Bus1-170 Exam 2

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It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage?

$1,041,170.40 If you take out a 15-year mortgage, you will make 180 payments of $9,133.94, and your total payments will be $1,644,109.20 (180 x $9,133.94). The loan is for $850,000, so $794,109.20 of the payments goes toward interest. Meanwhile, a 30-year mortgage requires 360 payments of $7,459.11, and your total payments will be $2,685,279.60 (360 x $7,459.11). The loan is for $850,000, so $1,835,279.60 of the payments goes toward interest. Therefore, even though the 15-year mortgage costs $1,674.83 more per month, it retires the loan 15 years earlier, and you will save $1,041,170.40 ($1,835,279.60 - $794,109.20 = $ in interest payments compared to a 30-year mortgage).

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $550,000 loan at a fixed nominal interest rate of 9% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be $1,153.05 ?(Note: Round the final value of any interest rate used to four decimal places. )

$1,153.05

Olivia deposited $800 at her local credit union in a savings account at the rate of 9.4% paid as simple interest. She will earn interest once a year for the next 5 years. If she were to make no additional deposits or withdrawals, how much money would the credit union owe Olivia in 5 years?

$1,176.00 = 800 + (800 x 9.4% x 5)

Now, assume that Olivia's credit union pays a compound interest rate of 9.4% compounded annually. All other things being equal, how much will Olivia have in her account after 5 years?

$1,253.65

The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next five years: Year 1 250,000 Year 2 20,000 Year 3 180,000 Year 4 450,000 Year 5 550,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$1,255,617

Before deciding to deposit her money at the credit union, Olivia checked the interest rates at her local bank as well. The bank was paying a nominal interest rate of 9.4% compounded quarterly. If Olivia had deposited $800 at her local bank, how much would she have had in her account after 5 years?

$1,273.05

$1,388,431.80 9257.51x12x30 - 10801.51x12x15 (payments 30 years - payments 15 years)

Hailey plans to loan $1,000 to her friend, who will pay a simple interest rate of 8.6% every year for the loan. If no payments are made and no further borrowing occurs between them for 5 years, then how much money will Hailey's friend owe her?

$1,430.00 = 1000 + (1000 x 8.6% x 5)

Now, assume that Hailey's friend volunteers to pay compound interest instead of simple interest for her loan. If interest is accrued at 8.6% compounded annually, all other things being equal, how much money will Hailey's friend owe her in 5 years?

$1,510.60

Hailey has another investment option in the market that pays 8.6% nominal interest, but it's compounded quarterly. Keeping everything else constant, how much money will Hailey have in 5 years if she invests $1,000 in this fund?

$1,530.27

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $850,000 loan at a fixed nominal interest rate of 10% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be $1,674.83 ?(Note: Round the final value of any interest rate used to four decimal places. )

$1,674.83

Zoe deposited $900 in a savings account at her bank. Her account will earn an annual simple interest rate of 7%. If she makes no additional deposits or withdrawals, how much money will she have in her account in 13 years?

$1,719.00 = 900 + (900 x 7% x 13)

The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next six years: Year 1 400,000 Year 2 20,000 Year 3 180,000 Year 4 450,000 Year 5 750,000 Year 6 725,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 6.5%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$1,936,306

You bought an annuity selling at $14,112.74 today that promises to make equal payments at the beginning of each year for the next twelve years (N). If the annuity's appropriate interest rate (I) remains at 11.00% during this time, then the value of the annual annuity payment (PMT) is $1,958.33 .

$1,958.33 .

Another bank is also offering favorable terms, so Rahul decides to take a loan of $13,000 from this bank. He signs the loan contract at 5% compounded daily for 12 months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$13,666.48 Periodic Rate: I/Y = 5/365 N = 365 PV = -13,000 PMT = 0 FV = ?

Now, assume that Zoe's savings institution modifies the terms of her account and agrees to pay 7% in compound interest on her $900 balance. All other things being equal, how much money will Zoe have in her account in 13 years?

$2,168.86 = 900x [(1 + 7%)^13]

Suppose Zoe had deposited another $900 into a savings account at a second bank at the same time. The second bank also pays a nominal (or stated) interest rate of 7% but with quarterly compounding. Keeping everything else constant, how much money will Zoe have in her account at this bank in 13 years?

$2,218.36 EFF% = (1 + Inom/ M)^M - 1 M = 4 is the number of compounding periods per year. EFF% = (1 + INOM / 4)^4 - 1 = (1 + 0.07/ 4)^4 - 1 = 0.07185903, or 7.1859% FV = PV x (1+I)^n = 900 x (1 + 1.71859%)^13 = 2,218.36

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won $21,019,005.43 —assuming annual interest rate of 11.00%.

$21,019,005.43

Another bank is also offering favorable terms, so Rahul decides to take a loan of $22,000 from this bank. He signs the loan contract at 16% compounded daily for nine months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$24,804.82

Suppose you decide to deposit $24,000 in a savings account that pays a nominal rate of 12%, but interest is compounded daily. Based on a 365-day year, how much would you have in the account after four months? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$24,979.57 N = (4/12)x365 I/Y = 12/365 PV = -24,000 PMT = 0 FV =?

Ashley has a large and growing collection of animated movies. She wants to replace her old television with a new LCD model, so she has started saving for it. At the end of each year, she deposits $1,620 in her bank account, which pays her 10% interest annually. Ashley wants to keep saving for two years and then buy the newest LCD model that is available. Ashley's savings are an example of an annuity. How much money will Ashley have to buy a new LCD TV at the end of two years?

$3,402.00 (at the end of each year) $3,742.20 (at the beginning of each year) no immediate payment (PV = 0) payment every year as $1,620 (PMT = -1,620)

In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 5% annual interest rate, what is its value as of 2012 (386 years later)?

$3,624,771,902.22

Your grandfather wants to establish a scholarship in his father's name at a local university and has stipulated that you will administer it. As you've committed to fund a $15,000 scholarship every year beginning one year from tomorrow, you'll want to set aside the money for the scholarship immediately. At tomorrow's meeting with your grandfather and the bank's representative, you will need to deposit $333,333 (rounded to the nearest whole dollar) so that you can fund the scholarship forever, assuming that the account will earn 4.50% per annum every year. Oops! The bank representative just reported that he misquoted the available interest rate on the scholarship's account. Your account should earn 7.00%. The amount of your required deposit should be revised to $214,286. This suggests there is an inverse relationship between the interest rate earned on the account and the present value of the perpetuity.

$333,333 (Perpetuity) PV = payment/interest rate = 15,000/4.5% =333.333 $214,286 an inverse

ou've decided to buy a house that is valued at $1 million. You have $450,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $550,000 mortgage, and is offering a standard 30-year mortgage at a 9% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be $4,425.42 per month. (Note: Round the final value of any interest rate used to four decimal places.)

$4,425.42

You just won the lottery. Congratulations! The jackpot is $60,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won $46,532,071.09 —assuming annual interest rate of 5.00%.

$46,532,071.09

The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next three years: Year 1 100,000 Year 2 20,000 Year 3 480,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 6.5%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$508,898

In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4.5% annual interest rate, what is its value as of 2012 (386 years later)?

$574,247,818.82

$589,026.60

You bought an annuity selling at $5,816.51 today that promises to make equal payments at the beginning of each year for the next twelve years (N). If the annuity's appropriate interest rate (I) remains at 5.00% during this time, then the value of the annual annuity payment (PMT) is $625.00 .

