Question

Mr. Clark is considering another bond, Bond D. It has an 8% semiannual coupon and a $1,000 face value (i.e., it pays a $40 coupon every 6 months). 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 nominal yield to maturity? What is the bond’s nominal yield to call? If Mr. Clark were to purchase this bond, would he be more likely to receive the yield to maturity or yield to call? Explain your answer.

Answer 1

Answer:

a) the bond’s nominal yield to maturity is 5.92% effective annual

b) the bond’s nominal yield to call is 5.33% effective annual

c)Mr. Clark is more likely to receive the bond´s yield to maturity because it is higher than the yield to call.

Explanation:

Hi, in order to find the YTM (yield to maturity) we need to solve the following equation for YTM.

$Price=\frac{Coupon((1+YTM)^{n}-1) }{YTM(1+YTM)^{n} } +\frac{FaceValue}{(1+YTM)^{n} }$

That is:

$1,150=\frac{40((1+YTM)^{18}-1) }{YTM(1+YTM)^{18} } +\frac{1,000}{(1+YTM)^{18} }$

Since it would take forever to solve this, we need to use the MS Excel function "IRR". The result to this is 2.92% effective semi-annual, but all rates should be presented in effective annual terms, therefore.

$YTM(annual)=((1+YTM(semi-annaul))^{2}-1$

Therefore.

$YTM(annual)=((1+0.0292)^{2}-1 =0.0592$

So the YTM is 5.92% annual

Now, the bond is callable in 5 years, that means that instead of receiving all the coupons from semester 10 to 18, Mr. Clark will receive $1,040 in semester 10, therefore our equation would be:

$1,150=\frac{40((1+YTM)^{10}-1) }{YTM(1+YTM)^{10} } +\frac{1,040}{(1+YTM)^{10} }$

Because he receives 10 copupons and 1,040 in year 5. Therefore, using the IRR excel function we get a YTC = 2.63%

Which in effective annual terms is

$YTM(annual)=((1+0.0263)^{2}-1 =0.0533$

So the effective annual rate of the YTC is 5.33%

For all of the above, Mr. Clark would like to receive the YTM because it is a higher rate.

Best of luck.