Interest Rates and Bond Valuation

Terminology

•Face value/par value - the original issue price (the amount borrowed). •Maturity date - date on which loan has to be repaid.

•Coupon interest rate - original interest rate on the bond. •Coupon payment - the fixed interest payment on the bond. •YTM=required rate of return.

Bonds pay fixed coupon payments at fixed intervals and the face value at maturity.

there is an inverse relationship between the price of an investment and the rate of return on the investment – if you pay a higher price for an investment your rate of return must be lower (holding all other factors constant)) If the YTM = coupon rate the bond will sell for the face value (i.e. current price = face value). If the YTM > coupon rate the bond will sell for a discount (yield goes up, price goes down). If the YTM < coupon rate the bond will sell for a premium (yield goes down, price goes up).

Discussion

1.Identify the three most important determinants of the price of a bond. Describe the effect of each? Answer

The three factors affecting the price of a bond are

- coupon

- yield

- term to maturity. T

=> The relationship between price and coupon is a direct one - the higher the coupon, the higher the price. The relationship between price and yield is an inverse one - the higher the yield the lower the price, all other factors held constant. The relationship between price and maturity is not so clearly evident. Price changes resulting from changes in yields will be more pronounced, the longer the term to maturity.

2.Given a change in the level of interest rates, discuss how two major factors will influence the relative change in price of individual bonds.

Answer

For a given change in the level of interest rates, two factors that will influence the relative change in bond prices are the coupon and maturity of the issues. Bonds with longer maturity and/or lower coupons will have the greatest price changes in response to a given change in interest rates. Other factors likewise cause differences in price volatility, including the call features, but these factors are typically much less important.

3.What is the purpose of bond ratings?

Answer

Bond ratings provide a very important service in the market for fixed income securities because they provide the fundamental analysis for thousands of issues. The rating agencies conduct extensive analyses of the intrinsic characteristics of the issue to determine the default risk for the investor and inform the market of the analyses through their ratings.

4.What are the important assumptions made when you calculate the promised YTM?

Answer

The most crucial assumption that the investor makes is that cash flows will be received in full (i.e. investors hold the bond to maturity) and reinvested at the promised yield.

5.You expect interest rates to decline over the next 6 months. What kind of bonds do you want in your portfolios in term of duration and explain your reasoning for this choice. Answer

Given that you expect interest rates to decline during the next six months, you should choose bonds that will have the largest price increase, that is, bonds with long durations.

6.Which of the following bonds will have the greatest percentage increase in value if all interest rates decrease by 1 percent? a.20-year, zero coupon bond.

b.10-year, zero coupon bond.

c.20-year, 10 percent coupon bond.

d.20-year, 5 percent coupon bond.

Answer

Since a zero coupon bond’s price today is determined just by the NPV of its par value, all of its payment is discounted for the maximum amount of time, whereas a coupon bond has many payments discounted for less than the maximum amount of time. Therefore, a zero coupon bond is most affected by interest rate changes. So, the longest zero coupon bond is the correct answer, which is statement a.

7.Which of the following statements is most correct?

a.All else...