$625.00

An ordinary annuity selling at $3,806.77 today promises to make equal payments at the end of each year for the next six years (N). If the annuity's appropriate interest rate (I) remains at 5.00% during this time, the annual annuity payment (PMT) will be $750.00 .

$750.00 PV = -3,806.77 FV =0

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with five years to maturity has a coupon rate of 4%. The yield to maturity (YTM) of the bond is 9.90%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note: $925,985.64 $771,654.70 $655,906.50 $486,142.46

$771,654.70

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with four years to maturity has a coupon rate of 3%. The yield to maturity (YTM) of the bond is 9.90%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note: $931,881.34 $660,082.61 $776,567.78 $489,237.70

$776,567.78

You just won the lottery. Congratulations! The jackpot is $10,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won $8,882,462.89 —assuming annual interest rate of 5.00%.

$8,882,462.89 Many lotteries express their lottery's jackpot as an amount equal to the total payments (PMT) that you will receive. In this case, it is $10,000,000, or $1,666,667 per year at the beginning of each year for six years. In reality, you have won far less—a fact that can be calculated as a simple PV problem. Because payments are received at the beginning of every year, set your calculator to BEGIN mode and solve as follows: N = 6 I = 5 FV = 0 PMT = 1,666,667 (10,000,000/6)

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with three years to maturity has a coupon rate of 3%. The yield to maturity (YTM) of the bond is 7.70%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note: $552,009.74 $744,775.04 $1,051,447.12 $876,205.93

$876,205.93

You've decided to buy a house that is valued at $1 million. You have $100,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $900,000 mortgage, and is offering a standard 30-year mortgage at a 12% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be $9,257.51 per month. (Note: Round the final value of any interest rate used to four decimal places.)

$9,257.51

Katie had a high monthly food bill before she decided to cook at home every day in order to reduce her expenses. She starts to save $850 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 9% annual interest. Katie's savings are an example of an annuity. If Katie decides to renovate her kitchen, how much would she have in her savings account at the end of eight years?

$9,374.20 (end) $10,217.88 (beginning)

Luana loves shopping for clothes, but considering the state of the economy, she has decided to start saving. At the end of each year, she will deposit $990 in her local bank, which pays her 10% annual interest. Luana decides that she will continue to do this for the next seven years. Luana's savings are an example of an annuity. How much will she save by the end of seven years?

$9,392.30 (end) $10,331.53 (beginning)

In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4% annual interest rate, what is its value as of 2012 (386 years later)?

$90,173,766.66 =24(1+4%)^386

Nicholai is willing to invest $30,000 for six years, and is an economically rational investor. He has identified three investment alternatives (A, B, and C) that vary in their method of calculating interest and in the annual interest rate offered. Since he can only make one investment during the six-year investment period, complete the following table and indicate whether Nicholai should invest in each of the investments. Note: When calculating each investment's future value, assume that all interest is earned annually. The final value should be rounded to the nearest whole dollar.

- A 8% simple interest $44,400 -> Yes - B 3% compound interest $35,822 -> No - C 5% compound interest $40,203 ->No

A local bank's advertising reads: "Give us $45,000 today, and we'll pay you $400 every year forever." If you plan to live forever, what annual interest rate will you earn on your deposit? 1.42% 0.89% 1.25% 0.71% Oops! When you went in to make your deposit, the bank representative said the amount of required deposit reported in the advertisement was incorrect and should have read $67,500. This revision, which will reduce the interest rate earned on your deposited funds, will adjust your earned interest rate to 0.59% .

0.89% reduce 0.59% .

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $900,000 loan at a fixed nominal interest rate of 12% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be $1,544.00 ?(Note: Round the final value of any interest rate used to four decimal places. )

1,544.00

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 10%. But the bank is compounding daily. What is the effective interest rate that Rahul would pay for the loan?

10.516%

Matthew needed money for some unexpected expenses, so he borrowed $3,878.06 from a friend and agreed to repay the loan in four equal installments of $1,250 at the end of each year. The agreement is offering an implied interest rate of 11.00% .

11.00% . PV = 3878.03

Joshua inherited an annuity worth $3,362.56 from his uncle. The annuity will pay him three equal payments of $1,400 at the end of each year. The annuity fund is offering a return of 12.00% .

12.00% . PV = -3,362.56

Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $500 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $4,500 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 8.5%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $5

15 years BEGIN mode I/Y = 8.5 PV = -4,500 PMT = 500 FV = 0 N =?

Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $750 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $7,000 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 8.9%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $7

17 years

Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $800 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $8,500 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 7.6%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $8

19 years

A local bank's advertising reads: "Give us $10,000 today, and we'll pay you $200 every year forever." If you plan to live forever, what annual interest rate will you earn on your deposit? 2.80% 2.00% 2.40% 3.20% Oops! When you went in to make your deposit, the bank representative said the amount of required deposit reported in the advertisement was incorrect and should have read $15,000. This revision, which will reduce the interest rate earned on your deposited funds, will adjust your earned interest rate to 1.33% .

2.00% reduce 1.33% .

Matthew's friend, Gregory, has hired a financial planner for advice on retirement. Considering Gregory's current expenses and expected future lifestyle changes, the financial planner has stated that once Gregory crosses a threshold of $2,909,046 in savings, he will have enough money for retirement. Gregory has nothing saved for his retirement yet, so he plans to start depositing $25,000 in a retirement fund at a fixed rate of 11.00% at the end of each year. It will take 25.15 years for Gregory to reach his retirement goal.

25.15 years

If a security currently worth $12,800 will be worth $16,843.93 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

4.00%

If a security currently worth $5,600 will be worth $6,299.24 three years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

4.00%

If the inflation rate was 2.60% and the nominal interest rate was 6.60% over the last year, what was the real rate of interest over the last year? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. Round intermediate calculations to four decimal places.

4.00% The nominal interest rate consists of the real rate of interest and inflation. In this case, the nominal interest rate is 6.60%, and the inflation rate is 2.60%. So the real rate of interest is 6.60% - 2.60% = 4.00%. The problem's instructions told you to ignore the cross-product term and just use arithmetic averages, but be aware that economists calculate this slightly differently (as you may recall from your economics courses). If you consider the cross-product terms and use geometric average rates, you would calculate the following: (1+ Real Rate)(1 + Inflation Rate) = (1 + Nominal Rate) (1+ Real Rate)(1 + 0.0260) = (1 + 0.066) Real Rate = 3.90%

Suppose you read an article about the Golden Gate Bridge and Highway District bonds. It includes the following information: Bridge Bonds Series A Dated 7-15-2005 4.375% Due 7-15-2055 @100.00 What is the coupon interest rate of this bond? 0.435% 4.375%

4.375%

If an investment of $30,000 is earning an interest rate of 8.00%, compounded annually, then it will take 4.50 years for this investment to reach a value of $42,415.85—assuming that no additional deposits or withdrawals are made during this time.

4.50 years

Michael inherited an annuity worth $7,105.97 from his uncle. The annuity will pay him six equal payments of $1,400 at the end of each year. The annuity fund is offering a return of 5.00% .

5.00% . PV = -7,105.97

Based on your calculations and understanding of semiannual coupon bonds, complete the following statement: When valuing a semiannual coupon bond, the time period variable(N) used to calculate the price of a bond reflects the number of 6-month periods remaining in the bond's life.

6-month

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 6%. But the bank is compounding semiannually. What is the effective interest rate that Rahul would pay for the loan?

