Deck 7: Time Value of Money Basics and Applications

Question 1

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today).At an interest rate of 10%,what is the future value of this contract exactly three years from today?

A)$248.69
B)$273.55
C)$331.00
D)$364.10

Answer 1

D

Question 2

Your parents paid $1,000 for a college fund bond when you were born.Today is your 20^th birthday and you are ready to cash the bond which has grown to a value of $3,361.85.What was the average annual rate of return on your college fund bond?

A)5.50%
B)6.25%
C)6.73%
D)There is not enough information to answer this question.

Answer 2

B

Question 3

You have been accepted into a prestigious private university in Southern California - congratulations! Since no one from this school has ever graduated in only four years,you anticipate that you will need to make 10 semi-annual tuition payments of $25,000 each with the first cash flow six months from today.If you choose to discount these cash flows at an annual rate of 6%,what is the present value cost of tuition to attend your university of choice?

A)$186,814.54
B)$184,002.18
C)$250,000.00
D)$213,255.07

Answer 3

D

Question 4

You own a contract that promises an annuity cash flow of $100 beginning-of-the-year cash flows for each of the next three years (note: the first cash flow is today).At an interest rate of 10%,what is the present value of this contract?

A)$248.69
B)$273.55
C)$331.00
D)$364.10

Question 5

You have decided to endow a Chair in Finance at Whatsamatta University.How much money must you deposit into the endowment account today if the Chair pays $125,000 per year (first payment one year from today),increases at a rate of 2% per year forever,and is invested at a rate that pays out 4.50% per year?

A)$2,777,777.78
B)$2,902,777.78
C)$5,000,000.00
D)There is not enough information to answer this question.

Question 6

Individuals and businesses require compensation for delaying consumption.Which of the following questions may contribute to the magnitude of the compensation?

A)Is there a possibility that the price may increase for the delayed good or service?
B)If current consumption is delayed is it possible that it may not be realized at all?
C)How badly does the firm or individual wish to consume now and what do they require for delaying?
D)All of the above are legitimate reasons to require additional compensation for delaying consumption.

Question 7

Your friend has agreed to lend you $5,000 today if you will repay him $5,061.36 in three months.What annual interest rate is your friend charging you for this loan?

A)1.23%
B)5.00%
C)2.47%
D)5.36%

Question 8

Peabody Books Inc.wishes to borrow $182,000 today for the purchase of publishing materials.They have an agreement with their commercial banker that they can borrow money at an annual rate of 4.75%.How much will the firm owe if they repay the loan in exactly one year?

A)$8,645
B)$173,747.02
C)$182,000
D)$190,645

Question 9

What is the present value of $3,500 received 3 years from today if the prevailing interest rate is 6.10%?

A)$2,732.98
B)$2,930.37
C)$3,625.14
D)$4,192.20

Question 10

You are about to purchase a new car from a dealer who has a new and unusual payment plan.You have the choice to pay $28,000 cash today or $31,000 in four years.If you have the opportunity to borrow the cash price value of the car at a rate of 2.5% and repay the loan in a lump sum in 4 years,which option should you take and why?

A)Pay the $31,000 in the future because it it always better to delay payment for new assets.
B)Pay the $31,000 in the future because the PV is less than $28,000 today.
C)Pay the $28,000 cash today even if you need to borrow the money because the FV of the repayment in 4 years is only $30,906.76.
D)Pay the $28,000 cash today because you pay a full $3,000 less than if you wait and pay the other option as presented.

Question 11

You own a contract that promises an annuity cash flow of $100 year-end cash flows for each of the next three years (note: the first cash flow is exactly one year from today).At an interest rate of 10%,what is the present value of this contract?

A)$248.69
B)$273.55
C)$331.00
D)$364.10

Question 12

Your new employer makes you an unusual salary offer.Choice A is to receive a $20,000 lump sum today and another $50,000 in one year.Choice B is to receive nothing today,and $80,000 in one year.You carefully consider what you have learned in your finance class and determine that the risk and uncertainty of this offer as well as the difficulty of having to find money for living expenses for one more year leads you to conclude that the appropriate interest rate at which to evaluate these offers is 40%.Based strictly on the results of your calculations,which offer should you accept and why?

A)Choice A because the present value of $57,142.86 is greater than the PV of $55,714.29 for Choice B.
B)Choice A because the present value of $70,000 is greater than the PV of $57,142.86 for Choice B.
C)Choice B because the present value of $80,000 is greater than the PV of $70,000 for Choice A.
D)Choice B because the present value of $57,142.86 is greater than the PV of $55,714.29 for Choice A.

