Question

Kebt Corporation's Class Semi bonds have a 12-year maturity and an 6.00% coupon paid semiannually (3% each 6 months), and those bonds sell at their $1,000 par value. The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value, but these bonds pay interest annually. Neither bond is callable. At what price should the annual payment bond sell?

Group of answer choices

$1,032.19

$1,002.42

$883.32

$1,071.89

$992.49

Answer 1

First the YTM of the semi bonds will be calculated

for this the below formula will be used

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=12*2=24

r-intrest rate per period=?

Semi annual Coupon payment=coupon rate *face value/2=6%*1000/2=30

Price of bond=1000

Putting values in formula

1000=30*((1-(1/(1+r)^24))/r)+1000/(1+r)^24

Solving we get

r=3.00%

Now r-3% is the semi annual YTM

Therefore the effective annual YTM=(1+semiannual YTM)^2-1

Putting values

the effective annual YTM=(1+.03)^2-1=6.09%

Now the price of ann bond will be calculated using the same formula used above

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=12

r-intrest rate per period=6.09%

annual Coupon payment=coupon rate *face value=6%*1000=60

Price of bond=?

Putting values in formula

Price of ann bond=60*((1-(1/(1+.0609)^12))/.0609)+1000/(1+.0609)^12

Solving we get

Price of annual bond=$992.49