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Chapter 6: Q5Q (page 301)

Question: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.

Short Answer

Expert verified

6.71008 shows the present value, 0.46319 shows the future value, 2.15892 shows the present value, and 14.48656 shows the future value of the ordinary annuity.

Step by step solution

01

Step-by-Step solution Step 1 Definition of the ordinary annuity

Ordinary annuityrefers to a series of frequent or regular payments made at the end of each period.Periods can be monthly, quarterly, half-yearly, and yearly.

02

Values representation

The four values mentioned in the question indicates the following:

6.71008 shows the present value of an ordinary annuity at an 8% interest rate for 10 periods (Table 6-4)

0.46319 represents thefuture valueof 1 at 8% for 10 periods.

2.15892 indicates the present value of 1 at 8% for 10 periods

14.48656 represents the future value of the ordinary annuity at 8% for 10 periods

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Most popular questions from this chapter

Howie Long has just learned he has won a \(500,000 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Howie takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Howie a payout of 20 equal payments of \)36,000 with the first payment occurring when Howie turns in the winning ticket. Howie will be taxed on each of these payments at a rate of 25%.

Instructions Assuming Howie can earn an 8% rate of return (compounded annually) on any money invested during this period, which payout option should he choose?

Answer each of these unrelated questions.

(a) On January 1, 2017, Fishbone Corporation sold a building that cost \(250,000 and that had accumulated depreciation of \)100,000 on the date of sale. Fishbone received as consideration a \(240,000 non-interest-bearing note due on January 1, 2020. There was no established exchange price for the building, and the note had no ready market. The prevailing rate of interest for a note of this type on January 1, 2017, was 9%. At what amount should the gain from the sale of the building be reported?

(b) On January 1, 2017, Fishbone Corporation purchased 300 of the \)1,000 face value, 9%, 10-year bonds of Walters Inc. The bonds mature on January 1, 2027, and pay interest annually beginning January 1, 2018. Fishbone purchased the bonds to yield 11%. How much did Fishbone pay for the bonds?

(c) Fishbone Corporation bought a new machine and agreed to pay for it in equal annual installments of \(4,000 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 8% applies to this contract, how much should Fishbone record as the cost of the machine?

(d) Fishbone Corporation purchased a special tractor on December 31, 2017. The purchase agreement stipulated that Fishbone should pay \)20,000 at the time of purchase and \(5,000 at the end of each of the next 8 years. The tractor should be recorded on December 31, 2017, at what amount, assuming an appropriate interest rate of 12%?

(e) Fishbone Corporation wants to withdraw \)120,000 (including principal) from an investment fund at the end of each year for 9 years. What should be the required initial investment at the beginning of the first year if the fund earns 11%?

James Kirk is a financial executive with McDowell Enterprises. Although James Kirk has not had any formal training in finance or accounting, he has a 鈥済ood sense鈥� for numbers and has helped the company grow from a very small company (\(500,000 sales) to a large operation (\)45 million in sales). With the business growing steadily, however, the company needs to make a number of difficult financial decisions in which James Kirk feels a little 鈥渙ver his head.鈥� He therefore has decided to hire a new employee with 鈥渘umbers鈥� expertise to help him. As a basis for determining whom to employ, he has decided to ask each prospective employee to prepare answers to questions relating to the following situations he has encountered recently. Here are the questions.

(a) In 2016, McDowell Enterprises negotiated and closed a long-term lease contract for newly constructed truck terminals and freight storage facilities. The buildings were constructed on land owned by the company. On January 1, 2017, McDowell took possession of the leased property. The 20-year lease is effective for the period January 1, 2017, through December 31, 2036. Advance rental payments of \(800,000 are payable to the lessor (owner of facilities) on January 1 of each of the first 10 years of the lease term. Advance payments of \)400,000 are due on January 1 for each of the last 10 years of the lease term. McDowell has an option to purchase all the leased facilities for \(1 on December 31, 2036. At the time the lease was negotiated, the fair value of the truck terminals and freight storage facilities was approximately \)7,200,000. If the company had borrowed the money to purchase the facilities, it would have had to pay 10% interest. Should the company have purchased rather than leased the facilities?

(b) Last year the company exchanged a piece of land for a non-interest-bearing note. The note is to be paid at the rate of \(15,000 per year for 9 years, beginning one year from the date of disposal of the land. An appropriate rate of interest for the note was 11%. At the time the land was originally purchased, it cost \)90,000. What is the fair value of the note?

(c) The company has always followed the policy to take any cash discounts on goods purchased. Recently, the company purchased a large amount of raw materials at a price of $800,000 with terms 1/10, n/30 on which it took the discount. McDowell has recently estimated its cost of funds at 10%. Should McDowell continue this policy of always taking the cash discount?

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

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 2021 and continuing through 2024. To develop this fund, Clarence intends to make equal contributions on June 30 of each of the years 2017鈥�2020. Instructions

(a) How much must the balance of the fund equal on June 30, 2020, in order for Clarence to satisfy his objective?

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