Question 13

Which choice has a greater present value if we assume a required rate of return of 10%? 1: A lump sum cash flow today of $248.69,2: $100 cash flows occurring one,two,and three years from today,or 3: a single cash flow of $331 three years from today.

A)Choice 1
B)Choice 2
C)Choice 3
D)The choices all have equal present values at a discount rate of 10%.

Question 14

Consider the equation for present value.If you wished to increase the present value of a future amount by changing only one variable,which of the following actions should you take?

A)increase the time period
B)decrease the future value
C)decrease the interest rate
D)This statement cannot be answered with the information provided.

Question 15

Autorola plans to invest money today at an interest rate of 6% compounded annually to have $40,000 available for the purchase of a car four years from now.How much does the firm need to invest today?

A)$50,499.08
B)$36,384.52
C)$31,683.75
D)$9,143.66

Question 16

If you were able to invest $2,500 at a rate of 6.40% for six months,how much money would you have at the end of that period?

A)$2,349.62
B)$2,423.65
C)$2,578.76
D)$2,660.00

Question 17

You have accumulated $8,000 toward the down payment on a piece of lake front property in rural Minnesota.You wish to accumulate $12,000 for the down payment in four years.If you choose not to contribute more new funds to your down payment fund,what rate of return must your fund earn to reach your objective in the specified time? Assume that your investment fund compounds annually.

A)10.67% per year
B)50.00% per year
C)12.50% per year
D)There is not enough information to answer this question.

Question 18

You have decided to endow a Chair in Finance at Whatsamatta University.How much money must you deposit into the endowment account today if the Chair pays $125,000 per year forever (first payment one year from today)and is invested at a rate that pays out 4.50% per year?

A)$277,777.78
B)$2,902,777.78
C)$2,777,777.78
D)There is not enough information to answer this question.

Question 19

________ is the cost of a foregone alternative.

A)Opportunity cost
B)Time value of money
C)Inflation
D)An annuity

Question 20

Eastinghome Inc.just paid $8,000 to a landowner to explore for but not extract valuable minerals.If the landowner invests the money at a rate of 5.5% compounded annually for 7 years what is the investment worth at the end of that time period?

A)$5,499.49
B)$11,637.43
C)$56,000.00
D)$66,135.15

Question 21

Given a discount rate of 0%,which of the following has the greatest present value? ONE,a series of 10 equal annual end-of-the cash flows of $100 each,TWO,just like ONE except the first 5 cash flows are only $50 but the last 5 cash flows are $150,or THREE,just like ONE except the 10 $100 cash flows are at the beginning of the period.

A)ONE
B)TWO
C)THREE
D)The choices all have equal present values.

Question 22

What is the future value of a series of $5,000 end-of-the-year cash flows to be received forever if the required rate of return is 6.00% per year and the first cash flow is one year from today?

A)$83,333,333.33
B)$8,333,333.33
C)$83,333.33
D)This question cannot be solved for a future value.

Question 23

To increase the future value of a present cash flow,you could increase the interest rate.

Question 24

Michael received a professional baseball contract paying $7,000,000 per year for 5 years,Bert received a two-year contract for $16,000,000 per year.For purposes of calculations,treat these contracts as ordinary annuities.Who's contract has a greater present value if we assume a discount rate of 6%?

A)Bert = $29,334,283
B)Michael = $29,486,547
C)Bert = $39,459651
D)Michael = $39,743,196

Question 25

To increase the present value of a future cash flow,you could increase the discount rate.

Question 26

You own a contract that promises an annuity cash flow of $100 end-of-the-year cash flows for each of the next three years (note: the first cash flow is exactly one year from today).At an interest rate of 10%,what is the future value of this contract exactly three years from today?

A)$248.69
B)$273.55
C)$331.00
D)$364.10

Question 27

Which has a greater present value,a future value of $300,000 received in year 6,or an end-of-the-year annuity (first cash flow exactly one year from today)of $75,000 that lasts for four years if the relevant interest rate is 0%?

A)The future value of $300,000 is preferred.
B)The annuity has a greater present value.
C)You are indifferent to these two sets of cash flows on a present value basis.
D)You can't properly answer this question because the interest rate is 0%.

Question 28

Which of the following could be considered a form of perpetuity?

