payment.