finance question…?
im doing a finance exam…here’s the question
Big Bear Inc.’s outstanding bonds have a $1,000 par value, and they mature in 5 years. Their yield to maturity is 9%, based on semiannual compounding, and the current market price is $853.61. The bonds have a par value of $1,000. What is the bond’s annual coupon interest rate?
can someone tell me the formula to figure this out. I don’t want the answer, I want to know how to do it. Thanks.
PV = Sum of cash flows
PV = Coupon(1)/(1+r)^(1) + Coupon(2)/(1+r)^2 + … Coupon(n)/(1+r)^n + FV/(1+r)^n
You know PV, you know r, you know FV. Solve for the coupon rate.
853.61 = C(1)/(1.044)+C(2)/(1.044^2)+…+C(10)(1.044^10)+1000/(1.044^10)
Proof:
FV = 1,000
PV = -853.61
APR = (1.09)^(1/2)-1 = 1.044-1 = 4.4% per semiannual period
Periods = 5×2 = 10 semiannual periods
Solve for PMT
PMT = 25.5903 per semiannual payment
Annual Coupon = 25.59×2 = 51.18 = 5.118% nominal annual coupon rate
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