FIN 3100 Exam 2

A bond is a ________ instrument by which a borrower of funds agrees to pay back the funds with interest on specific dates in the future.

long-term debt

As the rating of a bond increases (for example, from A, to AA, to AAA), it generally means that ________.

the credit rating increases, the default risk decreases, and the required rate of return decreases

The typical payments on a consumer loan are made at ________.

the end of each month

Assume you just bought a new boat and now have a boat loan to repay. The amount of the principal is $68,000, the loan is at 6.75% APR, and the monthly payments are spread out over 7 years. What is the monthly loan payment?

$1,018.01

Quality Production Products Inc. has issued 20-year semiannual coupon bonds with a face value of $1,000. If the annual coupon rate is 12% and the yield to maturity today is 10%, what is the firm's current price per bond?

$1,171.59

What is the future value at the end of year thirty-five of an ordinary annuity cash flow of $4,000 per year at an interest rate of 11.0% per year?

$1,366,358.22

The Canadian Government has once again decided to issue a consol (a bond with a never- ending interest payment and no maturity date). The bond will pay $60 in interest each year (at the end of the year), but it will never return the principal. The current discount rate for Canadian government bonds is 4%. What should this consol bond sell for in the market?

$1,500

TravelEasy Inc. has issued 30-year semiannual coupon bonds with a face value of $1,000. If the annual coupon rate is 14% and the yield to maturity today is 8%, what is the firm's current price per bond?

$1,678.70

Five years ago, CleanEnergy Corporation issued an 12% coupon per year (paid semi-annually), 20-year, AA-rated bond at its par value of $1000. Currently, the annual yield to maturity (APR) on these bonds is 8%. What is the current price per bond?

$1345.84 Price = 1000/1.04^30 + 60[1-1/1.04^30]/0.04 = $1345.84

Susan's goal is to retire with $500,000 in her retirement account. The local bank advertises with an interest rate of 1% per month and monthly compounding on retirement fund accounts. If she retires in 30 years how much should Susan save each month to reach her goal?

$143.06 Number of months = 360 500,000 = PMT [ (1.01360 - 1) / 0.01] PMT = $143.06

What if Jennifer were to invest $2,750 today, compounded semiannually, with an annual interest rate of 5.25%. What amount of interest will Jennifer earn in one year?

$146.27 With PV = $2,750, Rate =5.25%/2, Periods = 2, compounding semiannually solve for FV = $2,896.27. To solve for the interest earned use FV - PV = $2,896.27 - $2,750 = $146.27.

You want to buy a new Tesla car for $100,000. The contract is in the form of a 60-month annuity due at a monthly interest rate of 1%. What will your monthly payment be?

$2202.42 100,000 = (1+0.01) PMT [(1 - 1/1.0160) / 0.01] 100,000 = (1.01) PMT [44.955], So PMT = 2202.42

Delagold Corporation is issuing a zero-coupon bond that will have a maturity of fifty years. The bond's par value is $1,000, and the current annual yield on similar bonds is 7.5%. What is the expected price of this bond, using the semiannual convention?

$25.19

Kenna invests $5,000 today, compounded monthly, with an annual interest rate of 8.52%. What amount of interest will she earn in one year?

$443.04 With PV = -$5,000, Monthly Rate =8.52%/12, Periods = 12, compounding monthly solve for FV = $5,443.04. To solve for the interest earned use FV - PV = $5,443.04 - $5,000 = $443.04.

What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty years at an interest rate of 6.0% per year?

$55,059.32

You put down 20% on a home with a purchase price of $150,000, or $30,000. The remaining balance will be $120,000. The bank will loan you this remaining balance at 4.375% APR. You will make monthly payments with a 20-year payment schedule. What is the monthly annuity payment under this schedule?

$751.11 The bank will loan you $120,000 and this is the PV. r = 4.375%/12 = 0.36458%, n = 20 × 12 = 240 periods PMT = 120000/ [(1-1/1.0036458^240)/.003658] = 120000/159.763 = $751.11.

