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essentials managerial finance
Principles Of Managerial Finance 15th Global Edition Chad J. Zutter, Scott Smart - Solutions
=+b. What is the present value of $6,000 that you will receive after 6 years if the discount rate is 12%?
=+c. What is the most you would spend today for an investment that will pay $6,000 in 6 years if your opportunity cost is 12%?
=+d. Compare, contrast, and discuss your findings in parts a through c.Personal Finance Problem
=+LG 2 P5–13 Time value Aziz Hussain has been offered an investment that will pay him $6,000 3 years from today.
=+a. If he earns 8% compounded annually in a treasury bond, what value should he place on this opportunity today?
=+b. What is the most he should pay to purchase this investment today?
=+c. If Aziz can purchase this investment for less than the amount calculated in part
=+a, what does that imply about the rate of return he will earn on the investment?
=+P5–14 Time value An Iowa state savings bond can be converted to $100 at maturity 6 years from purchase. If the state bonds are to be competitive with U.S. savings bonds, which pay 3% annual interest (compounded annually), at what price must the state sell its bonds? Assume no cash payments on
=+LG 2 P5–15 Time value and discount rates John Ross has received his pension statement that promises to pay him a lump sum of £150,000 when he retires exactly 10 years from today. A pension release firm has offered him an immediate cash payment in exchange for his pension.
=+a. What is the least amount John should accept if he can earn the following rates of return on similar-risk investments during the 10-year period?(1) 4%(2) 8%(3) 12%
=+b. Rework part a under the assumption that the £150,000 payment will be received in 15 rather than 10 years.
=+c. Compare your findings in parts a andb, and explain the relationship indicated between future value, length of investment, and the applicable rate of return.Personal Finance Problem
=+LG 2 P5–16 Time value comparisons of single amounts In exchange for a $23,000 payment today, a well-known company will allow you to choose one of the alternatives shown in the following table. Your opportunity cost is 9%.Alternative Single amount A $28,500 at end of 3 years B $54,000 at end of
=+a. Find the value today of each alternative.
=+b. Are all the alternatives acceptable? That is, are they worth $23,000 today?
=+c. Which alternative, if any, will you take?Personal Finance Problem
=+LG 2 P5–17 Cash flow investment decision Tom Alexander has an opportunity to purchase any of the investments shown in the following table. The purchase price, the amount of the single cash inflow, and its year of receipt are given for each investment. Which purchase recommendations would you
=+P5–18 Calculating deposit needed Peter put £6,000 in an account earning 4% annually.After 4 years, he made another deposit into the same account. At the end of 6 years, the account balance is £13,000. What was the amount deposited at the end of year 4?
=+LG 3 P5–19 Future value of an annuity For each case in the accompanying table, answer the questions that follow.
=+a. Calculate the future value of the annuity, assuming that it is(1) An ordinary annuity.(2) An annuity due.
=+b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity—ordinary or annuity due—is preferable? Explain why.
=+LG 3 P5–20 Present value of an annuity Consider the following cases.
=+a. Calculate the present value of the annuity, assuming that it is(1) An ordinary annuity.(2) An annuity due.
=+b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity is preferable—ordinary or annuity due? Explain why.Personal Finance Problem
=+LG 3 P5–21 Time value: Annuities Marian Kirk wishes to select the better of two 10-year annuities. Annuity 1 is an ordinary annuity of $2,500 per year for 10 years. Annuity 2 is an annuity due of $2,300 per year for 10 years.
=+a. Find the future value of both annuities 10 years from now, assuming that Marian can earn (1) 6% annual interest and (2) 10% annual interest.
=+b. Use your findings in part a to indicate which annuity has the greater future value after 10 years for both the (1) 6% and (2) 10% interest rates.
=+c. Find the present value of both annuities, assuming that Marian can earn (1) 6%annual interest and (2) 10% annual interest.
=+d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 6% and (2) 10% interest rates.e. Briefly compare, contrast, and explain any differences between your findings using the 6% and 10% interest rates in parts b and d.Personal Finance Problem
=+LG 3 P5–22 Retirement planning Jill Smyth, a 22-year-old university graduate, has just landed her first job and has planned to retire at age 62. She has decided to deopsit £5,000 every year in an individual savings account (ISA), which is tax-free for British citizens and gives a 5% per annum
=+a. If Jill continues to make end-of-year $5,000 deposits into the ISA, how much will she have accumulated in 40 years when she turns 62?
=+b. If Jill decides to wait until age 32 to begin making deposits into the ISA, how much will she have accumulated when she retires after 30 years?
=+c. Using your findings in parts a andb, discuss the impact of delaying deposits into the ISA for 10 years on the amount accumulated by the end of the period?
