**____________________________________________________________**

**Chapter 6 Accounting and the Time Value of Money**

**QUESTIONS**

1. What is the time value of money? Why should accountants

**have an understanding of compound interest,**

**annuities, and present value concepts?**

2. Identify three situations in which accounting measures

**are based on present values. Do these present value**

**applications involve single sums or annuities, or both**

**single sums and annuities? Explain.**

3. What is the nature of interest? Distinguish between

**“simple interest” and “compound interest.”**

4. What are the components of an interest rate? Why is it

**important for accountants to understand these components?**

5. The following are a number of values taken from compound

**interest tables involving the same number of periods**

**and the same rate of interest. Indicate what each of**

**these four values represents.**

(a) 6.71008. (c) .46319.

(b) 2.15892. (d) 14.48656.

6. Jose Oliva is considering two investment options for a

**$1,500 gift he received for graduation. Both investments**

**have 8% annual interest rates. One offers quarterly compounding;**

**the other compounds on a semiannual basis.**

Which investment should he choose? Why?

7. Regina Henry deposited $20,000 in a money market certificate

**that provides interest of 10% compounded quarterly**

**if the amount is maintained for 3 years. How much**

**will Regina Henry have at the end of 3 years?**

8. Will Smith will receive $80,000 on December 31, 2019

(5 years from now), from a trust fund established by his

**father. Assuming the appropriate interest rate for discounting**

**is 12% (compounded semiannually), what is the**

**present value of this amount today?**

9. What are the primary characteristics of an annuity?

Differentiate between an “ordinary annuity” and an

**“annuity due.”**

10. Kehoe, Inc. owes $40,000 to Ritter Company. How much

**would Kehoe have to pay each year if the debt is retired**

**through four equal payments (made at the end of the**

**year), given an interest rate on the debt of 12%? (Round to**

**two decimal places.)**

11. The Kellys are planning for a retirement home. They

**estimate they will need $200,000 4 years from now to**

**purchase this home. Assuming an interest rate of 10%,**

**what amount must be deposited at the end of each of the 4 years to fund the home price? (Round to two decimal**

**places.)**

12. Assume the same situation as in Question 11, except that

**the four equal amounts are deposited at the beginning of**

**the period rather than at the end. In this case, what**

**amount must be deposited at the beginning of each**

**period? (Round to two decimals.)**

13. Explain how the future value of an ordinary annuity interest

**table is converted to the future value of an annuity**

**due interest table.**

14. Explain how the present value of an ordinary annuity interest

**table is converted to the present value of an annuity**

**due interest table.**

15. In a book named Treasure, the reader has to figure out

**where a 2.2 pound, 24 kt gold horse has been buried. If the**

**horse is found, a prize of $25,000 a year for 20 years is**

**provided. The actual cost to the publisher to purchase an**

**annuity to pay for the prize is $245,000. What interest rate**

(to the nearest percent) was used to determine the amount

**of the annuity? (Assume end-of-year payments.)**

16. Alexander Enterprises leases property to Hamilton, Inc.

Because Hamilton, Inc. is experiencing financial difficulty,

Alexander agrees to receive five rents of $20,000 at the end

**of each year, with the rents deferred 3 years. What is the**

**present value of the five rents discounted at 12%?**

17. Answer the following questions.

(a) On May 1, 2014, Goldberg Company sold some machinery

**to Newlin Company on an installment contract**

**basis. The contract required five equal annual**

**payments, with the first payment due on May 1, 2014.**

What present value concept is appropriate for this

**situation?**

(b) On June 1, 2014, Seymour Inc. purchased a new machine

**that it does not have to pay for until May 1, 2016.**

The total payment on May 1, 2016, will include both

**principal and interest. Assuming interest at a 12% rate,**

**the cost of the machine would be the total payment**

**multiplied by what time value of money concept?**

(c) Costner Inc. wishes to know how much money it will

**have available in 5 years if five equal amounts of**

**$35,000 are invested, with the first amount invested**

**immediately. What interest table is appropriate for**

**this situation?**

(d) Megan Hoffman invests in a “jumbo” $200,000, 3-year

**certificate of deposit at First Wisconsin Bank. What**

**table would be used to determine the amount accumulated**

**at the end of 3 years?**

18. Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesperson indicated that the price of