You borrow $40,000 at an annual interest rate of 11% for seven years, and promise to pay an equal amount back at the end of each year. What should be the amount of each annual payment?

$8,488.61

Four years ago, CleanEnergy Corporation issued an 10% coupon per year (paid semi-annually), 15-year, AA-rated bond at its par value of $1000. Currently, the annual yield to maturity (APR) on these bonds is 12%. What is the current price per bond?

$879.58 Price = 1000/1.06^22 + 50[1-1/1.06^22]/0.06 = $879.58

Twenty years ago Bison Enterprises Inc. issued thirty-year 9% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have risen and the yield to maturity on the firm's bonds is now 11%. Given this information, what is the price today for a bond from this issue?

$882.22

Ten years ago Pancake House Inc. issued twenty-five-year 8% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have risen and the yield to maturity on the Bacon bonds is now 9%. Given this information, what is the price today for such a bond?

$919.39

Suppose you postpone consumption and invest at 14% when inflation is 2%. What is the approximate real rate of your reward for saving?

12%

Suppose you postpone consumption and invest at 6% when inflation is 2%. What is the approximate real rate of your reward for saving?

4% We can see that an inflation rate of 2% is 4% less than our 6% investment rate. Thus, 4% is the real rate of your reward for saving.

Becky is seeking to expand her stamp collection. Each year, stamps increase in price at a seven percent rate. She believes that if she invests her money for one year, she should be able to buy 24 stamps for what 23 stamps would cost today. What is her real interest rate or reward for waiting?

4.35% 24/23 - 1

If your nominal rate of return is 6.59 percent and the inflation rate is 2.0 percent, what is the real rate of return?

4.50% (1+0.0659)/(1+0.02)-1=0.045

The real rate is 1.25% and inflation is 5.25%. What is the approximate nominal rate?

6.50% Roughly speaking, the nominal rate is the real rate plus inflation. Thus, the nominal rate is 1.25% plus 5.25% equals 6.50%.

Suppose you postpone consumption and invest at 9% when inflation is 2%. What is the approximate real rate of your reward for saving?

7%

Tony is offering Phil two repayment plans for a long overdue loan. Offer 1 is a visit from an enforcer and the debt is due in full at once. Offer 2 is to pay back $5,000 at the end of each year at 20% interest rate until the loan principal is paid off. Phil owes Tony $20,000. How long will it take for Phil to pay off the loan if he takes Offer 2?

8.83 years n=ln[1/(1-PV×r/PMT)]/ln(1+r) =ln[1/(1-20000×0.2/5000)]/ln(1+0.2)=ln5/ln1.2=8.83

MicroMedia Inc. $1,000 par value bonds are selling for $1,265. Which of the following statements is TRUE?

All of these are true.

Which of the following is NOT true regarding the total payment in an equal payment amortization table?

All of these are true.

Amortization tables are useful for each of the following reasons EXCEPT ________.

All of these are useful purposes of an amortization table.

A finite series of equal payments that occur at regular intervals is called a(n) .

Annuity

Present value calculations do which of the following?

Discount all future cash flows back to the present

Among the three principal repayments, the principal repayment at the end of year 3 is the lowest.

False

Which of the following is NOT an example of ordinary annuity cash flows?

Insurance payments due at the start of the period Insurance payments due at the start of the period are an annuity due.

The phrase "price to rent money" is sometimes used to refer to ________.

Interest rates

John borrows $500,000 at an annual rate of 7.62% for a 10 year term. At the end of each year interest payments of $38,100 are paid. At the maturity of the loan the principal amount is repaid, in addition to an interest payment. What type of loan is this?

Interest-only

You just entered into a $150,000 30-year home mortgage at an annual interest rate of 4.25% making monthly payments of $737.91. Suppose you add an additional payment of $295.97 each month to the $737.91 house payment making your total monthly payments equal to $1,033.88. This extra amount is applied against the principal of the original loan. How long will it take you to pay off your loan of $150,000?

