. Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%. a. What was the price of this bond when it was issued? b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment? c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
1. Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.
a. What was the price of this bond when it was issued?
b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?
c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?
Answer a.
Face Value = $1,000
Annual Coupon Rate = 7.00%
Annual Coupon = 7.00% * $1,000
Annual Coupon = $70
Time to Maturity = 10 years
Annual YTM = 6.00%
Price of Bond = $70/1.06 + $70/1.06^2 + … + $70/1.06^9 + $70/1.06^10 + $1,000/1.06^10
Price of Bond = $70 * (1 - (1/1.06)^10) / 0.06 + $1,000 * (1/1.06)^10
Price of Bond = $70 * 7.360087 + $1,000 * 0.558395
Price of Bond = $1,073.60
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