**the car was either $27,600 cash or $6,900 at the end of each**

**of 5 years. Compute the effective-interest rate to the nearest**

**percent that Glenda would pay if she chooses to make**

**the five annual payments.**

19. Recently, property/casualty insurance companies have been

**criticized because they reserve for the total loss as much as 5 years before it may happen. The IRS has joined the debate**

**because it says the full reserve is unfair from a taxation**

**viewpoint. What do you believe is the IRS position?**

**BRIEF EXERCISES**

BE6-1 Chris Spear invested $15,000 today in a fund that earns 8% compounded annually. To what amount

BE6-

**will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund**

**earns 8% annual interest compounded semiannually?**

BE6-2 Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns

12% compounded annually? What amount must he invest if his investment earns 12% annual interest

**compounded quarterly?**

BE6-3 Candice Willis will invest $30,000 today. She needs $150,000 in 21 years. What annual interest rate

**must she earn?**

BE6-4 Bo Newman will invest $10,000 today in a fund that earns 5% annual interest. How many years will

**it take for the fund to grow to $17,100?**

BE6-5 Sally Medavoy will invest $8,000 a year for 20 years in a fund that will earn 12% annual interest. If

**the first payment into the fund occurs today, what amount will be in the fund in 20 years? If the first**

**payment occurs at year-end, what amount will be in the fund in 20 years?**

BE6-6 Steve Madison needs $250,000 in 10 years. How much must he invest at the end of each year, at

11% interest, to meet his needs?

BE6-7 John Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. John has

**recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $300,000 when**

**he retires in 5 years. How much of his inheritance must he invest at an annual rate of 12% (compounded**

**annually) to buy the boat at retirement?**

BE6-8 Refer to the data in BE6-7. Assuming quarterly compounding of amounts invested at 12%, how

**much of John Fillmore’s inheritance must be invested to have enough at retirement to buy the boat?**

BE6-9 Morgan Freeman is investing $16,380 at the end of each year in a fund that earns 10% interest. In

**how many years will the fund be at $100,000?**

BE6-10 Henry Quincy wants to withdraw $30,000 each year for 10 years from a fund that earns 8% interest.

How much must he invest today if the first withdrawal is at year-end? How much must he invest today if

**the first withdrawal takes place immediately?**

BE6-11 Leon Tyler’s VISA balance is $793.15. He may pay it off in 12 equal end-of-month payments of $75

**each. What interest rate is Leon paying?**

BE6-12 Maria Alvarez is investing $300,000 in a fund that earns 8% interest compounded annually. What

**equal amounts can Maria withdraw at the end of each of the next 20 years?**

BE6-13 Adams Inc. will deposit $30,000 in a 12% fund at the end of each year for 8 years beginning December

31, 2014. What amount will be in the fund immediately after the last deposit?

BE6-14 Amy Monroe wants to create a fund today that will enable her to withdraw $25,000 per year for

8 years, with the first withdrawal to take place 5 years from today. If the fund earns 8% interest, how much

**must Amy invest today?**

BE6-15 Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. The

**current market rate of interest for bonds of similar risk is 8%. What amount will Clancey receive when it**

**issues the bonds?**

BE6-16 Zach Taylor is settling a $20,000 loan due today by making 6 equal annual payments of $4,727.53.

Determine the interest rate on this loan, if the payments begin one year after the loan is signed.

