Problem: In computing your answers to the cases below, you can round your answer

Question

Problem: In computing your answers to the cases below, you can round your answer to the nearest dollar. Find the appropriate present value tables in your materials. Use the following information in answering Cases 1 and 2 below: On January 1, 2008, Gray Company sold $900,000 of 10% bonds, due January 1, 2018. Interest on these bonds is paid on July 1 and January 1 each year. According to the terms of the bond contract, Gray must establish a sinking fund for the retirement of the bond principal starting no later than January 1, 2016. Since Gray was in a tight cash position during the years 2008 through 2013, the first contribution into the fund was made on January 1, 2014. Case 1: Assume that, starting with the January 1, 2014 contribution, Gray desires to make a total of four equal annual contributions into this fund. Compute the amount of each of these contributions assuming the interest rate is 8% compounded annually. Case 2: Assume, instead, that starting with the January 1, 2016 contribution, Gray desires to make a total of five equal semiannual contributions into this fund. Compute the amount of each of these contributions assuming the annual interest rate is 12%, compounded semiannually. Case 3: On January 2, 2014, Nelson Company loaned $100,000 to Holt Company. The terms of this loan agreement stipulate that Holt is to make 5 equal annual payments to Nelson at 10% interest compounded annually. Assume the payments are to begin on December 31, 2014. Compute the amount of each of these payments. Case 4: Jim Marsh, a lawyer contemplating retirement on his 65th birthday, decides to create a fund on an 8% basis which will enable him to withdraw $60,000 per year beginning June 30, 2017, and ending June 30, 2021. To provide this fund, he intends to make equal contributions on June 30 of each of the years 2012 through 2016. (a) How much must the balance of the fund equal after the last contribution on June 30, 2016 in order for him to satisfy his objective? (b) What are each of his contributions to the fund?

Explanation / Answer

CASE 1. Annuity Factor of 8% componded annualy for 4 years = 3.312
So Amount of installment = $900,000/3.312 = $271,739

Case 2. Annuity Factor of 12% pa componded Semi-annualy for next 5 installment =4.212
So Amount of installment = $900,000/4.212 = $213,656

Case3.Annuity Factor of 10% componded annualy for 5 years =3.791
So Amount of installment = 100000/3.791 = $26,380

case 4.
Time   Cash Inflows   DF @8%   PV
June 30, 2017   60000   0.926   55556
June 30, 2018   60000   0.857   51440
June 30, 2019   60000   0.794   47630
June 30, 2020   60000   0.735   44102
June 30, 2021   60000   0.681   40835
       Total PV   239563
a)The balance of the fund equal after the last contribution on June 30, 2016 in order for him to satisfy his objective = $239,563

b) Annuity factor of 8% compounded annually for 4 years = 3.993
From 30th June 2012 to 30th June 2015, He has to contribute equally = $239,563/3.993 = $60000

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