=+d. Rework parts a andb, assuming that Jill makes all deposits at the beginning, rather than the end, of each year. Discuss the effect of beginning-of-year deposits on the future value accumulated by the end of Jill’s sixty-second year.Personal Finance Problem
=+LG 3 P5–23 Value of a retirement annuity Your bank manager has informed you about a new investment plan that will provide you with $5,000 at the end of each of the next 20 years. If you have an opportunity to earn a guaranteed return of 6%, what is the most you would pay for this annuity right
=+LG 2 P5–24 Funding your retirement John Wick is 50 years old and has saved nothing for retirement. However, he has just inherited £150,000 from his great grandfather and wants to invest it in a retirement plan. He plans to put the money in an investment account earning a 10% return. He will
=+a. How much money must John invest to achieve his goal? Construct a timeline to help visualize the details of this investment plan.
=+b. John realizes that once he retires he will want to invest only in less risky assets, like government securities that will earn a slightly lower rate of return—5%. So he will earn 10% until age 65, and then 5% per annum from age 65 to 90. How much money does he need to set aside now to
=+c. Suppose John has changed his mind and invests the entire inheritance into the account earning 10%. After making his last withdrawal at age 90, he wants to leave the remaining money to his niece. How much would his niece receive when John withdraws the last annual installment of £40,000?
=+P5–25 Value of an annuity versus a single amount Assume that you just won the state lottery. Your prize can be taken either in the form of $40,000 at the end of each of the next 25 years (i.e., $1,000,000 over 25 years) or as a single amount of $500,000 paid immediately.
=+a. If you expect to earn 5% annually on your investments over the next 25 years, ignoring taxes and other considerations, which alternative should you take? Why?
=+b. Would your decision in part a change if you could earn 7% rather than 5% on your investments over the next 25 years? Why?
=+c. At approximately what interest rate would you be indifferent between the two options?
=+LG 3 P5–26 Perpetuities Consider the data in the following table.Perpetuity Annual payment Discount rate A €120,000 8%B 60,000 12 C 1,500 6 D 300,000 4 E 3000 7 Determine the present value of each perpetuity.
=+ P5–27 Perpetuities Suppose you have been offered an investment opportunity that will pay you $500 at the end of every year, starting 1 year from now and continuing forever.Assume the relevant discount rate is 6%.
=+a. What is the maximum amount you would pay for this investment?
=+b. What would you pay if the first cash flow from this investment comes immediately, and the following cash payments of £500 after 1 year thereafter.
=+c. Suppose the first cash flow from this investment is 4 years from now; that is, the first payment will be made at the end of fourth year and will continue every year thereafter. How much is this worth to you today?
=+ P5–28 Perpetuities You are evaluating an investment that will pay $75 in 1 year, and it will continue to make payments at annual intervals thereafter, but the payments will grow by 4% forever.
=+a. What is the present value of the first $75 payment if the discount rate is 10%?
=+b. How much cash will this investment pay 100 years from now? What is the present value of the 100th payment? Again, use a 10% discount rate.
=+c. What is the present value of the entire growing stream of perpetual cash flows?
=+d. Explain why the answers to parts a and b help to explain why an infinite stream of growing cash flows has a finite present value?Personal Finance Problem
=+ P5–29 Creating an endowment On completion of her introductory finance course, Marla Lee was so pleased with the amount of useful and interesting knowledge she gained that she convinced her parents, who were wealthy alumni of the university she was attending, to create an endowment. The
=+a. What will it cost 3 students to take the finance class next year?
=+b. How much will Marla’s parents have to give the university today to fund the endowment if it starts paying out cash flow next year?
=+c. What amount would be needed to fund the endowment if the university could earn 9% rather than 6% per year on the funds?
=+LG 4 P5–30 Value of a mixed stream For each of the mixed streams of cash flows shown in the following table, calculate the future value at the end of the final year if deposits are made into an account paying annual intertest of 8%. Assume that no withdrawls are made during the period and that
=+LG 4 P5–31 Value of a single amount versus a mixed stream Boris Miller has contracted to sell a piece of land that he owns, which has permission for a residential development. A property developer is willing to buy the land and has proposed two methods of payment. The developer is willing to
=+LG 4 P5–32 Value of mixed streams Find the present value of the streams of cash flows shown in the following table. Assume that the opportunity cost is 12%.A B C Year Cash flow Year Cash flow Year Cash flow 1 -$2,000 1 $10,000 1−5 $10,000/yr 2 3,000 2–5 5,000/yr 6–10 8,000/yr 3 4,000 6
=+P5–33 Present value: Mixed streams Consider the mixed streams of cash flows shown in the following table.Cash flow stream Year A B 0 -$50,000 $10,000 1 40,000 20,000 2 30,000 30,000 3 20,000 40,000 4 10,000 -50,000 Totals $50,000 $50,000
=+a. Find the present value of each stream using a 5% discount rate.
=+b. Compare the calculated present values and discuss them in light of the undiscounted cash flows totaling $50,000 in each case. Is there some discount rate at which the present values of the two streams would be equal?
=+P5–34 Value of a mixed stream Neil Tyson has developed a prototype of an armored fabric that is very light, but is capable of stopping projectiles as efficiently as a traditional bullet-proof jacket. A military supplier is considering the technology and has offered to pay Neil £30,000 in
=+a. Lay out the cash flows involved in the offer on a timeline.
