FIN 3715

You currently have a​ one-year-old loan outstanding on your car. You make monthly payments of $200. You have just made a payment. The loan has four years to go​ (i.e., it had an original term of five​ years). Show the timeline from your perspective. How would the timeline differ if you created it from the​ bank's perspective?

your perspective: 0= nothing 1= −$200 2= −$200 3= −$200 4= −$200 48= −$200 banks perspective: 0= nothing 1= 200 2= 200 3= 200 4= 200 48= 200

You have decided to buy a perpetual bond. The bond makes one payment at the end of every year forever and has an interest rate of 6 %. If the bond initially costs $ 2,000​, what is the payment every​ year?

C=(PV)(r)=2000*0.06=$120

You plan to deposit $600 in a bank account now and $400 at the end of the year. If the account earns 3% interest per​ year, what will be the balance in the account right after you make the second​ deposit?

FV1=C0*(1+r)+C1 1018

You are thinking about buying a piece of art that costs $ 20,000. The art dealer is proposing the following​ deal: He will lend you the​ money, and you will repay the loan by making the same payment every two years for the next 10 years​ (i.e., a total of 5 ​payments). If the interest rate is 7 % per​ year, how much will you have to pay every two​ years?

Find I/Y =(1+r)^m-1=(1+0.07)^2-1=0.1449=14.49% N=5, I/Y=14.49, PV=-20,000, SO PMT=5894.43

Suppose you currently have $ 4,700 in your savings​ account, and your bank pays interest at a rate of 0.52 % per month. If you make no further deposits or​ withdrawals, how much will you have in the account in 6 ​years?

N=*12=72, I/Y=0.52%, PV=-4,700, SO FV=6827.73

You have an investment opportunity that requires an initial investment of $ 7,600 today and will pay $ 9,000 in one year. What is the rate of return of this​ opportunity?

N=1, PV=-7,600, PMT=0, FV=9,000, I/Y=18.42%

What is the present value of $ 3000 paid at the end of each of the next 50 years if the interest rate is 9 % per​ year?

PV= C*(1/r)*(1-1/(1+r)^n)=32885.05 N=50, I/Y=9%, PMT=3000, FV=0, PV=32885.05

Each set contains the same cash flows ​($12​, $21​, $30​, $39​, $48​), so why is the present value​ different?

The present value in part (b​) is higher because the larger cash flows occur sooner.

What is the present value of the following set of cash​ flows, discounted at 9.4% per​ year? 1(8),2(19),3(30),4(41),5(52) 1(52),2(41),3(30),4(19),5(8)

The present value of the cash flow stream is ​$107.55, $122.83

You are looking to buy a car and can afford to pay $ 200 per month. If the interest rate on a car loan is 0.75 % per month for a 60​-month ​loan, what is the most expensive car you can afford to​ buy?

N=60, I/Y=0.75%, PMT=-200, SO PV=9635

You have just taken out a​ five-year loan from a bank to buy an engagement ring. The ring costs $5,500. You plan to put down $1,200 and borrow $4,300. You will need to make annual payments of $1,100 at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the​ bank's perspective?

0($4300)-1(-$1,100)-2(-$1,100)-3(-$1,100)-4(-$1,100)-5(-$1,100) 0(-$4300)-1($1,100)-2($1,100)-3($1,100)-4($1,100)-5($1,100)

You receive a ​$5,000 check from your grandparents for graduation. You decide to save it toward a down payment on a house. You invest it earning 11​% per year and you think you will need to have ​$10,000 saved for the down payment. How long will it be before the ​$5,000 has grown to ​$10,000 ​?

FIND N PV=-5000, I/Y=8%, FV=10,000, N=9YEARS

You are saving for retirement. To live​ comfortably, you decide you will need to save $ 3 million by the time you are 65. Today is your 25 th ​birthday, and you​ decide, starting today and continuing on every birthday up to and including your 65 th ​birthday, that you will put the same amount into a savings account. If the interest rate is 3 %​, how much must you set aside each year to make sure that you will have $ 3 million in the account on your 65 th ​birthday?

FIND PMT. N=65-25=40+1=41, I/Y=3%, PV=0, FV=2M, SO PMT=39137

A local bank is running the following advertisement in the​ newspaper: "For just $ 2,000 we will pay you $ 120 ​forever!" The fine print in the ad says that for a $ 2,000 ​deposit, the bank will pay $ 120 every year in​ perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising​ (what is the rate of return of this​ investment)?

FIND r r=C/PV=120/2000=0.06=6%

You are thinking about buying a savings bond. The bond costs ​$57 today and will mature in 10 years with a value of ​$114. What annual interest rate will the bond​ earn?