It will take about 204 months. n=ln[1/(1-PV×r/PMT)]/ln(1+r)

MacroMedia Inc. $1,000 par value bonds are selling for $832. Which of the following statements is TRUE?

None of these is true.

Most U.S. corporate and government bonds choose to make ________ coupon payments.

Semiannual

Which of the following types of bonds, as characterized by a feature, by definition has two coupon payments per year?

Semiannual

When a company is in financial difficulty and cannot fully pay all of its creditors, the first lenders to be paid are the ________.

Senior debtholders

What is the EAR if the APR is 10.52% and compounding is daily?

Slightly above 11.09% Using the EAR formula, we get 11.0916% or slightly above 11.09%. EAR = [(1 + APR/m)m] -1 = [(1 + 0.1052/365)365] -1 = 11.0916%.

Monthly interest on a loan is equal to ________.

The beginning balance times the monthly interest rate

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

The grocery bill that changes every week

Which of the following is NOT true with regard to an amortization table?

The remaining principal balance at the end of a payment period is equal to the beginning-of-the-period principal less the total payment. The remaining principal balance at the end of a payment period is equal to the beginning of the period principal less the principal payment.

The "Truth in Savings Law" requires banks to advertise their rates on investments such as CDs and savings accounts as annual percentage yields (APY).

True

A series of equal periodic finite cash flows that occur at the beginning of the period are known as a/an ________.

annuity due

A company selling a bond is ________ money.

borrowing

The ________ is the interest rate printed on the bond.

coupon rate

When the ________ is less than the yield to maturity, the bond sells at a/the ________ the par value.

coupon rate; discount to

The ________ is the annual coupon payment divided by the current price of the bond, and is not always an accurate indicator.

current yield

An annuity is a series of ________.

equal cash payments at regular intervals across time

Bonds are sometimes called ________ securities because they pay set amounts on specific future dates.

fixed-income

The ________ is the written contract between the bond issuer and the bondholder.

indenture

To determine the interest paid each compounding period, we take the advertised annual percentage rate and simply divide it by the ________ to get the appropriate periodic interest rate.

number of compounding periods per year

The number of periods for a consumer loan (n) is equal to the ________

number of years times compounding periods per year

A/An ________ is a series of equal end-of-the-period cash flows.

ordinary annuity

Theresa borrows $800 today in exchange for one payment of $1,000 five years from now. This is an example of a(n):

pure discount loan

The ________ is a market derived interest rate used to discount the future cash flows of the bond.

yield to maturity

The ________ is the return the bondholder receives on the bond if held to maturity.

yield to maturity

How much is the loan balance the end of year 1?

$6978.85 10000 - (4021.15-1000) = 6978.85

What is the total payment each year?

$4021.15 10,000 = PMT [(1 - 1/1.13 ) / 0.1 ] 10,000 = PMT [2.48685]

Ten years ago Salmon Acqua Farming Inc. issued twenty-five-year 8% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have fallen and the yield to maturity on the Bacon bonds is now 7%. Given this information, what is the price today for such a bond?

$1,091.08

Five years ago, CleanEnergy Corporation issued an 12% coupon per year (paid semi-annually), 25-year, AA-rated bond at its par value of $1000. Currently, the annual yield to maturity (APR) on these bonds is 10%. What is the current price per bond?

$1171.59 Price = 1000/1.05^40 + 60[1-1/1.05^40]/0.05 = $1171.59

What is the EAR if the APR is 5% and compounding is quarterly?

Slightly above 5.09% Using the EAR formula, we get 5.0945% or slightly above 5.09%. = (1 + APR/m)m -1 = (1 + .05/4)4 - 1 = 5.0945%.

You are paid to teach graduate-level classes for the university and want to determine how much money the university makes from your graduate-level classes. Based on historical data, you estimate that your graduate classes for the next six years will generate an average annual revenue of $99,850. If you discount these cash flows at an annual rate of 7.30%, what is the present value of the expected cash flows?

$471,562.95

Which one of the following has the highest effective annual rate?

