Task: Moerdyk Corporation\'s bonds have a 15-year maturity, a 7.25% semiannual c

Question

Task:

Moerdyk Corporation's bonds have a 15-year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) is 6.20%, based on semiannual compounding. What is the bond’s price?

Solution:

Par value = FV                                     $1,000

Coupon rate                                           7.25%

Periods/year                                                   2

Yrs to maturity                                             15

Periods = Years × 2 = N                               30

Going annual rate = YTM = rd               6.20%

Periodic rate = rd/2 = I/YR                     3.10%

Coupon rate × Par/2 = PMT                  $36.25

PV       $1,101.58


Question:

Please, explain in VERY DETAILED way how thw PV was calculated. Provide formula and substitute numbers from the task.

Explanation / Answer

Par Value or Maturity Value = $1,000

Annual coupon rate = 7.25%; Semi-annual coupon rate = 7.25%/2 = 3.625%

Semi-annual coupon = $1,000 * 3.625% = $36.25

Annual YTM = 6.20%; Semi-annual YTM = 3.10%

Time-to-maturity = 15 years or 30 semi-annual periods.

Bond current price = Semi-annual coupon * PVIFA at semi-annual YTM for semi-annual periods + Maturity Value * PVIF at Sem-annual YTM for Semi-annual periods

Or, Current Price = $36.25 * PVIFA at 3.10% for 30 periods + $1,000 * PVIF at 3.10% for 30 periods

Or, PVIFA = (1 - 1/(1+Semi-Annual YTM)^Semi-Annual Period) / Semi-Annual YTM
Or, PVIFA = (1 - 1/1.031^30) / 0.031 = 19.34949

PVIF = 1/(1+Semi-Annual YTM)^ Semi-Annual Period

Or, PVIF = 1 / 1.031^30 = 0.4002

Current Price = $36.25 * 19.3495 + $1,000 * 0.4002 = $1,101.58

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