=+b. If Neil applies a required rate of return of 10% to them, what is the present value of this series of payments?
=+c. Another company has made an offer of a one-time payment of £275,000 for the fabric. Which offer should Neil accept?
=+ P5-35 Value of a mixed stream Cook Energy Ltd plans to build a new low-cost nuclear power plant in France. The construction will cost €30 million right now, but cash flows of €12 million will start arriving at the end of years 1 to 8. The plant will need to be decommissioned at the end of
=+a. What is the total undiscounted cash flow associated with this project over its 9-year life? Given this answer, do you think Cook should accept this project?Why?
=+b. Assuming an interest rate of 8%, calculate the net present value of the project.What if the interest rate is 15%? Comment on what you find.
=+LG 4 P5–36 Relationship between future value and present value: Mixed stream Using the information in the accompanying table, answer the questions that follow. Assume all transactions take place at the end of the year.Year Cash flow 1 $3,000 2 0 3 4,000 4 8,000 5 12,000 6 6,000
=+a. Using a discount rate of 7%, determine the present value of the cash flows.
=+b. Suppose you had a lump sum equal to your answer in parta. You invested this sum in an account earning a 7% return each year. How much would you have after 6 years?
=+c. Calculate the future value of cash flows 6 years from now and compare it to your answer in part b.d. How much would you be willing to pay for this, assuming that you can earn 7%on your investments?
=+LG 4 P5–37 Relationship between future value and present value: Mixed stream The table below shows a mixed cash flow stream starting in 1 year, except that the cash flow for year 3 is missing.Suppose you somehow know that the present value of the entire stream is $32,911.03 and that the
=+LG 5 P5–38 Changing compounding frequency Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate the future value if £10,000 is deposited initially and (2) determine the effective annual rate (EAR).a. At 12% annual interest for 5 years.b. At 15%
=+LG 5 P5–39 Compounding frequency, time value, and effective annual rates For each of the cases in the table below:
=+a. Calculate the future value at the end of the specified deposit period.
=+b. Determine the effective annual rate, EAR.
=+c. Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship exists between compounding frequency and the nominal and effective annual rates?
=+P5–40 Continuous compounding For each of the cases in the following table, find the future value at the end of the deposit period, assuming that interest is compounded continuously at the given nominal annual rate.
=+P5–41 Compounding frequency and time value François plans to invest $4,000 in an individual savings account (ISA) at a nominal interest rate of 6%.a. How much will François have in the account after 10 years if interest is compounded (1) annually, (2) semiannually, and (3) daily (assuming
=+b. What is the effective annual rate (EAR) for each compounding period in part a?
=+c. How much greater will François’ ISA balance be if the interest is compounded continuously rather than semiannually for the same period?
=+d. Consider your answers in partsa, b, andc. What does it indicate about the relationship between compounding frequency and the compound value for nominal interest rates?Personal Finance Problem
=+LG 3 LG 5 P5–42 Annuities and compounding Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%.
=+a. Determine the future value that Janet will have in 10 years, given that end-of-period deposits are made and no interest is withdrawn, if(1) $300 is deposited annually and the credit union pays interest annually.(2) $150 is deposited semiannually and the credit union pays interest
=+b. Use your findings in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.
=+LG 6 P5–43 Deposits to accumulate future sums For each case shown in the following table, determine the amount of the equal, end-of-year deposits necessary to accumulate the given sum at the end of the specified period, assuming the stated annual interest rate.X MyLab Case Sum to be accumulated
=+LG 6 P5–44 Creating a retirement fund Harry Brolin plans to retire after 38 years and wants to accumulate €180,000 when he retires. Harry plans to make equal, end-of-year deposits into a savings account paying 8% annual interest.
=+a. What amount does he need to deposit every year to create €180,000 in 38 years?
=+b. If Josh can afford to deposit only €700 per year into the account, how much will he have accumulated in 38 years?Personal Finance Problem
=+LG 6 P5–45 Accumulating a growing future sum You have $30,000, and you are making the decision between consumption and investment. You are considering either using all of the money to buy a new car or investing the whole amount. You have two investment options: You can either put the money
=+a. If you choose to invest, how much will you have 6 years later if you invested in(1) the savings account, or (2) stocks?
=+b. If you invested in the savings account, how long will it take for you to double your money?
=+c. Suppose the price of the car inflates by 2% per year. If you choose to invest your money in stocks, how long will it take for you to be able to afford two cars?Personal Finance Problem
=+LG 2 LG 3 P5–46 Inflation, time value, and annual deposits Sadiq Ansari wants to support his daughter’s education by paying for her MBA degree from a premier university in Britain.Research indicates that the fees for a 1-year MBA course at any good British university will cost £35,000 now.
=+a. What is the expected fees for an MBA degree in 20 years, when Sadiq will have to pay for his daughter’s course?
=+b. How much must Sadiq invest at the end of each of the next 20 years if his investments pay 8% every year.
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