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Chapter 6: Q15E (page 305)

Andrew Bogut just received a signing bonus of \(1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually. Instructions (a) If Bogut plans to establish the AB Foundation once the fund grows to \)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?

Short Answer

Expert verified

The period required will be 9 years, and the annual payment will be $112,056.

Step by step solution

01

Calculation of period

FutureValueFactor=FutureValueAmountInvested=1,999,0001,000,000=1.999

The future value is 1.999 at 8% in 9 years.

02

Calculation of annual payment

AnnualPayment=RemainingFutureValuepresentValueofannuityfactor=1,999,000-300,000脳1.9990012.48756=$112,056

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Most popular questions from this chapter

Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns.

(a) What is the amount of the payments that Ned Winslow must make at the end of each of 8 years to accumulate a fund of \(90,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually?

(b) Robert Hitchcock is 40 years old today and he wishes to accumulate \)500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthday. What annual deposit must Robert make if the fund will earn 8% interest compounded annually?

(c) Diane Ross has \(20,000 to invest today at 9% to pay a debt of \)47,347. How many years will it take her to accumulate enough to liquidate the debt?

(d) Cindy Houston has a \(27,600 debt that she wishes to repay 4 years from today; she has \)19,553 that she intends to invest for the 4 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt?

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 5% 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 \)55,000, or a deferred bonus of $70,000 payable in 10 years. Ignoring tax considerations and assuming a relevant interest rate of 4%, which form of settlement should Walters accept?

The Procter & Gamble Company (P&G)

The financial statements of P&G are presented in Appendix B. The company鈥檚 complete annual report, including the notes to the financial statements, is available online.

Instructions (a) Examining each item in P&G鈥檚 balance sheet, identify those items that require present value, discounting, or interest computations in establishing the amount reported. (The accompanying notes are an additional source for this information.)

(b) (1) What interest rates are disclosed by P&G as being used to compute interest and present values?

(2) Why are there so many different interest rates applied to P&G鈥檚 financial statement elements (assets, liabilities, revenues, and expenses)?

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

Johnson Co. accepts a note receivable from a customer in exchange for some damaged inventory. The note requires the customer make semiannual installments of \(50,000 each for 10 years. The first installment begins six months from the date the customer takes delivery of the damaged inventory. Johnson鈥檚 management estimates that the fair value of the damaged inventory is \)679,517.

Accounting

(a) What interest rate is Johnson implicitly charging the customer? Express the rate as an annual rate but assume semiannual compounding.

(b) At what dollar amount do you think Johnson should record the note receivable on the day the customer takes delivery of the damaged inventory?

Analysis

Assume the note receivable for damaged inventory makes up a significant portion of Johnson鈥檚 assets. If interest rates increase, what happens to the fair value of the receivable? Briefly explain why.

Principles

The Financial Accounting Standards Board has issued an accounting standard that allows companies to report assets such as notes receivable at fair value. Discuss how fair value versus historical cost potentially involves a trade-off of one desired quality of accounting information against another.
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