A)The college tuition payments that students make for four years.
B)A 20-year corporate bond.
C)A university scholarship endowment that promises to pay out $10,000 per year for an indefinite time period.
D)A contract from the winning lottery ticket to receive cash flows for the next 30 years.

Question 29

Annuity A has a greater present value than annuity B when cash flows are discounted using the same positive interest rate for each annuity.Which annuity will have the larger future value if compounded at the same interest rate?

A)Annuity A will have a larger future value.
B)Annuity B will have a larger future value.
C)The future values will be the same.
D)There is not enough information to determine which annuity will have a greater future value.

Question 30

The time value of money implies that one dollar today is worth more than one dollar tomorrow,due primarily to the opportunity cost of foregoing consumption today

Question 31

You plan to purchase a new car with a retail price of $26,499 after your trade-in and astute negotiations with the dealership sales manager.You have agreed to make 5 ANNUAL payments with an annual interest rate of 3.90%.How large are your equal annual end-of-the-year payments for your new car?

A)$5299.80
B)$5,462.21
C)$5,841.89
D)$5,935.68

Question 32

Nic is a great basketball player with a long professional career in front of him.He plays for a European professional team that has made him a very interesting offer.If he will take a "below market" salary beginning one year from today,they will guarantee a 5% annual raise forever - even after he stops playing ball.If the offer is for a $5,000,000 salary to be received one year from today with subsequent payments as described,what is the present value of the contract offer if the cash flows should be discounted at a rate of 12%?

A)$71,428,571
B)$75,000,000
C)$41,666,667
D)$43,750,000

Question 33

Congratulations you have just won the tuition lottery! The lottery pays out four beginning-of-the-year cash flows of $50,000 each with the first cash flow today and the remaining cash flows to follow at the start of years 2,3,and 4.Since the lottery is managed by the Fergetaboutit University system you are considering their offer of a lump sum of $160,000 today.If after considering all of he relevant economic factors,you conclude it is reasonable to use a 12% interest rate to compare these two offers.Which offer should you take and why?

A)Take the lump sum because the annuity PV is only $151,867.47.
B)Take the annuity because the PV of $170,091.56 is greater than the lump sum.
C)Take the annuity because the PV of $238,966.40 is greater than the lump sum.
D)Take the lump sum because the annuity PV is only $135,595.95.

Question 34

Derek owns a perpetuity contract that promises to pay him $1,000 per year in end-of the-year cash flows with the first cash flow beginning one year from today.Derek perceives some risk with the promised cash flows and has discounted them at an annual rate of 10.00% to determine the present value of the contract.Derek has offered to sell a portion of the contract to his brother Cam.The agreement is that Derek will keep the first 25 cash flows and that Cam will keep the remaining cash flows beginning with the first cash flow 26 years from today.What is the present value of the original contract? What is the present value of the first 25 cash flows? What is the present value of the cash flows received in year 26 and beyond? If Derek makes the deal as described and charges Cam $1,000 for the year 26 and beyond cash flows,which brother is getting a better deal? Please provide dollar values for each of these questions.

Question 35

Perpetuities last "forever" but annuities have a finite life.

Question 36

If the discount rate used to compare the present value of two annuities is 0%,then the timing of the cash flows is unimportant in the present value calculation.

Question 37

What is the present value of a series of $5,000 end-of-the-year cash flows to be received forever if the required rate of return is 6.00% per year and the first cash flow is one year from today?

A)$8,333.33
B)$83,333.33
C)$300.00
D)This question cannot be answered because there is no time period provided.

Question 38

Your university is running a special offer on tuition.This year's tuition cost is $18,000.Next year's tuition cost is scheduled to be $19,080.The university offers to discount next year's tuition at a rate of 6% if you agree to pay both year's tuition in full today.How much is the total tuition bill today if you take the offer?

A)$34,981.13
B)$36,000.00
C)$37,080.00
D)$38,160.00

Question 39

You have two contracts available to you: ONE is a perpetuity with cash flows of $500 per year,with the first cash flow beginning today.TWO is a perpetuity with cash flows of $500 per year,with the first cash flow beginning one year from today.Which has a greater present value if the required rate of return is 5%?

A)Contract ONE is preferred because it has a present value that is $500 greater than contract TWO.
B)Contract TWO is preferred because it has a present value that is $500 greater than contract ONE.
C)Contract ONE is preferred because it has a present value that is $476.19 greater than contract TWO.
D)Because these are perpetuities with equal required rates of return,they have equal value.

