Question

Red Frog Brewery has $1,000-par-value bonds outstanding with the following characteristics:

currently selling at par; 5 years until final maturity; and a 9 percent coupon rate

(with interest paid semiannually). Interestingly, Old Chicago Brewery has a very similar

bond issue outstanding. In fact, every bond feature is the same as for the Red Frog

bonds, except that Old Chicago’s bonds mature in exactly 15 years. Now, assume that

the market’s nominal annual required rate of return for both bond issues suddenly fell

from 9 percent to 8 percent.

a.Which brewery’s bonds would show the greatest price change? Why?

b. At the market’s new, lower required rate of return for these bonds, determine the per

bond price for each brewery’s bonds. Which bond’s price increased the most, and by

how much?

Answer 1

Solution

The value of a bond is determined as follows:

Here,

The value of bond is .

The annual coupon interest is .

The market or face value is .

The bond paying coupon semi-annually is calculated as follows:

The value of and are found from their corresponding provided tables. The present value is ascertained from table at the rate and year.

In semi-annual bond the interest rate is divided by two and the period is multiplied by two.

(a)

If the bond is sold at par, the coupon interest and YTM are same. The price of bond and yield to maturity is determining factor for an investor to invest. They (price and YTM) are inversely related.

Hence, longer the duration more change in price of a bond. As they (price and period) are directly related.

Here, RF bond matures in five years and OC bond matures in 10 years. Therefore, as per the bond theory, the bond that would fluctuate more is OC bond.

In the price of a bond with less maturity period, the major proportion is the par value rather than the coupon payments as compared to that of a bond with longer maturity period. So, the change in the required rate of return has proportionally less impact on the price of a bond that has closer maturity period related to the bond with longer maturity period.

In other words, the price of a bond with shorter maturity period fluctuates less in response to the change in the required rate of interest than that of the price of a bond with longer maturity period. So, the bonds of OC would show the greatest price change in response to the change in the required rate of interest than that of the bonds of RF because the bonds of OC have longer maturity than the bonds of RF.

(b)

The price per bond is the estimated value of the bond, depending on the values of the associated parameters. The bond price of the given brewery’s bonds is calculated using the formula mentioned above.

RF Bonds

The given coupon rate is 9 percent and is paid semiannually. It is on the face value and so, annual coupon payment will be.

With face value, maturity period, coupon payment and nominal annual required rate of return, the value of a bond is calculated as shown below.

So, the required price per bond is.