Consider a 10-year, $1000 coupon bond, redeemable at par, and assume that the co
ID: 2773524 • Letter: C
Question
Consider a 10-year, $1000 coupon bond, redeemable at par, and assume that the coupon is paid continuousl with an annual coupon rate of 5%. The bond is said to be callable, if the borrower (the issuer) can redeem the bond at a time prior to the maturity data. Suppose that, in this case, that it can called (at par, i.e. $1000) at the end of Year 7,8, or 9. What price would you be willing to pay if:
a) you required a yield rate of 6%
b)you required a yield rate of 4%
c) Suppose that instead, the redeemable amount in Year 7,8, and 9 were 1100, 1050, 1025, respectively. What are your answers now to a) and b)?
Explanation / Answer
coupon bond = $1000
No of years =10
Annual coupen rate = 5%
Price at yield rate 4% is
price= C*(1-(1/(1+i)^n)) / i+M/(1+i)^n
C=coupen amount * coupen rate
C= 1000*.05
C =50
Price=50(1-(1/(1+.04)^10))/.04+1000/(1+.04)^10
Price= 50(1-(1/1.480))/.04+1000/1.480
Price =50(1-.675)/.04+675.67
Price= 406.25+675.67
Price=1081.92
Yield at 6%
Price=50(1-(1/(1+.06)^10))/.06+1000/(1+.06)^10
Price=368.33+558.65
Price =926.98
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