Gray House is issuing bonds paying $95 per year but paid semianaully that will m
ID: 1171331 • Letter: G
Question
Gray House is issuing bonds paying $95 per year but paid semianaully that will mature 15 years from today. The bond is currently selling for $980 for a face of $1,000. Calculate: a) Coupon rate b) Current yield c) The yield to maturity d) The market price of the bond if the market rates for bonds of equal risk changed to 7.5%. Gray House is issuing bonds paying $95 per year but paid semianaully that will mature 15 years from today. The bond is currently selling for $980 for a face of $1,000. Calculate: a) Coupon rate b) Current yield c) The yield to maturity d) The market price of the bond if the market rates for bonds of equal risk changed to 7.5%.Explanation / Answer
Answer a.
Annual Coupon = $95
Semiannual Coupon = Annual Coupon / 2
Semiannual Coupon = $95 / 2
Semiannual Coupon = $47.50
Coupon Rate = Annual Coupon / Par Value
Coupon Rate = $95 / $1,000
Coupon Rate = 9.50%
Answer b.
Current Yield = Annual Coupon / Current Price
Current Yield = $95 / $980
Current Yield = 9.69%
Answer c.
Par Value = $1,000
Semiannual Coupon = $47.50
Current Price = $980
Semiannual Period to Maturity = 30 (15 years)
Let semiannual YTM be i%
$980 = $47.50 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)
Using financial calculator:
N = 30
PV = -980
PMT = 47.50
FV = 1000
I = 4.878%
Semiannual YTM = 4.878%
Annual YTM = 2 * 4.878%
Annual YTM = 9.756% or 9.76%
Answer d.
Annual Market Rate = 7.50%
Semiannual Market Rate = 3.75%
Price of Bond = $47.50 * PVIFA(3.75%, 30) + $1,000 * PVIF(3.75%, 30)
Price of Bond = $47.50 * (1 - (1/1.0375)^30) / 0.0375 + $1,000 / 1.0375^30
Price of Bond = $1,178.29
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