6.090%

You want to invest $24,000 and are looking for safe investment options. Your bank is offering you a certificate of deposit that pays a nominal rate of 6% that is compounded quarterly. What is the effective rate of return that you will earn from this investment?

6.136%

If Eades Corp. issued new bonds today, what coupon rate must the bonds have to be issued at par? 6.84%

6.84% Exp: Eades Corp. is to issue new bonds at par, the new bonds must pay a coupon equal to their current YTM (6.84%). As a result, the new bonds also will have a YTM of 6.84%.

You've decided to buy a house that is valued at $1 million. You have $150,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $850,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be $7,459.11 per month. (Note: Round the final value of any interest rate used to four decimal places.)

7,459.11 You should think about this problem as having a loan period of 360 monthly periods (30 years x 12 months/year) instead of 30 years. Therefore, your $850,000 mortgage, (PV = -850,000) will be repaid using 360 monthly payments (N = 360) and its monthly payment will be based on the loan's monthly periodic interest rate (10% / 12 = 0.8333%, or I = 0.8333). At the end of the loan's life, it will be paid off, so there is no future value (FV = 0). Then, solve for the monthly payment (PMT) using a financial calculator as follows: N = 12x30 = 360 I/Y = 10/12 PV = -850,000 FV = 0 PMT = ?

7-15-2005

7-15-2055

Joshua's friend, Jamie, wants to go to business school. While his father will share some of the expenses, Jamie still needs to put in the rest on his own. But Jamie has no money saved for it yet. According to his calculations, it will cost him $39,846 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $4,200 at the end of every year in a mutual fund, from which he expects to earn a fixed 10% rate of return. It will take approximately 7.00 years for Jamie to save enough money to go to business school.

7.00 years

If an investment of $35,000 is earning an interest rate of 12.00%, compounded annually, then it will take 7.50 years for this investment to reach a value of $81,884.79—assuming that no additional deposits or withdrawals are made during this time.

7.50 years

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Badger Corp.'s bonds? 13 years 5 years 8 years 18 years

8 years

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Demed Inc.'s bonds? 18 years 5 years 13 years 8 years

8 years

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Eades Corp.'s bonds? 18 years 8 years 5 years 10 years

8 years Ex: The YTC is less than the YTM on Eades Corp.'s bonds. If interest rates remain constant, the firm will call the bonds. The bonds then have an expected remaining life of eight years. Remember that the YTM and YTC may not be what the investor receives, but they are what the issuer pays, so if the YTC is greater than the YTM, the issuer would not call the bonds, because doing so would be more expensive than just waiting for the bond to mature. The bond will only be called when the YTC is less than the YTM.

Michael's friend, Taylor, wants to go to business school. While his father will share some of the expenses, Taylor still needs to put in the rest on his own. But Taylor has no money saved for it yet. According to his calculations, it will cost him $49,487 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $5,000 at the end of every year in a mutual fund, from which he expects to earn a fixed 6% rate of return. It will take approximately 8.00 years for Taylor to save enough money to go to business school.

8.00 years

If a security currently worth $12,800 will be worth $18,807.40 five years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

8.00%

If an investment of $30,000 is earning an interest rate of 4.00%, compounded annually, then it will take 9.00 years for this investment to reach a value of $42,699.35—assuming that no additional deposits or withdrawals are made during this time.

9.00 years

Ordinary annuity

A 6% return that you could have earned if you had made a particular investment.

For example, assume Oliver wants to earn a return of 10.50% and is offered the opportunity to purchase a $1,000 par value bond that pays a 8.75% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value:

A Bond's semiannual coupon payment $43.75 B Bond's par value $1,000 C Semiannual required return 5.2500%

For example, assume Ethan wants to earn a return of 12.25% and is offered the opportunity to purchase a $1,000 par value bond that pays a 10.50% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value:

A Bond's semiannual coupon payment $52.50 B Bond's par value $1,000 C Semiannual required return 6.1250%

For example, assume Ella wants to earn a return of 8.00% and is offered the opportunity to purchase a $1,000 par value bond that pays a 14.00% coupon rate (distributed semiannually) with three years remaining to maturity. The following formula can be used to compute the bond's intrinsic value:

A Bond's semiannual coupon payment $70.00 B Bond's par value $1,000 C Semiannual required return4.0000%

Discounting

A cash flow stream that is created by a lease that requires the payment to be paid on the first of each month and a lease period of three years.

Time value of money

A cash flow stream that is created by a lease that requires the payment to be paid on the first of each month and a lease period of three years.

Time value of money

A cash flow stream that is created by an investment or loan that requires its cash flows to take place on the last day of each quarter and requires that it last for 10 years.

Discounting

A cash flow stream that is generated by a share of preferred stock that is expected to pay dividends every quarter indefinitely.

Ordinary annuity

A cash flow stream that is generated by a share of preferred stock that is expected to pay dividends every quarter indefinitely.

Discounting

A concept that maintains that the owner of a cash flow will value it differently, depending on when it occurs.

Perpetuity

A concept that maintains that the owner of a cash flow will value it differently, depending on when it occurs.

Which of the following is an example of an annuity? A job contract that pays an hourly wage based on the work done on a particular day A job contract that pays a regular monthly salary for three years

A job contract that pays a regular monthly salary for three years

Annual percentage rate

A loan in which the payments include interest as well as loan principal.

Annuity due

A loan in which the payments include interest as well as loan principal.

Which of the following is an example of an annuity?

A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time

Which of the following are characteristics of a perpetuity? Check all that apply. A perpetuity is a stream of regularly timed, equal cash flows that continues forever. The value of a perpetuity cannot be determined. A perpetuity is a stream of unequal cash flows. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

A perpetuity is a stream of regularly timed, equal cash flows that continues forever. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

Amortized loan

A process that involves calculating the current value of a future cash flow or series of cash flows based on a certain interest rate.

Amortization schedule

A rate that represents the return on an investor's best available alternative investment of equal risk.

Which of the following is an example of an annuity? A fund that invests in technology companies and distributes quarterly dividends for two out of four quarters per year but not always the same quarters A retirement fund set up to pay a series of regular payments

A retirement fund set up to pay a series of regular payments

Perpetuity

A schedule or table that reports the amount of principal and the amount of interest that make up each payment made to repay a loan by the end of its regular term.

Ordinary annuity

A series of equal (constant) cash flows (receipts or payments) that are expected to continue forever.

Amortized loan

A series of equal cash flows that occur at the beginning of each of the equally spaced intervals (such as daily, monthly, quarterly, and so on).

Annual percentage rate

A series of equal cash flows that occur at the end of each of the equally spaced intervals (such as daily, monthly, quarterly, and so on).

Time value of money

A series of equal cash flows that occur at the end of each of the equally spaced intervals (such as daily, monthly, quarterly, and so on).

Amortized loan

A table that reports the results of the disaggregation of each payment on an amortized loan, such as a mortgage, into its interest and loan repayment components.

Annual percentage rate

A table that reports the results of the disaggregation of each payment on an amortized loan, such as a mortgage, into its interest and loan repayment components.

Future value

A type of security that is frequently used in mortgages and requires that the loan payment contain both interest and loan principal.

Annuity due

A value that represents the interest paid by borrowers or earned by lenders, expressed as a percentage of the amount borrowed or invested over a 12-month period.

Which of the following statements about annuities are true? Check all that apply. An annuity is a series of equal payments made at fixed intervals for a specified number of periods. An annuity due earns more interest than an ordinary annuity of equal time. An annuity due is an annuity that makes a payment at the beginning of each period for a certain time period. Ordinary annuities make fixed payments at the beginning of each period for a certain time period.

