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# Pricing of bonds, Yield to maturity, Yield to call

Problem 1: You intend to purchase an 18-year, \$1,000 face value bond that has coupon rate of 11% pays semiannually. If you expect to earn a 9.5 percent simple rate of return on this bond, how much should you be willing to pay for this bond immediately before it makes its first coupon payment?

Problem 2: Laser Industries has just issued callable twelve-year, 6% coupon bonds with semi-annual coupon payments. The bonds can be called at 103 in four years or anytime thereafter on a coupon payment date. The current bond price is 101. For an investment today in these bonds (assuming no transaction costs):

a. What is an investor's Yield to Maturity?
b. What is an investor's Yield to Call?

#### Solution Preview

Please refer attached file for better clarity of formulas and tables.
Solution:
Problem 1

Number of coupon payments=n= 36
Coupon payment=C=1000*11%/2=55
Required rate of return=r=9.5%/2=4.75%
Maturity Amount=M=\$1,000
It is equivalent to the situation that coupon payments are made at the beginning of period.
PV of all coupon payment=(C/r*(1-1/(1+r)^n))*(1+r)= 984.7145284
PV of maturity amount=(M/(1+r)^n)*(1+r)=197.0647255
PV of all cash flows=1181.779254
Maximum Price of bond=PV of all cash ...

#### Solution Summary

There are two problems. Solution to first problem depicts the steps to estimate the value of a coupon paying bond. Solution to second problem explains the methodology to calculate YTC and YTM.

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