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%
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%
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