APR of 6 percent compounded daily

A bond may be issued by ________.

All of the above

William wishes to save enough money to purchase a retirement lake cabin. He is willing to spend $200,000 for the cabin and he can save $20,000 per year and invest the money into an account earning 7.00% per year. If his investments come in the form of equal annual end-of-the-year cash flows and the first cash flow is in exactly one year, how long will it take him to save enough money to buy the lake cabin?

Between 7 and 8 years

How much is the interest payment at the end of year 1?

$1000 10000*.1 = $1000

You put 20% down on a home with a purchase price of $250,000. The down payment is thus $50,000, leaving a balance owed of $200,000. The bank will loan the remaining balance at 3.91% APR. You will make annual payments with a 30-year payment schedule. What is the annual annuity payment under this schedule?

$11,439.96 PV=PMT[1-1/(1+r)^n]/r

Five years ago, CleanEnergy Corporation issued an 10% coupon per year (paid semi-annually), 15-year, AA-rated bond at its par value of $1000. Currently, the annual yield to maturity (APR) on these bonds is 8%. What is the current price per bond?

$1135.9 Price = 1000/1.04^20 + 50[1-1/1.04^20]/0.04 = $1135.90

You are saving up for retirement and decide to deposit $3,000 each year for the next 20 years, starting today (annuity due), into an account which pays a rate of interest of 8% per year. What is the total value of your investments in the account 20 years from today?

$148,268.76 FV = PMT × [(1+r)n-1]/1 × (1 + r) = $3,000 × [((1.08)20 - 1)/0.08]× (1.08) =$3,000 × 45.76196×1.08 = $137,285.89×1.08 = $148,268.76

Lily invested $10,000 ten years ago with an insurance company that has paid her 10 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the ten years?

$16,533 6-month rate = 10%/2 = 5% = 0.05, Number of 6-month periods = 20 FV= 10,000(1.05)^20 = $26532.98 Interest earned = $26532.98- $10,000 = $16532.98

Severson has an annuity due that pays $400 per year for 20 years. What is the value of the cash flows 20 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

$18,621.01

RadicaL CREATIONS Inc. just issued zero-coupon bonds with a par value of $1,000. If the bond has a maturity of 15 years and a yield to maturity of 10%, what is the current price of the bond if it is priced in the conventional manner?

$231.38 The conventional way to price a zero-coupon bond is to discount the par value assuming semiannual compounding

Flashstream Productions Inc. is issuing a zero-coupon bond that will have a maturity of fifty years. The bond's par value is $1,000, and the current yield on similar bonds is 7.5%. What is the expected price of this bond, using the semiannual convention?

$25.19

The present value of a $100 three-year annuity due (first cash flow occurs today) discounted at a rate of 10% is equal to ________.

$273.55

Lily invested $10,000 seven years ago with an insurance company that has paid her 4 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the 7 years?

$3,194.79 6-month rate = 4%/2 = 2% = 0.02, Number of 6-month periods = 14 FV= 10,000(1.02)^14 = $13194.79 Interest earned = $13194.79- $10,000 = $3194.79

Your firm intends to finance the purchase of a new construction crane. The cost is $2,500,000. What is the size of the annual ordinary annuity payment if the loan is amortized over a ten-year period at a rate of 7.50%?

$364,214.82 PMT = PV / (1-1/[1+r]n)/r = $2,500,000 / (1-1/[1.075]10)/.075 = $364,214.82

Assume you just bought a new car and now have a car loan to repay. The amount of the principal is $22,000, the loan is at 6% APR, and the monthly payments are spread out over 6 years. What is the monthly loan payment?

$364.6

On your first through fifth birthdays your parents placed $2,000 into your college fund (five total deposits of $2,000 each). The account has earned an average of 8.5% per year until today, your twenty-first birthday. How much money is in the account today?

$43,714.09

Susan's goal is to retire with $500,000 in her retirement account. The local bank advertises an APR of 6% with monthly compounding on retirement fund accounts. If she retires in 30 years how much should Susan save each month to reach her goal?