An annuity is a series of equal payments made at fixed intervals for a specified number of periods. An annuity due earns more interest than an ordinary annuity of equal time. An annuity due is an annuity that makes a payment at the beginning of each period for a certain time period.

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $500 at the end of every six months An annuity that pays $1,000 at the beginning of each year An annuity that pays $500 at the beginning of every six months An annuity that pays $1,000 at the end of each year

An annuity that pays $1,000 at the beginning of each year

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $1,000 at the end of each year An annuity that pays $500 at the end of every six months An annuity that pays $500 at the beginning of every six months An annuity that pays $1,000 at the beginning of each year

An annuity that pays $1,000 at the beginning of each year

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $500 at the end of every six months An annuity that pays $1,000 at the end of each year An annuity that pays $1,000 at the beginning of each year An annuity that pays $500 at the beginning of every six months

An annuity that pays $1,000 at the beginning of each year

Based on your understanding of bond ratings and bond-rating criteria, which of the following statements is true? An indenture is a legal document that details the rights of bondholders. If the indenture includes a sinking funds provision, the bond will have more default risk. An indenture is a legal document that details the rights of bondholders. If the indenture includes a sinking funds provision, the bond will have less default risk.

An indenture is a legal document that details the rights of bondholders. If the indenture includes a sinking funds provision, the bond will have less default risk.

Future value

An interest rate that reflects the return required by a lender and paid by a borrower, expressed as a percentage of the principal borrowed.

Perpetuity

An interest rate that reflects the return required by a lender and paid by a borrower, expressed as a percentage of the principal borrowed.

Which of the following statements is true—assuming that no additional deposits or withdrawals are made?

An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time.

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 8.20%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? An investment that matures in six years An investment that matures in five years

An investment that matures in six years

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 9.60%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? An investment that matures in six years An investment that matures in five years

An investment that matures in six years

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 6.80%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? An investment that matures in five years An investment that matures in six years

An investment that matures in six years PV-5Years = $1,000/(1+0.068)^5 = $719.69 PV-6Years = = $1,000/(1+0.068)^6 = $673.86

Which of the following statements about annuities are true? Check all that apply. An ordinary annuity of equal time earns less interest than an annuity due. Annuities are structured to provide fixed payments for a fixed period of time. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due. When equal payments are made at the beginning of each period for a certain time period, they are treated as ordinary annuities.

An ordinary annuity of equal time earns less interest than an annuity due. Annuities are structured to provide fixed payments for a fixed period of time. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due.

Which of the following statements about annuities are true? Check all that apply. When equal payments are made at the end of each period for a certain time period, they are treated as an annuity due. An ordinary annuity of equal time earns less interest than an annuity due. When equal payments are made at the end of each period for a certain time period, they are treated as ordinary annuities. A perpetuity is a series of equal payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity.

An ordinary annuity of equal time earns less interest than an annuity due. When equal payments are made at the end of each period for a certain time period, they are treated as ordinary annuities. A perpetuity is a series of equal payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity.

Aakash borrowed some money from his friend to start a new business. He promises to pay his friend $2,650 every year for the next five years to pay off his loan along with interest.

Annuity Payments

British consols are British government bonds that promise to make payments of a specified amount at regular intervals to the bearer forever.

Annuity Payments

You deposit a certain equal amount of money every year into your pension fund.

Annuity Payments

You have committed to deposit $600 in a fixed interest-bearing account every quarter for four years.

Annuity Payments

You recently moved to a new apartment and signed a contract to pay monthly rent to your landlord for a year.

Annuity Payments

You signed up to make a monthly payment of $10 for one year for a lifetime tosubscription to your favorite magazine.

Annuity Payments

Which feature of a bond contract allows the issuer to redeem a bond issue immediately in its entirety at an amount greater than par value prior to maturity? Deferred call provision Put provision Call provision Sinking fund provision

Call provision

Which feature of a bond contract allows the issuer to redeem a bond issue immediately in its entirety at an amount greater than par value prior to maturity? Sinking fund provision Put provision Call provision Convertible provision

Call provision

Which type of bonds offer a higher yield? Noncallable bonds Callable bonds

Callable bonds

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? Simple interest?

Compound interest? FV = PV x (1 + I)^N Simple interest? FV = PV + (PV x I x N)

Innovative Energy LLC is a start-up company that just raised $100,000 to conduct a third-party feasibility study on its business model. The company agreed to treat the $100,000 investment as debt at 10% interest rate; however, the investor has the right to exchange the debt for common stock during the company's next financing round. Which of the following terms best describes the $100,000 investment? Warrant Convertible bond

Convertible bond

Which of the following best describes the difference between a convertible bond and a warrant? Convertible bonds give the investor the option to exchange bonds for shares at a certain price, whereas warrants give the investor the option to buy shares at a certain price. Convertible bonds give the investor the option to buy shares at a certain price, whereas warrants give the investor the option to exchange bonds for shares at a certain price.

Convertible bonds give the investor the option to exchange bonds for shares at a certain price, whereas warrants give the investor the option to buy shares at a certain price.

Smith Corporation 6% Irwin Incorporated 12% Johnson, LLC 9%

Curve A Irwin Incorporated Curve B Johnson, LLC Curve C Smith Corporation

Irwin, LLC 6% Johnson Corporation 12% Smith Incorporated9%

Curve A Johnson Corporation Curve B Smith Incorporated Curve C Irwin, LLC

Johnson Incorporated 6% Smith, LLC 12% Irwin Corporation 9%

Curve A Smith, LLC Curve B Irwin Corporation Curve C Johnson Incorporated

These bonds are not backed by any physical collateral. They are backed by the reputation and creditworthiness of the issuing company.

Debentures

These bonds are traded in the bond markets based on investors' belief that the issuer will not default on the repayment. These bonds have no collateral and usually offer higher yields.

Debentures

It is based on the bond's rating; the higher the rating, the lower the premium added, thus lowering the interest rate.

Default risk premium - DRP

This is the difference between the interest rate on a US Treasury bond and a corporate bond of the same profile—that is, the same maturity and marketability.

Default risk premium - DRP

This is the premium added as a compensation for the risk that an investor will not get paid in full.

Default risk premium - DRP

Which term is used to describe a call provision in which the issuer is prevented from calling a portion or the entire issue for several years during the early years of the bond issue? Sinking fund provision Declining call provision Deferred call provision

Deferred call provision

Discounting is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.

Discounting

Based on your understanding of bond ratings and bond-rating criteria, which of the following statements is true? During a period of economic growth and in an optimistic environment, the yield spread between US government bonds and corporate bonds could be higher than during an economic recession and a pessimistic environment. During an economic recession and in a pessimistic environment, the yield spread between US government bonds and corporate bonds could be higher than during good economic times.

During an economic recession and in a pessimistic environment, the yield spread between US government bonds and corporate bonds could be higher than during good economic times.

Actions that lower short-term interest rates will always lower long-term interest rates.

False

After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.

False

Assuming all else is equal, the shorter a bond's maturity, the more its price will change in response to a given change in interest rates

False

If the Fed injects a huge amount of money into the markets, inflation is expected to decline, and long-term interest rates are expected to rise.

False

When the economy is weakening, the Fed is likely to increase short-term interest rates.

False

Which of the following is true about finding the present value of cash flows?

Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return.

Consider the case of an investor, Nazim: Nazim wants to include putable bonds in his investment portfolio. Nazim is likely to put the bonds when: He is in need of cash. He expects to use the cash when the bond matures.

He is in need of cash.

Nazim wants to include putable bonds in his investment portfolio. Nazim is likely to put the bonds when: He expects to use the cash when the bond matures. He is in need of cash.

He is in need of cash.

Firms require capital to invest in productive opportunities. The best firms with the most profitable opportunities can attract capital away from inefficient firms with less profitable opportunities. Investors supply firms with capital at a cost called the interest rate. The interest rate that investors require is determined by several factors, including the availability of production opportunities, the time preference for current consumption, risk, and inflation. Suppose the Federal Reserve (the Fed) decides to tighten credit by contracting the money supply. Use the following graph by moving the black X to show what happens to the equilibrium level of borrowing and the new equilibrium interest rate.

If the Fed contracts the money supply, less capital is available to be invested. As a result, firms are competing for fewer funds to invest in their production opportunities. The supply of capital decreases, and the supply curve shifts to the left. The new equilibrium shows that $3 billion of capital will be available and borrowed at an interest rate of 12.0%.

Which of the following statements is not true about mortgages? Every payment made toward an amortized loan consists of two parts—interest and repayment of principal. Mortgages are examples of amortized loans. If the payment is less than the interest due, the ending balance of the loan will decrease. The ending balance of an amortized loan contract will be zero.

If the payment is less than the interest due, the ending balance of the loan will decrease.

A 10-year bond with a 9% annual coupon has a yield to maturity of 8%. Which of the following statements is CORRECT? If the yield to maturity remains constant, the bond's price one year from now will be higher than its current price The bond is selling below its par value. The bond is selling at a discount. If the yield to maturity remains constant, the bond's price one year from now will be lower than its current price. 4. 5. The bond's current yield is greater than 9%.

If the yield to maturity remains constant, the bond's price one year from now will be lower than its current price. 4. 5.

Which of the following statements is true—assuming that no additional deposits or withdrawals are made?

If you invest $1 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000.

Which of the following are characteristics of a perpetuity? Check all that apply. The principal amount of a perpetuity is repaid as a lump-sum amount. A perpetuity continues for a fixed time period. In a perpetuity, returns—in the form of a series of identical cash flows—are earned. A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future.

In a perpetuity, returns—in the form of a series of identical cash flows—are earned. A perpetuity is a series of regularly timed, equal cash flows that is assumed to continue indefinitely into the future.

Consider the following scenario: Due to recent political and economic events, general prices of goods and services are expected to increase significantly over the next five years. You were about to purchase a five-year bond. You now require a higher return on the bond than you did before you found out about these expected price increases. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Time preferences for consumption Risk Inflation

Inflation

Over the past several years, Germany, Japan, and Switzerland have had lower interest rates than the United States due to lower values of this premium.

Inflation premium - IP

This is the premium added to the real risk-free rate to compensate for a decrease in purchasing power over time.

Inflation premium - IP

This is the premium added to the risk-free rate that reflects the average sustained increase in the general level of prices for goods and services expected over the security's entire life.

Inflation premium - IP

The graph's yield curve is referred to as a humped yield curve. Based on the yield curve shown, which of the following statements is true? Interest rates on medium-term maturities are higher than rates on long- and short-term maturities. A market with a yield curve as shown on the graph has higher rates on debt securities that mature within 10 to 30 years than those with maturities of less than 1 to 5 years.

Interest rates on medium-term maturities are higher than rates on long- and short-term maturities.

The graph's yield curve represents a downward-sloping yield curve. Based on the yield curve shown, which of the following statements is true? Interest rates on short-term maturities are higher than rates on medium- and long-term maturities. If inflation in the future is expected to increase, the yield curve on US Treasuries is likely to be downward sloping.

Interest rates on short-term maturities are higher than rates on medium- and long-term maturities.

The graph's yield curve is referred to asa normal yield curve. Based on the yield curve shown, which of the following statements is true? Interest rates on short-term maturities are lower than rates on long-term maturities. Corporate bond yield curves are lower than US Treasury bond yield curves.

Interest rates on short-term maturities are lower than rates on long-term maturities.

Which of the following statements is true—assuming that no additional deposits or withdrawals are made?

It takes 14.21 years for $500 to double if invested at an annual rate of 5%.

All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 8%, or 16%. Identify the interest rate that corresponds with each line.

Line A: 16% Line B: 8% Line C: 0%

All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 12%, or 23%. Identify the interest rate that corresponds with each line.

Line A: 23% Line B: 12% Line C: 0%

In January 2009, American electronics retailer Circuit City Inc. closed all of its stores and sold all of its merchandise. Source: "Circuit City to Shut Down." CNN Money. Cable News Network, n.d. Web. August 31, 2010. http://money.cnn.com/2009/01/16/news/companies/circuit_city This is an example of: Liquidation Reorganization

Liquidation

It is based on the bond's marketability and trading frequency; the less frequently the security is traded, the higher the premium added, thus increasing the interest rate.

Liquidity risk premium - LP

This is the premium added to the equilibrium interest rate on a security that cannot be bought or sold quickly enough to prevent or minimize loss.

Liquidity risk premium - LP

This premium is added when a security lacks marketability, because it cannot be bought and sold quickly without losing value.

Liquidity risk premium - LP

As interest rates rise, bond prices fall, and as interest rates fall, bond prices rise. Because interest rate changes are uncertain, this premium is added as a compensation for this uncertainty.

Maturity risk premium - MRP

This is the premium that reflects the risk associated with changes in interest rates for a long-term security.

Maturity risk premium - MRP

Which of the following statements is not true about mortgages? Mortgages always have a fixed nominal interest rate. The payment allocated toward principal in an amortized loan is the residual balance—that is, the difference between total payment and the interest due. Mortgages are examples of amortized loans. The ending balance of an amortized loan contract will be zero.

Mortgages always have a fixed nominal interest rate.

Which of the following statements is not true about mortgages? The payment allocated toward principal in an amortized loan is the residual balance—that is, the difference between total payment and the interest due. Mortgages are examples of amortized loans. The ending balance of an amortized loan contract will be zero. Mortgages always have a fixed nominal interest rate.

Mortgages always have a fixed nominal interest rate.

Which of the following factors could be responsible for the change in demand shown in the graph? The Federal Reserve (the Fed) decided to relax its monetary policy and expanded the money supply. Households began saving a greater percentage of their income. New technological advances opened up more production opportunities for businesses. Expected inflation decreased.

New technological advances opened up more production opportunities for businesses.

An investor can invest money with a particular bank and earn a stated interest rate of 11.00%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Nominal rate 11.00% Periodic rate 2.75% Effective annual rate 11.46%

An investor can invest money with a particular bank and earn a stated interest rate of 6.60%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Nominal rate 6.60% Periodic rate1.65% Effective annual rate6.77% It is important to know proper interest rate terminology when considering investments. This investment has a nominal interest rate of 6.60%. A nominal rate is also called the annual percentage rate. Therefore, the nominal interest rate (IIII) is 6.60%. Interest is compounded (or paid) quarterly, so there are four periods per year. The periodic interest rate is the interest earned each period, and it is calculated by dividing the nominal interest rate by the number of periods. The periodic interest rate in this example is I = 6.60% / 4 = 1.65%. The effective annual rate is the interest actually being earned by the investment. If interest is compounded more than once per year, the effective annual rate is greater than the nominal interest rate, because the investment earns interest on the principal as well as on the interest previously earned. The effective annual rate of this investment is solved using the following equation: EFF%=[1+(I / M)]^M−1 In this equation, IIII is the nominal interest rate, and M is the number of compounding periods per year. Remember, in this equation, the interest rate must be expressed in decimal form. Solve for the effective rate as follows: EFF%=[1 + (0.06600 / 4)]^4 - 1 = 6.77%

It is calculated by adding the inflation premium to r*.

