On June 30, 2016, Gaston Corporation sold $800,000 of 11% face value bonds for $

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.

Explanation / Answer

The YTM (yield to maturity) can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Coupon Payment, PV = Present Value and FV = Face Value

__________

June 30, 2016 Issuance:

Here, Nper = 7*2 (31st December 2023 - 31st December 2016) + .5 (1st July 2016 to 31st December 2016) = 14.5 (total number of interest payments upto maturity), PMT = 800,000*11%*1/2 = $44,000, PV = $761,150.96 and FV = $800,000 [we use 2 since the payments are semi-annual]

Using these values in the above function/formula for Rate, we get,

YTM = Rate(14.5,44000,-761150.96,800000)*2 = 12.02%

Effective Yield Rate = (1+YTM/2)^2 - 1 = (1+12.02%/2)^2 - 1 = 12.38% or 12% (if rounded off to whole percentages)

__________

December 31, 2016 Issuance:

Here, Nper = 7*2 (31st December 2023 - 31st December 2016) = 14 (total number of interest payments upto maturity), PMT = 700,000*11%*1/2 = $38,500, PV = $734,645.28 and FV = $700,000 [we use 2 since the payments are semi-annual]

Using these values in the above function/formula for Rate, we get,

YTM = Rate(14,38500,-734645.28,700000)*2 = 10%

Effective Yield Rate = (1+10%/2)^2 -1 = 10.25% or 10% (if rounded off to whole percentages)

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.