BE6-17 Consider the loan in BE6-16. What payments must Zach Taylor make to settle the loan at the same

**interest rate but with the 6 payments beginning on the day the loan is signed?**

EXERCISES

EXERCISES

E6-1 (Using Interest Tables) For each of the following cases, indicate (a) to what rate columns, and (b) to

**what number of periods you would refer in looking up the interest factor.**

1. In a future value of 1 table Annual Number of Rate Years Invested Compounded

a. 9% 9 Annually

b. 12% 5 Quarterly

c. 10% 15 Semiannually

2. In a present value of an annuity of 1 table Annual Number of Number of Frequency of Rate Years Involved Rents Involved Rents

a. 9% 25 25 Annually

b. 10% 15 30 Semiannually

c. 12% 7 28 Quarterly

E6-2 (Simple and Compound Interest Computations) Alan Jackson invests $20,000 at 8% annual interest,

**leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years,**

Alan withdraws the accumulated amount of money.

Instructions

Instructions

(a) Compute the amount Alan would withdraw assuming the investment earns simple interest.

(b) Compute the amount Alan would withdraw assuming the investment earns interest compounded

**annually.**

(c) Compute the amount Alan would withdraw assuming the investment earns interest compounded

**semiannually.**

E6-3 (Computation of Future Values and Present Values) Using the appropriate interest table, answer

**each of the following questions. (Each case is independent of the others.)**

(a) What is the future value of $7,000 at the end of 5 periods at 8% compounded interest?

(b) What is the present value of $7,000 due 8 periods hence, discounted at 11%?

(c) What is the future value of 15 periodic payments of $7,000 each made at the end of each period and

**compounded at 10%?**

(d) What is the present value of $7,000 to be received at the end of each of 20 periods, discounted at

5% compound interest?

E6-4 (Computation of Future Values and Present Values) Using the appropriate interest table, answer

**the following questions. (Each case is independent of the others).**

(a) What is the future value of 20 periodic payments of $4,000 each made at the beginning of each

**period and compounded at 8%?**

(b) What is the present value of $2,500 to be received at the beginning of each of 30 periods, discounted

**at 10% compound interest?**

(c) What is the future value of 15 deposits of $2,000 each made at the beginning of each period and

**compounded at 10%? (Future value as of the end of the fifteenth period.)**

(d) What is the present value of six receipts of $1,000 each received at the beginning of each period,

**discounted at 9% compounded interest?**

E6-5 (Computation of Present Value) Using the appropriate interest table, compute the present values of

**the following periodic amounts due at the end of the designated periods.**

(a) $30,000 receivable at the end of each period for 8 periods compounded at 12%.

(b) $30,000 payments to be made at the end of each period for 16 periods at 9%.

(c) $30,000 payable at the end of the seventh, eighth, ninth, and tenth periods at 12%.

E6-6 (Future Value and Present Value Problems) Presented below are three unrelated situations.

(a) Dwayne Wade Company recently signed a lease for a new office building, for a lease period of

10 years. Under the lease agreement, a security deposit of $12,000 is made, with the deposit to be

**returned at the expiration of the lease, with interest compounded at 10% per year. What amount will**

**the company receive at the time the lease expires?**

(b) Serena Williams Corporation, having recently issued a $20 million, 15-year bond issue, is committed

**to make annual sinking fund deposits of $600,000. The deposits are made on the last day of each**

**year and yield a return of 10%. Will the fund at the end of 15 years be sufficient to retire the bonds?**

If not, what will the deficiency be?

(c) Under the terms of his salary agreement, president Rex Walters has an option of receiving either an

**immediate bonus of $40,000, or a deferred bonus of $70,000 payable in 10 years. Ignoring tax considerations**

**and assuming a relevant interest rate of 8%, which form of settlement should Walters accept?**

E6-7 (Computation of Bond Prices) What would you pay for a $50,000 debenture bond that matures in

15 years and pays $5,000 a year in interest if you wanted to earn a yield of:

(a) 8%? (b) 10%? (c) 12%?

E6-8 (Computations for a Retirement Fund) Clarence Weatherspoon, a super salesman contemplating

**retirement on his fifty-fifth birthday, decides to create a fund on an 8% basis that will enable him to withdraw**

**$20,000 per year on June 30, beginning in 2018 and continuing through 2021. To develop this fund,**

Clarence intends to make equal contributions on June 30 of each of the years 2014–2017.