Nominal risk-free rate - rRF

This is the rate for a riskless security that is exposed to changes in inflation.

Nominal risk-free rate - rRF

This is the rate on a Treasury bill or a Treasury bond.

Nominal risk-free rate - rRF

As the name suggests, convertible bonds allow the owner the option to convert the bonds into a fixed number of shares of common stock. Which of the following are most likely to have higher yields? Convertible bonds Nonconvertible bonds

Nonconvertible bonds

Amortization schedule

One of the four major time value of money terms; the amount to which an individual cash flow or series of cash payments or receipts will grow over a period of time when earning interest at a given rate of interest.

Which of the following is true about present value calculations?

Other things remaining equal, the present value of a future cash flow decreases if the discount rate increases.

Which of the following is true about present value calculations?

Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases.

Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of the following equations can be used to solve for the present value of an ordinary annuity?

PMT x {1 - [1/(1 + r)^n]}/r

PMT x {[(1 + r)^n - 1]/r} x (1 + r)

PMT/r

5% coupon bond paying semi-annual payments 11 years until maturity and currently selling for $989 What is the yield to maturity?

PV = -989 FV = 1000 I/Y = ? 2.5661 N = 11x2 PMT = 50/2 PMT = countpon rate x face value = 0.05 x 1000 = 50 YTM = 2.5661 x 2 = 5.1322%

You want to retire in 40 years with 1M in the bank. You can save $350/month at the end of each month. What annual percentage rate (APR) do you need to earn to achieve this goal? What is your effective rate (EAR)?

PV = 0 FV = 1,000,000 I/Y = ? = 0.61 N = 40 x 12 PMT = -350 APR = 0.61 x 12 = 7.32% EAR = (1 + 1/40)^40 - 1 = 7.587%

You will receive $500 today and every month for the next 20 years. You will receive this payment at the beginning of the month. Assume you can earn 5% on this annuity. How much is it worth? What is the value if the annuity pays at the end of the month? What is the difference between the two annuities?

PV = ? = -76,078.3 FV = 0 I/Y = 5/12 N = 20x12 PMT = 500 -75762.63 76,078.3 - 75762.63 = 315.67

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,500?

PV = PMT/r 1500 = PMT/6.5% -> PMT = 97.5

The Cowboys just signed a new rookie to a 5 year contract with a 10M signing bonus and $292,000 to be paid per month. Assume an 8% discount rate. What is his contract worth?

PV =? FV = 0 I/Y = 8/12 N = 5x12 PMT = + 292,000 Contract Worth = 14,400,982.53 + 10,000,000 = 24,400,982,53

Consider the case of an investor, Nazim: Nazim wants to include bonds in his investment portfolio, but he wants the option to sell the bond to the issuer at a specified price on a certain date before the maturity of the bond. Which of the following bond redemption features should he pick? Warrants Putable bond

Putable bond

It changes over time, depending on the expected rate of return on productive assets exchanged among market participants and people's time preferences for consumption.

Real risk-free rate - r*

This is the rate for a short-term riskless security when inflation is expected to be zero.

Real risk-free rate - r*

This is the rate on short-term US Treasury securities, assuming there is no inflation.

Real risk-free rate - r*

Frank Barlowe is retiring soon, so he's concerned about his investments providing him with a steady income every year. He's aware that if interest rates increase , the potential earnings power of the cash flow from his investments will increase. In particular, he is concerned that a decline in interest rates might lead to less annual income from his investments. What kind of risk is Frank most concerned about protecting against?

Reinvestment risk

In December 2008, Hawaiian Telcom took action to strengthen its balance sheet by reducing debt. Although the company continued to operate, its creditors could not collect their debts or loan payments that were due prior to the legal action that the company took. However, on November 30, 2009, the company had $75 million in cash on hand. This is an example of: Liquidation Reorganization

Reorganization

In May 2009, General Motors started closing 2,600 of its retail outlets and finally filed for bankruptcy in June. It emerged from the bankruptcy protection by July 2009, after it received funding from the US government, the Canadian government, United Automobile Workers Union, and GM bondholders. Source: Farfan, Barbara. "General Motors Chapter 11 Bankruptcy Overview and Details." About.com, Retail Industry. About.com, n.d. Web. August 31, 2010. http://retailindustry.about.com/od/americanretailhistory/a/GM_chapter_11_bankruptcy_details.htm This is an example of: Liquidation Reorganization

Reorganization

Consider the following scenario: A friend comes to you and asks you to invest in his business instead of investing in Treasury bonds. You think he has a good business model, so you tell him you are willing to invest as long as the expected return on the investment is at least four times the return you would have received on the Treasury bonds. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Risk Inflation Time preferences for consumption

Risk

These bonds are backed by real estate holdings and equipment, and if a company goes bankrupt, the collateral can be sold off to compensate for the default. These bonds, more so than other collateralized securities, have prior claims over assets.

Senior mortgage bonds

These bonds are collateralized securities with first claims in the event of bankruptcy.

Senior mortgage bonds

Which tend to be more volatile, short- or long-term interest rates? Short-term interest rates Long-term interest rates

Short-term interest rates

Based on the preceding information, which of the following statements are true? Check all that apply. The current yield for Johnson Corporation's bonds is between 0% and 9%. Smith Incorporated's bonds are selling at par. The current yield for Johnson Corporation's bonds is greater than 9%. Johnson Corporation's bonds have the highest expected total return.

Smith Incorporated's bonds are selling at par. The current yield for Johnson Corporation's bonds is greater than 9%.

These bonds are considered the riskiest of all corporate bonds and thus offer the highest interest rates.

Subordinated debentures

These bonds have a claim on assets only after senior debt has been paid in full.

Subordinated debentures

Yield to maturity (YTM) is the rate of return expected from a bond held until its maturity date. However, the YTM equals the expected rate of return under certain assumptions. Which of the following is one of those assumptions? The bond will not be called. The bond has an early redemption feature.

The bond will not be called.

Based on the preceding information, which of the following statements are true? Check all that apply. The bonds have the same expected total return. Johnson Incorporated's bonds have the highest expected total return. The expected capital gains yield for Smith, LLC's bonds is negative. The expected capital gains yield for Smith, LLC's bonds is greater than 12%.

The bonds have the same expected total return. The expected capital gains yield for Smith, LLC's bonds is negative.

Future value

The concept that states that the timing of the receipt or payment of a cash flow will affect its value to the holder of the cash flow.

Which of the following are characteristics of a perpetuity? Check all that apply. The value of a perpetuity cannot be determined. A perpetuity is a stream of unequal cash flows. The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

Based on the preceding information, which of the following statements are true? Check all that apply. The expected capital gains yield for Smith Corporation's bonds is positive. Johnson, LLC's bonds are a better investment than Irwin Incorporated's bonds. All of the bonds will have the same value when they reach maturity. Irwin Incorporated's bonds are a better investment than Smith Corporation's bonds.

