Question

Page 2 ACCOUNTİNG2101/6101-TESTİNG YOUR KNOWLEDGE CHAPTER 6 3) Goldsboro Corporation has an outstanding bond obligation for $100,000,000 due lin 10 years. The company wants to create a bond retirement fund In order to have the $100,000,000 needed when the bonds mature on December 31, 20x10 On December 31, 20x1, the company deposited $20,000,000 into the fund. In addition, the company plans to make annual contributions into the fund to be certain that the $100,000,000 will be available when the bonds mature. The first payment will be made on December 31, 20x2; the last payment is scheduled for December 31, 20x9. The fund is expected to earn interest at 6%, compounded annually REQUIRED: Determine the amount of each of the annual contributions into the bond retirement fund needed to assure that $100,000,000 is accumulated at December 31, 20x10.

Answer 1

It should be noted that Company have to make available $100 million by 31st dec,2010.

For this Company has deposited $20 million on 31st dec 2001 in a fund which will fetch 6% income compounded every year for 9 years

Hence the Future value of $20 million will be as : $20,000,0000 * (1+6%)^9

= $20,000,000 * 1.689479

= $33,789,580

Remaining fund to be arranged = $100,000,000 - $33,789,580 = $66,210,420

We also know that Annual payment to fund has to be started from 31st december , 2002; let's suppose the annual payment is X.

Payment of X at 31st december 2002 will fetch as X * (1+6%)^8 at 31st december 2010

Hence, Payment of X at 31st december 2003 will fetch as X * (1+6%)^7 at 31st december 2010

Also, Payment of X at 31st december 2004 will fetch as X * (1+6%)^6 at 31st december 2010

.

.

.

Payment of X at 31st december 2009 will fetch as X * (1+6%)^1 at 31st december 2010.

We can frame one equation as :

X* {(1+6%)^8 + (1+6%)^7 + (1+6%)^6 ............................... + (1+6%)^1} = $66,210,420

X * 10.4913160 = $66,210,420

X = $66,210,420 / 10.4913160

= $6,310,973.76

Hence Annual Contribution will be $6,310,973.76 from Year 2002. Also, Company will deposit $20 million in Year 2001end.