Question

A two-year bond with par value $1,000 making annual coupon payments of $99 is priced at $1,000.

Answer 1

Answer:

(a) 9.9%

(b)  10.09%

The further explanation is given below.

Explanation:

The given values are:

Coupon payment

=  $99

Price

=  $1,000

(a)

The Yield to maturity (YTM) will be:

= $\frac{C+\frac{F-P}{n} }{\frac{F+P}{2} }$

where,

C = Coupon payment

P = Price

n = years to maturity

F = Face value

On putting the estimated values is the above formula, we get

⇒  $99+\frac{0}{1000}$

⇒  $.099$

⇒  $9.9$%

(b)

Although the 1st year coupon was indeed reinvested outside an interest rate of r%, cumulative money raised will indeed be made at the end of 2nd year.  

= $[99\times (1 + r)] + 1,099$

Came to the realization compound YTM is therefore a function of r, as is shown throughout the table below:

Rate (r)             Total proceeds         Realized YTM ($(\frac{proceeds}{1000} )^{.5} - 1$)

7.9%                      1205.8                                   9.8%

9.9%                             1207.8                                   9.9%

11.9%                      1209.8                                  9.99%

Now,

Overall proceeds realized YTM:

= $\frac{proceeds}{1000} -18 \ percent \ 1,\frac{2081208}{1000} - 1$

= $0.0991$

= $9.91 \ percent \ 10 \ percent \ 1,\frac{2101210}{1000}- 1$

= $0.1000$

= $10.00 \ percent \ 12 \ percent \ 1,\frac{2121212}{1000}-1$

= $0.1009$

= $10.09$%