The expected capital gains yield for Smith Corporation's bonds is positive. All of the bonds will have the same value when they reach maturity.

Opportunity cost of funds

The name given to the amount to which a cash flow, or a series of cash flows, will grow over a given period of time when compounded at a given rate of interest.

The probability of default is zero.

Annuity due

The process of determining the present value of a cash flow or series of cash flows to be received or paid in the future.

Opportunity cost of funds

The process of determining the present value of a cash flow or series of cash flows to be received or paid in the future.

Which of the following investments that pay will $10,000 in 5 years will have a higher price today? The security that earns an interest rate of 15.00%. The security that earns an interest rate of 10.00%.

The security that earns an interest rate of 10.00%.

Which of the following investments that pay will $18,500 in 5 years will have a higher price today? The security that earns an interest rate of 8.25%. The security that earns an interest rate of 5.50%.

The security that earns an interest rate of 5.50%.

Which of the following investments that pay will $15,500 in 8 years will have a lower price today?

The security that earns an interest rate of 8.25%.

Which of the following investments that pay will $15,500 in 8 years will have a lower price today? The security that earns an interest rate of 5.50%. The security that earns an interest rate of 8.25%.

The security that earns an interest rate of 8.25%. PV = FV/[(1 + I)^N]

The process for converting present values into future values is called [compounding] . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?

The trend between the present and future values of an investment

Consider the following scenario: Your accountant has convinced you that you should invest your bonus from this year into your retirement account—instead of buying a new sports car—because of the high expected return on the investment. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Time preferences for consumption Inflation Risk

Time preferences for consumption

Which of the following types of bonds have the least default risk? Corporate bonds Treasury bonds Municipal bonds

Treasury bonds

Which of the following statements about Treasury bonds is the most accurate? Treasury bonds are completely riskless. Treasury bonds are not completely riskless, since their prices will decline when interest rates rise. Treasury bonds have a very small amount of default risk, so they are not completely riskless.

Treasury bonds are not completely riskless, since their prices will decline when interest rates rise.

After the end of the second year and all other factors remaining equal, a future value based on compound interest will exceed a future value based on simple interest.

True

All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.

True

All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound interest.

True

Assuming all else is equal, long-term securities are exposed to higher interest rate risk than short-term securities

True

Assuming all else is equal, short-term securities are exposed to higher reinvestment risk than long-term securities.

True

Countries with strong balance sheets and declining budget deficits tend to have lower interest rates.

True

During recessions, short-term interest rates decline more sharply than long-term interest rates.

True

During the credit crisis of 2008, investors around the world were fearful about the collapse of real estate markets, shaky stock markets, and illiquidity of several securities in the United States and several other nations. The demand for US Treasury bonds increased, which led to a rise in their price and a decline in their yields.

True

Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest.

True

Long-term interest rates are not as sensitive to booms and recessions as are short-term interest rates.

True

The Federal Reserve Board has a significant influence over the level of economic activity, inflation, interest rates in the United States.

True

The Federal Reserve's ability to use monetary policy to control economic activity in the United States is limited because US interest rates are highly dependent on interest rates in other parts of the world.

True

The larger the federal deficit, other things held constant, the higher are interest rates.

True

The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods.

True

When the Fed increases the money supply, short-term interest rates tend to decline.

True

When the economy is weakening, the Fed is likely to decrease short-term interest rates.

True

Based on your understanding of bond ratings and bond-rating criteria, which of the following statements is true? US government bonds usually have the lowest yields in the bond markets. BBB bonds usually have the lowest yields in the bond markets.

US government bonds usually have the lowest yields in the bond markets.

Amit receives quarterly dividends from his investment in a high-dividend yield, index exchange-traded fund.

Uneven Cash Flows

Debbie has been donating 10% of her salary at the end of every year to charity for the last three years. Her salary increased by 15% every year in the last three years.

Uneven Cash Flows

Franklinia Venture Capital (FVC) invested in a budding entrepreneur's restaurant. The restaurant owner promises to pay FVC 10% of the profit each month for the next 10 years.

Uneven Cash Flows

SOE Corp. hires an average of 10 people every year and matches the contribution of each employee toward his or her retirement fund.

Uneven Cash Flows

Shania bought a new dress for her brother's wedding for $450. She negotiated a deal with the retailer in which she would pay for the dress in three installments of $250, $100, and $100 over the next three months.

Uneven Cash Flows

You receive interest earnings from variable deposits in a regular interest-bearing savings account.

Uneven Cash Flows

Issuers can gradually reduce the outstanding balance of a bond issue by using a sinking fund account into which they deposit a specified amount of money each year. To operationalize the sinking fund provision of an indenture, issuers can (1) purchase a portion of the debt in the open market or (2) call the bonds if they contain a call provision. Under what circumstances would a firm be more likely to buy the required number of bonds in the open market as opposed to using one of the other procedures? When interest rates are higher than they were when the bonds were issued When interest rates are lower than they were when the bonds were issued

When interest rates are higher than they were when the bonds were issued

When are issuers more likely to call an outstanding bond issue? When interest rates are lower than they were when the bonds were issued When interest rates are higher than they were when the bonds were issued

When interest rates are lower than they were when the bonds were issued

Given your computation and conclusions, which of the following statements is true? A bond should trade at a par when the coupon rate is greater than Ella's required return. When the coupon rate is greater than Ella's required return, the bond's intrinsic value will be less than its par value. When the coupon rate is greater than Ella's required return, the bond should trade at a premium. When the coupon rate is greater than Ella's required return, the bond should trade at a discount.

When the coupon rate is greater than Ella's required return, the bond should trade at a premium.

Given your computation and conclusions, which of the following statements is true? When the coupon rate is greater than Ethan's required return, the bond should trade at a discount. A bond should trade at a par when the coupon rate is greater than Ethan's required return. When the coupon rate is greater than Ethan's required return, the bond should trade at a premium. When the coupon rate is greater than Ethan's required return, the bond's intrinsic value will be less than its par value.

When the coupon rate is greater than Ethan's required return, the bond should trade at a premium.

Given your computation and conclusions, which of the following statements is true? When the coupon rate is greater than Oliver's required return, the bond should trade at a premium. A bond should trade at a par when the coupon rate is greater than Oliver's required return. When the coupon rate is greater than Oliver's required return, the bond's intrinsic value will be less than its par value. When the coupon rate is greater than Oliver's required return, the bond should trade at a discount.

When the coupon rate is greater than Oliver's required return, the bond should trade at a premium.

Based on the information given in the following statement, answer the questions that follow: In July 2009, Hungary successfully issued 1 billion euros in bonds. The transaction was managed by Citigroup. Who is the issuer of the bonds? The Hungarian government Hungary Bank Citigroup What type of bonds are these? Government bonds Municipal bonds Corporate bonds

Who is the issuer of the bonds? The Hungarian government What type of bonds are these? Government bonds

Based on the information given in the following statement, answer the questions that follow: New York City issued a general obligation bond for a canal in 1812. It was the first formal debt instrument with a fixed repayment schedule issued by a city. Who is the issuer of the bonds? Federal Reserve Bank of New York Bank of New York The New York City government What type of bonds are these? Municipal bonds Treasury bonds Corporate bonds

Who is the issuer of the bonds? The New York City government What type of bonds are these? Municipal bonds

Based on the information given in the following statement, answer the questions that follow: In July 2009, Walmart sold 100 billion yen of five-year samurai bonds. Lead managers in the deal were Mizuho Securities, BNP Paribas, and Mitsubishi UFJ Securities. Who is the issuer of the bonds? BNP Paribas Walmart Mitsubishi UFJ Securities What type of bonds are these? Municipal bonds Corporate bonds Government bonds

Who is the issuer of the bonds? Walmart What type of bonds are these? Corporate bonds

Eades Corp. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1,220.35. However, Eades Corp. may call the bonds in eight years at a call price of $1,060. What are the YTM and the yield to call (YTC) on Eades Corp.'s bonds? Value YTM 6.84% YTC 6.05%

YTM 6.84% YTC 6.05%

Investments and loans base their interest calculations on one of two possible methods: the [simple] interest and the [compound] interest methods. Both methods apply three variables—the amount of principal, the interest rate, and the investment or deposit period—to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.

