Question

Moussawi Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 5 years. Their yield to maturity is 9% and their current price is $98241. What is the bond's annual coupon rate? (Hint: first solve for payment, and then determine the coupon rate). 

• 6.5% 

• 9.5% 

• 10.5% 

• 7.5% 

• 8.7%

Answer 1

Given for Moussawi Ltd.'s bond,

Face value = $1000

time to maturity = 5 years

Yield to maturity = 9%

current price = $982.41

Let the coupon payment on bond be C

We know that current price of bond is sum of all PV of coupon and Face value discounted at YTM

So, Price 982.41 = C/1.09 + C/1.09^2 + C/1.09^3 + C/1.09^4 + C/1.09^5 + 1000/1.09^5

Using sum of a GP formula S = a*(1-r^n)/(1-r)

where a = C/1.09

r = 1/1.09

n = 5

So we get, 982.41 = (C/1.09)*(1 - (1/1.09^5))/(1 - 1/1.09) + 1000/1.09^5

982.41 = 3.89C + 649.93

=> C = 85.48

So coupon rate = coupon/Face value = 85.48/1000 = 8.55%

So approximately correct answer is option E, 8.7%