Question

Jason Greg is a recent retiree who is interested in investing some of his savings in corporate bonds. Listed below are the bonds he is considering adding to his portfolio.

Bond A has a 7.5% semiannual coupon, matures in 12 years, and has a $1,000 face value.

Bond B has a 10% semiannual coupon, matures in 12 years, and has a $1,000 face value.

Bond C has an 11.5% semiannual coupon, matures in 12 years, and has a $1,000 face value.

Each bond has a YTM of 10%.

e.Mr. Greg is considering another bond, Bond D. It has an 8% semiannual coupon and a $1,000 face value. Bond D is scheduled to mature in 9 years and has a price of $1,150. It is also callable in 5 years at a call price of $1,040. What is the bond’s YTM? What is the bond’s YTC? If Mr. Greg were to purchase this bond, would he be more likely to receive the YTM or YTC? Explain your answer.

f.Price each bond and explain how the number of years to maturity and the coupon rate affect the current price of bonds. Assume a YTM of 7%.

a.A 4-year bond with a 9% annual coupon

b.A 4-year bond with a zero coupon

c.A 15-year bond with a 9% annual coupon

d.A 15-year bond with a zero coupon

Please answer each part of the question in its entirety!!!! Thank you!!!!

Answer 1

For bond D considering semiannual coupon payments and applying YTM formula we get annual YTM = 6%.

And Yield to call (YTC) = 7% annually.

He is more likely to receive YTM as the YTM or YTC is the cost that is incurred by the issuer from this point of view. BUT still it depends on issuer as the cost differs only by about 1% and if the issuer is ready to repay the amount raised within 5 years it would be better for him to call the bond and accordingly pay the price at call providing an extra returnn of 1%. More factors need to be taken care off here i.e if issuer continues with bond for 4 more years what are the inflationary costs that he has to bear. And the extra coupon payments that he has to make can be invested at the risk free rate which is definately provide higher return than 1% which is the cost that issuer has to bear. So Mr Greg has high chance to receive YTC instead of YTM.

f. For the 4 given bonds assuming face value = 1000

a). Price = $ 1067.74.

b). Price = $ 763

c). Price = $ 1182.16

d). Price = 362.45

Now for two zero coupon cases we see that as years to maturity is increased the price of bond drastically falls. And for the a) and b) cases where maturtity if same but as coupon payments are removed the price drastically reduces and bond trading at a premium of of $ 67 then trades at a discount of $ 233.

So as coupon increases price goes up and with maturity price falls