[simple] compound

Smith Corporation just registered and issued its bonds, which will be sold in the bond market for the first time. Smith Corporation's bonds would be referred to as a new issue .

a new issue .

What happens to the PV of a set amount to be received in 10 years if your rate of return decreases? a) The PV increases b) The PV decreases c) The PV doesn't change d) The PV goes to infinity

a) The PV increases

Kempton Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 11% annual coupon payment, and their current price is $1,185. The bonds may be called in 5 years at 109% of face value (Call price = $1,090). a)What is the yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places. b)What is the yield to call if they are called in 5 years? Do not round intermediate calculations. Round your answer to two decimal places. c)Which yield might investors expect to earn on these bonds? Why? I. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC. II. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM. III. Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC. IV. Investors wo

a)PV = -1185 FV = 1000 I/Y = ? 8.22 N = 10 PMT = 0.11x1000 = 110 b)PV = -1185 FV = 1090 I/Y = ? 7.91 N = 5 PMT = 110 c) II. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.

What happens to the PV of a set amount if the length of time shrinks, but the rate stays the same? a) The PV increases b) The PV decreases c) The PV doesn't change d) The PV goes to infinity

b) The PV decreases

A bond's call provision gives the issuer the right to call, or redeem, a bond at specific times and under specific conditions.

call provision

compounding The inflation rate indicating the change in average prices

A bond's convertibility provision allows a bondholder or preferred stockholder to convert their bond or preferred share, respectively, into a specified number or value of common shares.

convertibility provision

A bond's coupon payment refers to the interest payment or payments paid by a bond.

coupon payment

A bond issuer is said to be in default if it does not pay the interest or the principal in accordance with the terms of the indenture agreement or if it violates one or more of the issue's restrictive covenants.

default

The mathematics of bond valuation imply a predictable relationship between the bond's coupon rate, the bondholder's required return, the bond's par value, and its intrinsic value. These relationships can be summarized as follows: •When the bond's coupon rate is equal to the bondholder's required return, the bond's intrinsic value will equal its par value, and the bond will trade at par. •When the bond's coupon rate is greater than the bondholder's required return, the bond's intrinsic value will exceed its par value, and the bond will trade at a premium. •When the bond's coupon rate is less than the bondholder's required return, the bond's intrinsic value will be less than its par value, and the bond will trade at a discount.

exceed a discount

A bond's face or maturity value is generally $1,000 and represents the amount borrowed from the bond's first purchaser.

face or maturity value

If the coupon interest rate is 4.375% for the first six months and changes to a rate equal to the 10-year Treasury bond rate plus 1.3% thereafter, the bond is called a floating-rate bond.

floating-rate

Nazim also recently bought bonds with a clause stating that interest will be paid only when the company has enough earnings to pay for it. Nazim has invested in income bonds .

income bonds

The following graph shows the supply of and demand for capital in a market over the last year. You can see that the demand for capital has increased over the last year (the demand curve shifted to the right). Place the black X at the equilibrium interest rate and the quantity of capital. The market interest rate increased by 2.0%, and the amount of capital borrowed increased by $2.0 billion.

increased 2.0% Ex: The market interest rate is the rate at which the supply of capital equals the demand for capital. Place the black X on the point where the supply of and new demand for capital intersect. Last year, the market interest rate was 10.0%, but it has increased to 12.0%. The amount of capital exchanged increased from $8.0 billion to $10.0 billion.

The contract that describes the terms of a borrowing arrangement between a firm that sells a bond issue and the investors who purchase the bonds is called the indenture .

indenture

Nazim also recently bought bonds that have their interest rate tied to the consumer price index (CPI) so that he will be protected if inflation rates increase. Nazim has invested in indexed bonds .

indexed bonds .

The entity that promises to make the interest and maturity payments for a bond issue is called the issuer .

issuer

A bond's par value refers to its face value and the amount of money that the issuing entity borrows and promises to repay on the maturity date.

par value

Nazim also recently bought bonds with a clause stating that interest will be paid based on the inflation rate. When the inflation rate increases, the interest on the bonds will also increase. Nazim has invested in purchasing power bonds .

purchasing power bonds .

You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.2%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums: Inflation premium = 3.00% ▪ Liquidity premium = 0.8% ▪ Maturity risk premium = 1.40% ▪ Default risk premium = 2.90% On the basis of these data, what is the real risk-free rate of return? Round your answer to two decimal places.

r = r* + IP + LP + DRP + MRP For treasury, LP = DRP = 0 For shorterm, MRP = 0 -> 5.2 = r*+3 r* = 5.2 - 3 = 2.2%

A Treasury bond that matures in 10 years has a yield of 4.75%. A 10-year corporate bond has a yield of 8.75%. Assume that the liquidity premium on the corporate bond is 0.35%. What is the default risk premium on the corporate bond? Round your answer to two decimal places.

rTb = 4.75, rCb = 8.75, LP = 0.35 DRP = ? r = r* + IP + LP + DRP + MRP rTb = 4.75 = r* + IP + MRP (1) (Treasure LP = DRP = 0) rCb = 8.75 = r* + IP + 0.35 + DRP + MRP (2) from (1) and (2): 8.75 = 4.75 + 0.35 + DRP -> DRP = 8.75 - 4.75 - 0.35 = 3.65%

Based on this equation and the data, it is reasonable to expect that Ella's potential bond investment is currently exhibiting an intrinsic value greater than $1,000.

reasonable

Based on this equation and the data, it is reasonable to expect that Oliver's potential bond investment is currently exhibiting an intrinsic value less than $1,000.

reasonable

Smith Incorporated's bonds have exhibited a substantial trading volume in the past few years. Its bonds would be referred to as a seasoned issue .

seasoned issue

simple compound

A bond contract feature that requires the issuer to retire a specified portion of the bond issue each year is called a sinking fund provision .

sinking fund provision

Based on this equation and the data, it is unreasonable to expect that Ethan's potential bond investment is currently exhibiting an intrinsic value greater than $1,000.

unreasonable

The process of bond valuation is based on the fundamental concept that the current price of a security can be determined by calculating the present value of the cash flows that the security will generate in the future. There is a consistent and predictable relationship between a bond's coupon rate, its par value, a bondholder's required return, and the bond's resulting intrinsic value. Trading at a discount, trading at a premium, and trading at par refer to particular relationships between a bond's intrinsic value and its par value. This also results from the relationship between a bond's coupon rate and a bondholder's required rate of return. Remember, a bond's coupon rate partially determines the interest-based return that a bond will pay, and a bondholder's required return reflects the return that a bondholder would like to receive from a given investment.

will would like

If the price of the bond is initially discounted and offers no coupon payments, the bond is called a zero coupon bond.

Bus1-170 Exam 2

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