Question

A coupon bond that pays interest semiannually has a par value of $1,000, matures in 8 years, and has a yield to maturity of 6%. If the coupon rate is 7%, the intrinsic value of the bond today will be ________.
a.$1,000
b.$1,062.81
c.$1,100.03
d.$1,081.82

Answer 1

Answer:

b. 1,062.81

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:

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

where: principal as said before is the value lended, coupon is the rate of interest paid, i is the interest rate and n is the number of periods

so applying to this particular exercise, as it is not said we will assume that 6% and 7% are interest rate convertible seminually, so the price of the bond will be:

$price=\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{1} } +\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{2} }+\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{3} }+...+\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{15} }+\frac{1,000+1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{16} }$

price=1,062.81

take into account that here we are asked about semianually payments, so in 8 years there are 16 semesters.