$497.75 Monthly rate = 6%/12 = 0.5% =0.005, Number of months = 360, 500,000 = PMT [ (1.0005^360 - 1) / 0.005] PMT = $497.75

Assume a five-year equal payment amortization schedule with an annual interest rate of 7% and annual payments. If the beginning principal is $8,000, then the first interest payment will be how large?

$560.00 The first payment will be equal to the beginning balance times the annual interest rate = $8,000 × 0.07 = $560.00.

Your employer has agreed to place year-end deposits of $1,000, $2,000 and $3,000 into your retirement account. The $1,000 deposit will be one year from today, the $2,000 deposit two years from today, and the $3,000 deposit three years from today. If your account earns 5% per year, how much money will you have in the account at the end of year three when the last deposit is made?

$6,202.50 FV = Σ PV × (1 + r)n = $1,000 × (1.05)2 + $2,000 × (1.05)1 + $3,000 × (1.05)0 = $6,202.50.

You dream of endowing a chair in finance at the local university that will provide a salary of $250,000 per year forever, with the first cash flow to be one year from today. If the university promises to invest the money at a rate of 4% per year, how much money must you give the university today to make your dream a reality?

$6,250,000 PV = PMT/r = $250,000/.04 = $6,250,000

You dream of endowing a chair in finance at the local university that will provide a salary of $250,000 per year forever, with the first cash flow to be one year from today. If the university promises to invest the money at a rate of 4% per year, how much money must you give the university today to make your dream a reality?

$6,250,000 PV = PMT/r = $250,000/.04 = $6,250,000.

Assume that Ray is 20 years old and has 45 years for saving until he retires. He expects an APR of 6% on his investments. How much does he need to save if he puts money away monthly in equal end-of-the-month amounts to achieve a future value of $2,000,000 dollars in 45 years' time?

$725.69

The future value three years from today of a $200 three-year annuity due compounded at a rate of 10% is equal to ________.

$728.20

You have accumulated $1,200,000 for your retirement. How much money can you withdraw in equal annual beginning-of-the-year cash flows if you invest the money at a rate of 5% for thirty years?

$74,344.50

Creative Solutions Inc. has issued 10-year $1,000 face value, 8% annual coupon bonds, with a yield to maturity of 9.0%. The annual interest payment for the bond is ________.

$80 The annual interest or coupon payment is equal to the coupon rate multiplied by the par value of the bond. Here that is (0.08) × ($1,000) = $80.

Big House Nursery Inc. has issued 20-year $1,000 face value, 8% annual coupon bonds, with a yield to maturity of 10%. The current price of the bond is ________.

$829.73

The Cougar Corporation has issued 20-year semi-annual coupon bonds with a face value of $1,000. If the annual coupon rate is 10% and the current annual yield to maturity is 12%, what is the firm's current price per bond?

$849.54

Susan's goal is to retire with $1,000,000 in her retirement account. The local bank advertises an APR of 12% with monthly compounding on retirement fund accounts. If she retires in 40 years how much should Susan save each month to reach her goal?

$85 Monthly rate = 12%/12 = 1% =0.01, Number of months = 40*12=480 1,000,000 = PMT [ (1.01^480 - 1) / 0.01] PMT = $85

Five years ago, Simpson Warehouses Inc. issued twenty-five-year 10% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have risen and the yield to maturity on the Thompson bonds is now 12%. Given this information, what is the price today for a Thompson Tarps bond?

$850.61

Five years ago, Thompson Tarps Inc. issued twenty-five-year 10% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have risen and the annual yield to maturity on the Thompson bonds is now 12%. Given this information, what is the price today for a Thompson Tarps bond?

$850.61

Douglas Distributing Inc. has issued 30-year semiannual coupon bonds with a face value of $1,000. If the annual coupon rate is 6% and the yield to maturity today is 7%, what is the firm's current price per bond?

