Question

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.)

Answer 1

To calculate the price of Olsen's Clothing Stores bonds, the present value of the future cash flows, including the semiannual interest payments and the principal at maturity, need to be determined. This involves using the semiannual interest rate and number of periods to discount the cash flows back to their present value.

Step-by-step explanation:

To compute the price of Olsen's Clothing Stores bonds with a $1,000 par value, and an 8% quoted annual interest rate that is paid semiannually, given a yield to maturity of 10% annual interest with 20 years to maturity, we need to look at the present value of the future cash flows from the bond. These cash flows include the semiannual interest payments and the principal repayment at maturity.

The bond's semiannual interest payment (Coupon Payment) is $40 ($1,000 x 8% / 2). The number of semiannual periods (n) is 40 (20 years x 2). The semiannual yield to maturity (Discount Rate) is 5% (10% / 2).

We can calculate the present value of the annuity (interest payments) using the following formula:
PV (interest payments) = PMT x ((1 - (1 + r)^-n) / r)
Where PMT is the semiannual payment, r is the semiannual discount rate, and n is the number of semiannual periods.

Then, we calculate the present value of the principal (face value) that will be received at the end of the maturity:
PV (face value) = Face Value / (1 + r)^n

The bond's price will be the sum of the present value of the annuity and the present value of the face value.

Answer 2

Ans. The price of the bonds based on semiannual analysis is $846.35

Step-by-step explanation:

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:

`Coupon=(FaceValue*CouponRate)/(2) =(1,000*0.08)/(2) =40`

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

`r(SemiAnnual)=(1+r(Annual)^{(1)/(2) }) -1=(1+0.1)^{(1)/(2) } -1=0.048809`

So, our semi-annual discount rate is 4.8809%

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

`Price=(Coupon((1+r)^(n)-1) )/(r(1+r)^(n) ) +(FaceValue)/((1+r)^(n) )`

It should look like this:

`Price=(40((1+0.048809)^(40)-1) )/(0.048809(1+0.048809)^(40) ) +(1,000)/((1+0.048809)^(40) )`

`Price=697.71+148.64=846.35`

So the price of this bond is $846.35

Best of luck.