N=10, PV=-57, FV=114 I/Y= 7.18% r=(FV/PV)^1/n-1=7.18%

You have just turned 22 years​ old, received your​ bachelor's degree, and accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as​ follows: Every dollar in the plan earns 7.2 % per year. You cannot make withdrawals until you retire on your 65th birthday. After​ that, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in​ retirement, you will need $ 100,000 per​ year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your​ retirement?

N=100-65=35, I/Y=7.2%, PMT=100,000 SO PV=-1267032 N=65-22=43, I/Y=7.2%, FV=1267032, SO PV=-3,739.9685 N=43, I/Y=7.2%, PV=-3,739.985, SO PMT=4832.3778

Assume that Social Security promises you $ 41,000 per year starting when you retire 45 years from today​ (the first $ 41,000 will get paid 45 years from​ now). If your discount rate is 5 %​, compounded​ annually, and you plan to live for 14 years after retiring​ (so that you will receive a total of 15 payments including the first​ one), what is the value today of Social​ Security's promise?

N=15, I/Y=5, PMT=41,000, PV=425565.98 N=44, I/Y=5, FV=425565.98, PV=49,732.21

Your grandmother has been putting $ 2000 into a savings account on every birthday since your first​ (that is, when you turned​ one). The account pays an interest rate of 3 %. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday

N=18, 1/Y=3%, PMT=$2,000, FV=$46,828.87 FV=C/r*((1+r)^n-1)=$46828.89

You are thinking of purchasing a house. The house costs $ 250,000. You have $ 36,000 in cash that you can use as a down payment on the​ house, but you need to borrow the rest of the purchase price. The bank is offering a 30​-year mortgage that requires annual payments and has an interest rate of 5 % per year. What will be your annual payment if you sign this​ mortgage?

N=30, I/Y=5%, PV=214,000, FV=0, PMT= $13,921

You would like to buy a house that costs $ 350,000. You have $ 50,000 in cash that you can put down on the​ house, but you need to borrow the rest of the purchase price. The bank is offering you a​ 30-year mortgage that requires annual payments and has an interest rate of 8 % per year. You can afford to pay only $ 26,120 per year. The bank agrees to allow you to pay this amount each​ year, yet still borrow $ 300,000. At the end of the mortgage​ (in 30​ years), you must make a balloon​ payment; that​ is, you must repay the remaining balance on the mortgage. How much will be this balloon​ payment? ​Hint: The balloon payment will be in addition to the 30th payment.

N=30, I/Y=8%, PV=?, PMT=26,120, FV=0 SO PV=294,053.3009 THEN PV=300,000-294,053.3009=5946.6991 N=30, I/Y=8%, PV=5946.991, PMT=0,FV=? SO FV=59,840

You figure that the total cost of college will be $ 104,000 per year 18 years from today. If your discount rate is 11 % compounded​ annually, what is the present value today of four years of college costs starting 18 years from​ today?

N=4, I/Y=11%, PMT=$104,000, PV=$322654.35 N=17, I/Y=11%, FV=322654.35, PV=$54,733

You have just entered college and have decided to pay for your living expenses using a credit card that has no minimum monthly payment. You intend to charge $ 900 per month on the card for the next 45 months. The card carries a monthly interest rate of 1.1 %. How much money will you owe on the card 46 months from​ now, when you receive your first statement​ post-graduation?

N=45, I/Y=1.1%, PMT=-900, FV=52042.13 FV46=FV45*(1+r)=(52043.13*(1+0.011)=52614.593

You have a loan outstanding. It requires making nine annual payments of $ 5000 each at the end of the next nine years. Your bank has offered to restructure the loan so that instead of making the nine payments as originally​ agreed, you will make only one final payment in nine years. If the interest rate on the loan is 8 %​, what final payment will the bank require you to make so that it is indifferent to the two forms of​ payment?

N=9 ,I=8, NPV=31234, FV=62438

You want to endow a scholarship that will pay $ 6000 per year​ forever, starting one year from now. If the​ school's endowment discount rate is 8 %​, what amount must you donate to endow the​ scholarship?

PV=C/r =6000/0.08=$75000

You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the​ drug's profits will be $ 4 million in its first year and that this amount will grow at a rate of 5 % per year for the next 17 years. Once the patent​ expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 7 % per​ year?

PV=C/r-g *(1-(1+g/1+r)^n= $54881139.62

Your firm spends $ 5,300 every month on printing and mailing​ costs, sending statements to customers. If the interest rate is 0.48 % per​ month, what is the present value of eliminating this cost by sending the statements​ electronically?