Instructions

Instructions

(a) How much must the balance of the fund equal on June 30, 2017, in order for Clarence Weatherspoon

**to satisfy his objective?**

(b) What are each of Clarence’s contributions to the fund?

E6-9 (Unknown Rate) LEW Company purchased a machine at a price of $100,000 by signing a note payable,

**which requires a single payment of $123,210 in 2 years. Assuming annual compounding of interest,**

**what rate of interest is being paid on the loan?**

E6-10 (Unknown Periods and Unknown Interest Rate) Consider the following independent situations.

(a) Mike Finley wishes to become a millionaire. His money market fund has a balance of $92,296 and

**has a guaranteed interest rate of 10%. How many years must Mike leave that balance in the fund in**

**order to get his desired $1,000,000?**

(b) Assume that Sally Williams desires to accumulate $1 million in 15 years using her money market

**fund balance of $182,696. At what interest rate must Sally’s investment compound annually?**

E6-11 (Evaluation of Purchase Options) Sosa Excavating Inc. is purchasing a bulldozer. The equipment

**has a price of $100,000. The manufacturer has offered a payment plan that would allow Sosa to make 10**

**equal annual payments of $16,274.53, with the first payment due one year after the purchase.**

Instructions

Instructions

(a) How much total interest will Sosa pay on this payment plan?

(b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%. Should

Sosa borrow from the bank or use the manufacturer’s payment plan to pay for the equipment?

E6-12 (Analysis of Alternatives) The Black Knights Inc., a manufacturer of low-sugar, low-sodium,

**low-cholesterol TV dinners, would like to increase its market share in the Sunbelt. In order to do so, Black**

Knights has decided to locate a new factory in the Panama City area. Black Knights will either buy or lease

**a site depending upon which is more advantageous. The site location committee has narrowed down the**

**available sites to the following three buildings.**

Building A: Purchase for a cash price of $600,000, useful life 25 years.

Building B: Lease for 25 years with annual lease payments of $69,000 being made at the beginning of

**the year.**

Building C: Purchase for $650,000 cash. This building is larger than needed; however, the excess space

**can be sublet for 25 years at a net annual rental of $7,000. Rental payments will be received at the end**

**of each year. The Black Knights Inc. has no aversion to being a landlord.**

Instructions

Instructions

In which building would you recommend that The Black Knights Inc. locate, assuming a 12% cost of funds?

E6-13 (Computation of Bond Liability) George Hincapie Inc. manufactures cycling equipment. Recently,

**the vice president of operations of the company has requested construction of a new plant to meet the increasing**

**demand for the company’s bikes. After a careful evaluation of the request, the board of directors**

**has decided to raise funds for the new plant by issuing $2,000,000 of 11% term corporate bonds on March 1,**

2014, due on March 1, 2029, with interest payable each March 1 and September 1. At the time of issuance,

**the market interest rate for similar financial instruments is 10%.**

Instructions

Instructions

As the controller of the company, determine the selling price of the bonds.

E6-14 (Computation of Pension Liability) Nerwin, Inc. is a furniture manufacturing company with 50

**employees. Recently, after a long negotiation with the local labor union, the company decided to initiate a**

**pension plan as a part of its compensation plan. The plan will start on January 1, 2014. Each employee**

**covered by the plan is entitled to a pension payment each year after retirement. As required by accounting**

**standards, the controller of the company needs to report the pension obligation (liability). On the basis of**

**a discussion with the supervisor of the Personnel Department and an actuary from an insurance company,**

**the controller develops the following information related to the pension plan.**

Average length of time to retirement 15 years

Expected life duration after retirement 10 years

Total pension payment expected each year after retirement

**for all employees. Payment made at the end of the year. $700,000 per year**

The interest rate to be used is 8%.

Instructions

Instructions

On the basis of the information above, determine the present value of the pension obligation (liability).

