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%.

Answer 1

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