Question

Watters Umbrella Corp. issued 20-year bonds 2 years ago at a coupon rate of 9 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of the par value, what is the YTM?

Answer 1

Solution

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

Assume Face value =1000

n=number of periods to maturity=18*2=36

r-YTM semiannual

Assume Face value =1000

Semi annual Coupon payment=Coupon rate*face value/2=9%*1000/2=45

Current price of bond=105%*Face value=105%*1000=1050

Putting values in formula

1050=45*((1-(1/(1+r)^36))/r)+1000/(1+r)^36

Solving we get

r=4.23%

Thus Annual YTM=4.23*2=8.46%