You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 8 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 20 years to maturity. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. a. Compute the price of the bonds based on semiannual analysis. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Hi, well, first, we need to find the coupon value (semi-annual) and the discount rate in semi-annual terms. After that, take into account that we have to multiply 20 years by 2 since this exercise is based on semi-annual analysis (so we use 40 for the periods to pay the bond and the face value of the bond).

For the coupon:

[tex]Coupon=\frac{FaceValue*CouponRate}{2} =\frac{1,000*0.08}{2} =40[/tex]

Now, let´s convert the rate to semi-annual terms.

[tex]r(SemiAnnual)=(1+r(Annual)^{\frac{1}{2} }) -1=(1+0.1)^{\frac{1}{2} } -1=0.048809[/tex]

So, our semi-annual discount rate is 4.8809%

With all the above information, let´s introduce the formula we need to use

[tex]Price=\frac{Coupon((1+r)^{n}-1) }{r(1+r)^{n} } +\frac{FaceValue}{(1+r)^{n} }[/tex]

It should look like this:

[tex]Price=\frac{40((1+0.048809)^{40}-1) }{0.048809(1+0.048809)^{40} } +\frac{1,000}{(1+0.048809)^{40} }[/tex]

[tex]Price=697.71+148.64=846.35[/tex]

So the price of this bond is $846.35

Best of luck.