E6-15 (Investment Decision) Andrew Bogut just received a signing bonus of $1,000,000. His plan is to

**invest this payment in a fund that will earn 8%, compounded annually.**

Instructions

Instructions

(a) If Bogut plans to establish the AB Foundation once the fund grows to $1,999,000, how many years

**until he can establish the foundation?**

(b) Instead of investing the entire $1,000,000, Bogut invests $300,000 today and plans to make 9 equal

**annual investments into the fund beginning one year from today. What amount should the payments**

**be if Bogut plans to establish the $1,999,000 foundation at the end of 9 years?**

E6-16 (Retirement of Debt) Jesper Parnevik borrowed $70,000 on March 1, 2012. This amount plus accrued

**interest at 12% compounded semiannually is to be repaid March 1, 2022. To retire this debt, Jesper**

**plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2017, and for the next**

4 years. The fund is expected to earn 10% per annum.

Instructions

Instructions

How much must be contributed each year by Jesper Parnevik to provide a fund sufficient to retire the debt

**on March 1, 2022?**

E6-17 (Computation of Amount of Rentals) Your client, Keith Moreland Leasing Company, is preparing

**a contract to lease a machine to Souvenirs Corporation for a period of 25 years. Moreland has an investment**

**cost of $365,755 in the machine, which has a useful life of 25 years and no salvage value at the end of**

**that time. Your client is interested in earning an 11% return on its investment and has agreed to accept**

25 equal rental payments at the end of each of the next 25 years.

Instructions

Instructions

You are requested to provide Moreland with the amount of each of the 25 rental payments that will yield

**an 11% return on investment.**

E6-18 (Least Costly Payoff) Assume that Sonic Foundry Corporation has a contractual debt outstanding.

Sonic has available two means of settlement. It can either make immediate payment of $2,600,000, or it can

**make annual payments of $300,000 for 15 years, each payment due on the last day of the year.**

Instructions

Instructions

Which method of payment do you recommend, assuming an expected effective interest rate of 8% during

**the future period?**

E6-19 (Least Costly Payoff) Assuming the same facts as those in E6-18 except that the payments must

**begin now and be made on the first day of each of the 15 years, what payment method would you**

**recommend?**

E6-20 (Expected Cash Flows) For each of the following, determine the expected cash flows.

Cash Flow Probability

Estimate Assessment

(a) $ 4,800 20%

6,300 50%

7,500 30%

(b) $ 5,400 30%

7,200 50%

8,400 20%

(c) $(1,000) 10%

3,000 80%

5,000 10%

E6-21 (Expected Cash Flows and Present Value) Keith Bowie is trying to determine the amount to set

**aside so that he will have enough money on hand in 2 years to overhaul the engine on his vintage used car.**

While there is some uncertainty about the cost of engine overhauls in 2 years, by conducting some research

**online, Keith has developed the following estimates.**

Engine Overhaul Probability

Estimated Cash Outfl ow Assessment

**$200 10%**

450 30%

600 50%

750 10%

Instructions

Instructions

How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that he

**will have enough money on hand in 2 years to pay for the overhaul?**

E6-22 (Fair Value Estimate) Killroy Company owns a trade name that was purchased in an acquisition of

McClellan Company. The trade name has a book value of $3,500,000, but according to GAAP, it is assessed

**for impairment on an annual basis. To perform this impairment test, Killroy must estimate the fair value of**

**the trade name. (You will learn more about intangible asset impairments in Chapter 12.) It has developed**

**the following cash flow estimates related to the trade name based on internal information. Each cash flow**

**estimate reflects Killroy’s estimate of annual cash flows over the next 8 years. The trade name is assumed**

**to have no salvage value after the 8 years. (Assume the cash flows occur at the end of each year.)**

Probability

Cash Flow Estimate Assessment

**$380,000 20%**

630,000 50%

750,000 30%

Instructions

Instructions

(a) What is the estimated fair value of the trade name? Killroy determines that the appropriate discount

**rate for this estimation is 8%.**

(b) Is the estimate developed for part (a) a Level 1 or Level 3 fair value estimate? Explain.