Respuesta :
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.
[tex]Price=\frac{Coupon((1+YTM)^{n}-1) }{YTM(1+YTM)^{n} } +\frac{FaceValue}{(1+YTM)^{n} }[/tex]
That is:
[tex]1,150=\frac{40((1+YTM)^{18}-1) }{YTM(1+YTM)^{18} } +\frac{1,000}{(1+YTM)^{18} }[/tex]
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.
[tex]YTM(annual)=((1+YTM(semi-annaul))^{2}-1[/tex]
Therefore.
[tex]YTM(annual)=((1+0.0292)^{2}-1 =0.0592[/tex]
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:
[tex]1,150=\frac{40((1+YTM)^{10}-1) }{YTM(1+YTM)^{10} } +\frac{1,040}{(1+YTM)^{10} }[/tex]
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
[tex]YTM(annual)=((1+0.0263)^{2}-1 =0.0533[/tex]
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.