$875.28

TravelEasy Enterprises Inc. has issued 30-year semiannual coupon bonds with a face value of $1,000. If the annual coupon rate is 14% and the yield to maturity today is 15%, what is the firm's current price per bond?

$934.20

You put 20% down on a home with a purchase price of $250,000. The down payment is thus $50,000, leaving a balance owed of $200,000. A bank will loan you this remaining balance at 3.9% APR. You will make monthly end-of-the-period payments with a 30-year payment schedule. What is the monthly annuity payment under this schedule?

$943.34

You are running short of cash and really need to pay your rent. A friend suggests that you check out the local title pawn shop. At the shop they offer to loan you $1,000 if you pay them back $1,200 in one week. It seems like a good idea to you because you don't want to sell your car and you are sure you will be able to pay the money back in a week. What is the APR on this loan?

1040% (1200-1000)/1000=20% 20%*52=1040%

You are running short of cash and really need to pay your rent. A friend suggests that you check out the local title pawn shop. At the shop they offer to loan you $5,000 if you pay them back $6,000 in one week. It seems like a good idea to you because you don't want to sell your car and you are sure you will be able to pay the money back in a week. What is the APR on this loan?

1040% Weekly rate = (6000-5000)/5000 = 0.2 APR=0.2×52 = 10.40 = 1040%

You are running short of cash and really need to pay your rent. A friend suggests that you check out the local title pawn shop. At the shop they offer to loan you $2,000 if you pay them back $2,200 in one week. It seems like a good idea to you because you don't want to sell your car and you are sure you will be able to pay the money back in a week. What is the APR on this loan?

520% (2200-2000)/1000=10% 10%*52=52%

Your parents have an investment portfolio of $450,000, and they wish to take out cash flows of $60,000 per year as an ordinary annuity. How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%?

9.35 years 450,000=60,000(1-1/1.045^n)/0.045 1/1.045^n=0.6625 n=ln(1/0.6625)/ln1.045=9.35

Tony is offering Phil two repayment plans for a long overdue loan. Offer 1 is a visit from an enforcer and the debt is due in full at once. Offer 2 is to pay back $4,000 at the end of each year at 15% interest rate until the loan principal is paid off. Phil owes Tony $20,000. How long will it take for Phil to pay off the loan if he takes Offer 2?

9.92 years 20,000=4,000(1-1/1.15^n)/0.15 1/1.15^n=0.25 n=ln(1/0.25)/ln1.15=9.92

You are comparing two separate investments. Each one is for a period of 10 years and pays $2,500 a year. You require a 10 percent return on these investments. Investment A pays at the beginning of each year and investment B pays at the end of each year. Given this situation, which one of the following statements is accurate?

Investment A has both a higher present value and a higher future value than investment B

Which is greater, the present value of a five-year ordinary annuity of $300 discounted at 10%, or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

The second annuity because the cash flows are discounted at a 0% interest rate.

When quoting rates on loans, the "Truth in Lending Law" requires the bank to state the rate as an APR, effectively understating the true cost of the loan when interest is computed more often than once a year.

True

Lily invested $10,000 five years ago with an insurance company that has paid her 4 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the 5 years?

$2,189.94 6-month rate = 4%/2 = 2% = 0.02, Number of 6-month periods = 10 FV= 10,000(1.02)^10 = $12189.94 Interest earned = $12189.94- $10,000 = $2189.94

Suppose you invest $3,500 today, compounded semiannually, with an annual interest rate of 8.50%. What amount of interest will you have earned in one year?

$303.82 PV = $3,500, APR = 8.50%, periodic interest rate = r = APR/2 = 0.0425, (1.0425)2 = 1.086806. Multiplying this number times PV gives $3,803.82. Thus, the interest earned is $3,803.82 - $3,500 = $303.82.

Plimpton has an annuity due that pays $800 per year for 11 years. What is the present value of the cash flows if they are discounted at an annual rate of 7.50%?

$6,291.26

What is the EAR if the APR is 5% and compounding is quarterly?

Slightly above 5.09%