PV=C/r=5300/0.0048=1104167

Suppose you receive ​$200 at the end of each year for the next three years. a. If the interest rate is 7%​, what is the present value of these cash​ flows? b. What is the future value in three years of the present value you computed in ​(a​)? c. Suppose you deposit the cash flows in a bank account that pays 7 %interest per year. What is the balance in the account at the end of each of the next three years​ (after your deposit is​ made)? How does the final bank balance compare with your answer in ​(b​)?

a) $524.86 b)FV=PV*(1+r)^n=642.98 c)FV1=C1(1)=200, FV2=C1*(1+R)^n+C2=445

Assume you can earn 9.5% per year on your investments. a. If you invest $190,000 for retirement at age​ 30, how much will you have 3535 years later for​ retirement? b. If you wait until age 40 to invest the $190,000​, how much will you have 25 years later for​ retirement? c. Why is the difference so​ large?

a) FV(35)=C*(1+r)^n=4552477 b) FV(25)=C*(1+r)^n=1836989 c) The difference is large because the compounding effect is accentuated the longer the time of investment.

You have just received a windfall from an investment you made in a​ friend's business. She will be paying you $21,757 at the end of this​ year, $43,514 at the end of next​ year, and $65,271 at the end of the year after that​ (three years from​ today). The interest rate is 4.1% per year. a. What is the present value of your​ windfall? b. What is the future value of your windfall in three years​ (on the date of the last​ payment)?

a) N=3, I=4.1, 0-CF1, 21757-CF2, 43514-CF3, 65271-CF4 shift-NPV ($118913) b) FV=PV*(1+r)^n ($134147)

Assume that your parents wanted to have $ 110,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 9.0 % per year on their investments. a. How much would they have to save each year to reach their​ goal? b. If they think you will take five years instead of four to graduate and decide to have $ 150,000 saved just in​ case, how much would they have to save each year to reach their new​ goal?

a) N=4, I/Y=6.3%, PMT=$5,100, P.V=$17551.31 b) N-1, I/Y=6.3%, PMT=%5,100, P.V=4,797.74

When Alfred Nobel​ died, he left the majority of his estate to fund five​ prizes, each to be awarded annually in perpetuity starting one year after he died​ (the sixth​ one, in​ economics, was added​ later). a. If he wanted the cash award of each of the five prizes to be ​$35000 and his estate could earn 8​% per​ year, how much would he need to fund his​ prizes? b. If he wanted the value of each prize to grow by 6​% per year​ (perhaps to keep up with​ inflation), how much would he need to​ leave? Assume that the first amount was still ​$35000. c. His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in ​(b​), and had invested it at 8​% per​ year, how much would they have in​ 2014, 118 years after his​ death?

a) PV=C/r= 35000*5/0.08 b) PV=C/r-g =35000*5/(.08-.06)=8750000 c) FV= C*(1+r)^n=7691 M

You want to endow a scholarship that will pay $ 7000 per year​ forever, starting one year from now. If the​ school's endowment discount rate is 10 %​, what amount must you donate to endow the​ scholarship? How would your answer change if you endow it​ now, but it makes the first award to a student 10 years from​ today?

a) PV=C/r=7000/.10=$70,000 b) PV=PV/(1+r)^n=70000/(1+.10)^9=29686.83

You have an investment account that started with ​$1000 10 years ago and which now has grown to ​$10 000. a. What annual rate of return have you earned​ (you have made no additional contributions to the​ account)? b. If the investment account earns 15 % per year from now​ on, what will the​ account's value be 10 years from​ now?

a)N=10, PV=-1,000, FV=10,000, I/Y= 25.89% b)N=10, PV=-10,000, PMT=0, I/Y=15%, FV=$40,455.57

The British government has a consol bond outstanding paying pound £400 per year forever. Assume the current interest rate is 4% per year. a. What is the value of the bond immediately after a payment is​ made? b. What is the value of the bond immediately before a payment is​ made?

a)PV=C/r = 400/0.04 = 10000 b) PV=C/r +C = 400/0.04 +400= 10400

You are thinking of making an investment in a new factory. The factory will generate revenues of $ 1,710,000 per year for as long as you maintain it. You expect that the maintenance costs will start at $ 100,890 per year and will increase 4 % per year thereafter. Assume that all revenue and maintenance costs occur at the end of the year. You intend to run the factory as long as it continues to make a positive cash flow​ (as long as the cash generated by the plant exceeds the maintenance​ costs). The factory can be built and become operational immediately and the interest rate is 5 % per year. a. What is the present value of the​ revenues? b. What is the present value of the maintenance​ costs? c. If the plant costs $ 17 comma 100,000 to​ build, should you invest in the​ factory?

a)SOLVE FOR N C1-M1*(1+g)^n-1 n=73years SOLVE FOR PV PV=C1*1/r(1-(1/1+r)^n) PV=33229027 b) PV=M1*1/r-g(1-(1+g/1+r)^n) PV=5071781 c) NPV=33229027-5071781-17100000=11057246

If the present value of your payments is equal to or larger than the amount of the​ loan, you will be able to pay off your loan as planned. The present value of your payments is smaller than the amount of the​ loan, so you will not be able to pay off the loan.

equal to then you will be able to pay loan smaller than you will not be able to pay loan