McConnel corporation has bonds on the market with 16.5 years to maturity, a YTM of 7.7 percent, a par value of 1000 and current
price of 1065. The bonds make semiannual payment and have a par value of $1,000.Required:What must the coupon rate be on these bonds?
1 answer:
Answer:
Coupon rate = 0.08402 or 8.402%
Explanation:
To calculate the price of the bond, we need to first calculate the coupon payment per period. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,
Coupon Payment (C) = x
Total periods (n)= 16.5 * 2 = 33
r or YTM = 7.7% * 1/2 = 3.85% or 0.0385
The formula to calculate the price of the bonds today is attached.
Using the bond price formula and the available values, we calculate the coupon rate to be,
1065 = x * [( 1 - (1+0.0385)^-33) / 0.0385] + 1000 / (1+0.0385)^33
1065 = x * (18.50739407) + 287.4653284
1065 - 287.4653284 = x * 18.50739407
777.5346716 / 18.50739407 = x
x = 42.012 rounded off to $42.01
If the semi annual coupon payment is $42.01, the annual coupon payment will be 42.01 * 2 = $84.02
The coupon rate on bonds is = 84.02 / 1000
Coupon rate = 0.08402 or 8.402%
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<h3>What is a transition diagram?</h3>
A specific type of flowchart used for language analysis is called a transition diagram.
The boxes of the flowchart are represented as circles and are referred to as states in the transition diagram.
<h3>What is the Transition Matrix?</h3>
The transition matrix is given as follows:
If 10% of the people are using Brand X, then 90% are not using brand x. thus the initial state matrix is:
S₀ = [ 0.1, 0.9]. Thus one week later, the state matrix is:
S₁ = S₀P = [0.1, 0.9] *
c11 = 0.1 x 0.6 + 0.9 x 0.6 = 0.6
c12 = 0.1 x 0.4 + 0.9 x 0.4 = 0.4
Hence
S₁ = [0.6, 0.4]
This means that the percentage that will be using it 1 week later is:
0.38 = 38%
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