Financial Management When Bonds Trade

Financial Management

When bonds trade below par, this means that they the coupon rate is below the yield to maturity. The bonds are priced at a discount because the rate is below the prevailing rates. In order to compensate investors for the fact that the bond is not paying the prevailing rates, the price of the bond must be at a discount. This gives the investors additional gains, as they redeem the bond at maturity for more than they paid to purchase the bond.

The current yield refers to the yield if the bond was held for just one year. While the true yield is going to be unknown since the sale price is unknown, the current yield is therefore calculated on the basis of the interest only. If the bond is trading below par, then the coupon rate is below the current yield. The coupon rate is the current yield if the bond is at par; therefore if the bond is below part, the coupon rate will be lower than the current yield. Again, investors need to be compensated for the fact that the coupon is lower than the prevailing interest rate.

3. If inflation increases unexpectedly, the market price of bonds will decrease. Bond prices reflect the net present value of future payments. Those payments are fixed, so their value is wholly dependent on the prevailing interest rates. Inflation therefore reduces the buying power of the future payments. To compensate for the reduction in buying power, the market price of the bonds must decrease.

4. Under the above scenario, I would prefer to be holding three-year bonds from the same issuer. The longer the time frame, the more the bond is subject to changes in interest rates. The inflation rate will decrease the value of payments for all future time periods, but will decrease it more for longer time periods. As such, the longer the time period of the bond, the more it will fluctuate with unexpected inflation changes. An increase in inflation is an adverse change; therefore, I would want to hold three-year bonds as they will see less decrease in value.

5. The price of this bond would be 1148.775 based on the bond pricing formula:

P = 40 [1- [1/[(1+.03)^20]]/.03 + [1000/[(1+.03)^20]]

6. The formula for calculating the price of a zero coupon bond is

P = M / (1 + I )^n

In this case, the interest is priced to 9% and the term to 20 years. These figures are doubled, because the price of zero coupon bonds is based on semi-annual. Therefore, the price of this bond would be 1000 / (1 + .045) ^ 40 = 171.93.

7. We would use the regular bond pricing formula to calculate the YTM for this bond. This is a difficult equation to solve for, so it is typically either estimated by trial and error, or solved on a spreadsheet. Having taken the latter approach, the yield to maturity would therefore be 6.6033% for this bond.

8. To calculate the most I would be willing to pay for this preferred share investment, we must consider that the dividend is a perpetuity. The payment is quarterly, so the discount rate is adjusted accordingly to 2%. The formula for valuing a perpetuity is

P = coupon / discount rate so P = 1 / 0.02 = $50.

9. The basic formula for the dividend discount model is

P = Dividends / ( D -- G)

a) The first analyst will run a basic model that begins with the existing dividends, expected growth rate and discount rate. The current dividend is $6.60. Thus, the first analyst will value the stock as follows:

P = 6.60 / ( .11 -- .07) = $165.

b) The second analyst uses a more complicated version of the dividend discount model to value the stock. This equation must be conducted in two parts, each reflecting the different growth rates. The PV of the expected cash flows for the first three years is calculated, with the dividend discount model used to calculate the value of the remaining flows.