Question

Suppose a US company issued 10-year bonds 5 years ago with a face value of $1,000 and an annual coupon rate of 6%. The coupons are paid semi-annually and the bonds are currently trading in the market at a price of $1,089.83. The company is considering whether to call the bonds and issue new 5- year bonds at a par value of $1,000. Based on this information, answer the following four questions.

(i) What is the yield to maturity on the currently outstanding bonds with a remaining time to maturity of 5 years? If we assume that the company’s credit rating has not changed, what is the annual coupon rate the company would pay on the newly issued bond? Would you advise the company to call the bond and refinance?

(ii) Suppose the yield that the US government would pay on a 5-year bond with a coupon rate of 6% equals 1.5%. What would be the current market price of the government bond?

(iii) Looking at current interest rates in the market, 10-year government bonds have a higher yield to maturity than 5-year government bonds. The yield curve on corporate bonds shows that 5-year corporate bonds trade at a higher yield than 5-year government bonds. Can you explain both of these observations?

(iv) Suppose that after a contentious meeting at the Fed, the chairperson decides that it is time for a drastic interest rate increase. As a result the yield on 5-year government bonds goes up to 3.5%. What is the effect of this interest rate increase on the price of this bond? Would zero-coupon bonds respond more or less aggressively to the change in the interest rate? Explain your answer

Answer 1

Existing Bond : Residual term = 5 years, Maturity Value = $1000 , Annual Coupon = 6% paid semi annually and current price = $ 1089.83

The YTM will be the discount rate which will equate the future cash flows to current price. Since the coupon is semi annual, we adjust the rate and time period accordingly.

1089.83 = 30/(1+r%) + 30/(1+r%)² + .... + (1000+30)/(1+r%)¹⁰ ; solving for r = 2% or annualised YTM = 4%

If the credit rating has not changed, then the expected yield on the new bonds should also be 4%.

Let us assume that the company has 1000 bonds outstanding then in the current scenario its interest cost will be = 1000 * 1000 * 6% = 60000

If it recalls these bonds by paying 1089.83 per bond, then they will require incremental bonds to be issued for = (1089.83 * 1000)/1000 = 1089.83 new bonds and its interest cost will be 43593.2 per annum. Hence it should be beneficial to refinance.

(ii) Since we are not given coupon frequency we assume the usual semi annual frequency. At face value of $1000, we have :

Price = 30/(1+1.5%/2) + 30/(1+1.5%/2)² + .... + (1000+30)/(1+1.5%/2)¹⁰ = 1215.99

(iii) 10 year government bonds have longer term to maturity and hence they come with higher market risk (they are default risk free) hence to entice investors to take on additional market risk, they will have to be at a higher rate indicating an upward sloping yield curve. When it comes to corporate bonds, since they have an element of credit risk in them, their yields have to be higher than government bonds to reflect the credit premium necessary for investors to take the additional risk

(iv) The bond prices have inverse relationship to yields, hence an increase in yield will result in lower bond prices since the investors will require higher yield (return) on all bonds and to provide higher returns, the prices will have to come down. However the prices of zero coupon bonds are more sensitive than the coupon bonds since they do not pay any intermediate cash flows and their entire return comes in the form of discount to maturity value, the changes in yields are magnified for all the residual years hence their prices react more aggressively compared to coupon bonds.