Yield to maturity Fitzgeralds 35year bonds pay 7 percent int

(Yield to maturity) Fitzgerald\'s 35-year bonds pay 7 percent interest annually on a $1,000 par value. If the bonds sell at $845, what is the bond\'s yield to maturity? What would be the yield to maturity if the bonds paid interest semiannually? Explain the difference a. The bond\'s yield to maturity if the bond pays interest annually is %. (Round to three decimal places.)

Solution

Answer a.

Face Value = $1,000
Current Price = $845

Annual Coupon Rate = 7%
Annual Coupon = 7% * $1,000
Annual Coupon = $70

Time to Maturity = 35 years

Let Annual YTM be i%

$845 = $70 * PVIFA(i%, 35) + $1,000 * PVIF(i%, 35)

Using financial calculator:
N = 35
PV = -845
PMT = 70
FV = 1000

I = 8.382%

Annual Yield to Maturity = 8.382%

Answer b.

Face Value = $1,000
Current Price = $845

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50% * $1,000
Semiannual Coupon = $35

Time to Maturity = 35 years
Semiannual Period to Maturity = 70

Let Semiannual YTM be i%

$845 = $35 * PVIFA(i%, 70) + $1,000 * PVIF(i%, 70)

Using financial calculator:
N = 70
PV = -845
PMT = 35
FV = 1000

I = 4.188%

Semiannual Yield to Maturity = 4.188%
Annual Yield to Maturity = 2 * 4.188%
Annual Yield to Maturity = 8.376%

Answer c.

Difference in yield to maturity arises due to the change in number of compounding period per year.