Question

A bond has a face value of $1,000, a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 8%?

Answer 1

Answer:

-11.8%

Explanation:

the key to answer this question is to remember that valuation of a bond depends basically of calculating the present value of a series of cash flows, so let´s think about a bond as if you were a lender so you will get interest by the money you lend (coupon) and at the end of n years you will get back the money you lend at the beginnin (principal), so applying math we have the bond value given by:

$price=\frac{principal*coupon}{(1+i)^{1} }+ \frac{principal*coupon}{(1+i)^{2} } \frac{principal*coupon}{(1+i)^{3} }+...+\frac{principal+principal*coupon}{(1+i)^{n} }$

so in this particular case that one year later there are 29 years to maturity so we have:

$price=\frac{1,000*0.04}{(1+0.08)^{1} }+ \frac{1,000*0.04}{(1+0.08)^{2} } \frac{1000*0.04}{(1+0.08)^{3} }+...+\frac{1,000+1,000*0.04}{(1+0.08)^{30} }$

$price=553.6638$

so as we have a higher rate the investment has the next return:

$return=\frac{553.66}{627.73} -1$

$return=-11.8\%$