Question

On June 30, 2016, Gaston Corporation sold $800,000 of 11% face value bonds for $761,150.96. On December 31, 2016, Gaston sold $700,000 of this same bond issue for $734,645.28. The bonds were dated January 1, 2016, pay interest semiannually on each December 31 and June 30, and are due December 31, 2023.

Required:

Compute the effective yield rate on each issuance of Gaston's 11% bonds. Click here to access the tables to use with this problem. Round your answers to the nearest whole percentage.

June 30, 2016 issuance:	%
December 31, 2016 issuance:	%

Answer 1

No. of interest periods from June 30,2016 to December 31, 2023 is 15 periods

Lets assume an yield rate which is higher that the interest rate per period(11%/2) since the issue price is less than the face value.

Say 6%(per period)

Effective rate for June 30, 2016 issuance:

Present Value of Bonds issued on June 30, 2016= $7,61,150.96

This includes both the principal amount as well as the interest part($8,00,000*11%*2/12 = $44,000)

Lets assume effective yield rate be "i" and it be 6%(assumption)

Therefore,

$7,61,150.96 = ($8,00,000 * pv factor for the last period ) + ($44,000 * pv factor for 15 periods )

$7,61,150.96 = ($8,00,000 *0.4172) + ($44,000 * 9.7122)

                   = $3,33,760 + $4,27,337

                   = $7,61,097

Therefore, the effective yield rate on issuance for June 30, 2016 is 12%( since 6% is semi-annual rate)

No. of interest periods from Dec 31,2016 to December 31, 2023 is 14 periods

Lets assume an yield rate which is lower that the interest rate(11%/2) per period since the issue price is more than the face value.

Say 5%(per period)

Effective rate for December 31, 2016 issuance:

Present Value of Bonds issued on December 31, 2016= $7,34,645.28

This includes both the principal amount as well as the interest part($7,00,000*11%*2/12 = $38,500)

Lets assume effective yield rate be "i" and it be 5%(assumption)

Therefore,

$7,34,645.28 = ($7,00,000 * pv factor for the last period ) + ($38,500 * pv factor for 14 periods )

$7,34,645.28 = ($7,00,000 *0.505067) + ($38,500 * 9.89864)

                   = $3,53,547 + $3,81,098

                   = $7,34,645

Therefore, the effective yield rate on issuance for December 31, 2016 is 10%( since 5% is semi-annual rate)