Question 40

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

A)Your pay check which is the same every month.
B)Your tuition payments which are the same every term.
C)The identical payment you make every two years for your share of a lake cabin that you own with other family members.
D)These are all annuity cash flows.

Question 41

Another name for the lump sum cash flow that occurs when a bond matures is the:

A)face value.
B)maturity value.
C)par value.
D)All of the above could be used to describe the cash flow in question.

Question 42

Five years ago Rogue Construction Inc.issued 20-year maturity fixed-rate bonds at par with a 10% coupon rate.Today those same bonds carry a 14% yield to maturity.Which of the following statements about this bond issue could be true?

A)Since issue,the economy-wide rate of inflation has increased.
B)The market believes there is greater risk associated with this bond than at the issue date.
C)Both A and B may be true.
D)Neither A nor B could be true.

Question 43

Which of the following is a type of financial security issued by a corporation in need of capital?

A)bonds
B)preferred stock
C)common stock
D)all of the above

Question 44

Flyover Airlines Inc.issued 20-year,8% per annum semi-annual coupon bonds at their face value of $1,000.Immediately after issue a major disaster befell the airline and the yield to maturity on their bonds rose to 15%.per annum.What is the new price of the firm's bonds?

A)$559.20
B)$613.22
C)$1,000
D)$1324.18

Question 45

Five years ago Fairfield Farms Inc.issued 20 year semi-annual coupon bonds with a 9% annual coupon rate and a $1,000 face value.If the bonds currently carry a yield to maturity of 6%,what is the current price of a bond?

A)$1,346.72
B)$1,294.01
C)$1,344.10
D)$1,291.37

Question 46

The ________ is used to determine the annual or semi-annual interest cash flow for a bond whereas the ________ is the rate used to determine the price of the bond.

A)coupon rate; yield to maturity
B)yield to maturity; coupon rate
C)yield to maturity; discount rate
D)current yield; yield to maturity

Question 47

Firms attempt to price bonds so that at issue they sell for the:

A)face value.
B)coupon value.
C)firm value.
D)same price as shares of preferred stock.

Question 48

Skye Industries Inc.bonds currently have 14 years remaining to maturity.What is the yield to maturity of the firm's semi-annual bonds if they carry a face value of $1,000,an annual coupon rate of 8% and have a current price of $885.16?

A)8.00%
B)8.75%
C)9.50%
D)10.25%

Question 49

Preferred stock is often referred to as a hybrid security for which of the following reasons?

A)Preferred stock dividends are fixed like bond payments but the maturity is indefinite like common stock.
B)Preferred stockholders have preference over common stock holders in bankruptcy,but are subordinate to bondholders.
C)Both A and B are typically true.
D)Neither A nor B are typically true.

Question 50

Simpson Industries Inc.bonds currently have 12 years remaining to maturity.What is the current price of the firm's semi-annual bonds if they carry a face value of $1,000,an annual coupon rate of 8% and an annual yield to maturity of 7%?

A)$924.64
B)$1,000.00
C)$1,079.43
D)$1,080.29

Question 51

Suppose a preferred share pays perpetual quarterly dividends of $0.25 and has a per annum dividend yield of 6 percent.What is the fair value of this preferred share?

A)$14.67
B)$15.33
C)$16.00
D)$16.67

Question 52

Michael received a professional baseball contract paying $7,000,000 for 5 years,Bert received a two-year contract for $16,000,000 per year.For purposes of calculations,treat these contracts as ordinary annuities.What are the present values of each contract if we assume a discount rate of 6%? It is not clear that the higher present value is the preferred contract in this situation.What other factors might you consider when determining which contract has greater value?

Question 53

If a bond is selling for its face value,which of the following statements is true?

A)The coupon rate and the yield to maturity are the same.
B)The par value is less than the face value.
C)This is only possible if this is a zero coupon bond.
D)All of the statements above are true.

Question 54

The interest rate used to discount bond cash flows to determine the bond price is known as the:

A)coupon rate.
B)yield to maturity.
C)compound rate.
D)coupon yield.

Question 55

Your plans for the future have finally materialized because you have won the lottery.Congratulations! The lottery marketing material says you have won $20,000,000 but a more careful examination of the terms and conditions means that you have won twenty $1,000,000 beginning-of-the-year cash flows with the first cash flow today.Further,the lottery contract says that instead of waiting for so many years to collect your winnings,you could accept a lump sum check today in the amount of $12,000,000.If you determine that the appropriate interest rate to compare these two alternatives is 6%,which alternative is preferred? To answer this question,solve for the present value of each alternative and make your decision based strictly on the values.You may ignore taxes in your decision

Question 56

Most bonds issued in the United States have ________ coupon payments and ________ face values.

A)annual; $1,000
B)annual; $500
C)semi-annual; $1,000
D)semi-annual; $500

Question 57

Epo Pharmaceuticals Inc.has an issue of preferred stock outstanding that has a required rate of return of 9% and pays $6 annual dividends.If the preferred share were issued 3 years ago,what is the current price per share?

A)$51.48
B)$66.67
C)$86.34
D)There is not enough information to answer this question.

Question 58

The maturity of an issue of preferred stock is:

A)the same as the longest maturity bond issued by the firm.
B)variable between 15 and 30 years.
C)indefinite,just as the maturity of common shares.
D)renewable every five years.

Question 59

Zero coupon bonds have which of the following features?

A)annual interest payments
B)semi-annual interest payments
C)no interest payments
D)Any of the above may apply.

Question 60

After a bond issue if the yield to maturity increases a conventional bond will see the price:

A)increase.
B)decrease.
C)stay the same.
D)Not enough information to answer this question.

Question 61

Johnson Signs Inc.has been able to increase dividends at the rate of 2% per year since the company first started paying dividends in 1957.Johnson has developed a new production technique and can sell their signs at a premium price for the next three years.This immediate revenue boost will allow Johnson to increase dividends at a rate of 12% per year next year,then 10% the following year,and 8% the next year.After that,they intend to revert to their previous slow but steady increase in annual dividends.If current dividends are $2.45 per share and Johnson investors require an annual rate of return of 11%,what is the current price per share for the company's stock?

Question 62

Zero coupon bonds pay no intermediate cash flows prior to maturity.

Question 63

Preferred stock share prices tend to act much like bond prices - so long as the firm is not experiencing any financial distress.

Question 64

If a bond sells for less than its par value then the yield to maturity is greater than the coupon rate.

Question 65

Preferred stockholders are the residual claimants of the firm.

Question 66

Zero coupon bonds sell at a steep premium to the face value.

Question 67

What is the pecking order of payments (from first to last)for a firm's creditors and owners?

A)bondholders,then preferred stockholders,then common stockholders
B)preferred stockholders,then common stockholders,then bondholders
C)common stockholders,then bondholders,then preferred stockholders
D)bondholders,then common stockholders,then preferred stockholders

Question 68

Blanton Consulting Inc.just paid a $2.00 per share dividend.The firm also announced that it anticipates a long-run growth in dividends of 3% per year.Inflation is also expected to be 3% per year,and the firms required rate of return on common stock is 11%.What is the current price per share of the firm's stock?

A)$14.71
B)$14.29
C)$25.75
D)$25.00

Question 69

Bueno Media preferred stock shares pay a $4 annual dividend and sell for $57.14 per share.What is the current required rate of return for their shares?

A)7.00%
B)6.93%
C)6.51%
D)5.29%

Question 70

If a bond sells for its par value then the yield to maturity is greater than the coupon rate.

Question 71

Common stockholders are subordinate to all other creditors in their payments.

Question 72

Explain the rationale for why anyone would choose to buy a zero coupon bond that pays no interest prior to maturity and pays only the face value of the bond at maturity.

Question 73

If we are simply interested in determining whether the market as a whole,such as the S&P 500,is over- or undervalued,then the perpetual constant growth model is reasonable.

Question 74

Cascade Industries Inc.intends to pay a common stock dividend of $3.18 one year from today and the firm anticipates that the dividend will continue to grow at a rate of 2% per year indefinitely.If the firm has a 13% required rate of return,what is the current price per share of stock?

A)$21.20
B)$28.91
C)$21.62
D)$29.49

Question 75

Just as a yield to maturity can change on a day-to-day basis,so can a preferred stock share's dividend yield.

Question 76

The next dividend payment (one year from now)by Bacon Signs Inc.,will be $2.50 per share.The dividends are anticipated to maintain a 2% growth rate,forever.If the required rate of return for Bacon Signs Inc.is 11%,what is the current price per share:

A)$27.78.
B)$28.33.
C)$19.23.
D)$19.62.

Question 77

An unattractive feature of U.S.corporate bonds is that there is no secondary market and the investor is forced to hold the bond until maturity.