Find Coupon Rate: bonds,16yr mat., $1051; 6.8% yield

[momoanzu]

I am having a lot of trouble in my corporate finance class. I have very little skill in math, and am trying to strengthen my skills by going over things we have done in class. This is a problem we have done in class, am I am unsure how we got the answer my teacher got. Can anyone help me?

Merton Enterprises has bonds on the market making annual payments, with 16 years to maturity, selling for $1051. At this price, the bonds yield 6.8%. What must the coupon rate be on Merton's bonds?

My teacher used the PMT function in excel, then divided the answer by the Present Value, $1000. His final answer was 0.733. Can anyone help me in finding this answer? Thank you!

 

[Denis]

Re: Corporate Finance: Find Coupon Rate

What d'heck kind of teacher have you got? He uses a function, divides by 1000 and tells the class:
"Ok you suckers, that's the way it's done; now go figure out why" :shock:

OK, to start, he used NOT ONLY the PMT function, but also the PV of the $1000 due in 16 years.
The PMT function determines the PV of the equal payment flows over the 16 years.

Next, his final answer was NOT .733, but .0733; .733 means 73.3% ! Did you make a typo?

This is not a classroom, so quite difficult to TEACH; more so if your skills are as you say.

Anyway, I'll do my best, keeping it short: if that's not enough, too bad.

The payment flows represent the interest amounts paid each year; let that be represented by P.
So you have the following:
[6.8% ; 1051] ......[1]P....[2]P.......................[16]P + 1000

PV formula for equal flows of $1: PV = (1 - f) / i where f = 1 / (1 + i)^n
PV formula for future amount of $1: PV = 1 / (1 + i)^n
With your problem, i = .068 and n = 16.

So in order to solve for P:
P(1 - f) / i + 1000 / (1 + i)^n = 1051
Solving for P results in P = 73.327.....; divide by 1000 to get .0733

Now that equation will probably bewilder(!) you.
Would you be able to solve this one for P:
Pa / b + c / d = x
Can you isolate P? That means end up with P = something in terms of a,b,c,d,x
If you can't, well it's game over, unless you get a private tutor, I guess.

Perhaps Jonah will ride in and make that easier for you to "see" :wink:

 

[jonah]

Re: Corporate Finance: Find Coupon Rate

Perhaps Jonah will ride in and make that easier for you to "see"

Glad to chip in, Sir Denis.
I prefer to use r as the coupon rate myself, so
\(\displaystyle \begin{gathered} 1,051 = 1,000\left( {1 + \tfrac{{.068}}{1}} \right)^{ - \left( {16 \times 1} \right)} + \left( {1,000 \times \frac{r}{1}} \right) \cdot \frac{{1 - \left( {1 + \tfrac{{.068}}{1}} \right)^{ - \left( {16 \times 1} \right)} }}{{\tfrac{{.068}}{1}}} \hfill \\ \Leftrightarrow \hfill \\ 1,051 = \frac{{1,000}}{{\left( {1 + \tfrac{{.068}}{1}} \right)^{\left( {16 \times 1} \right)} }} + \left( {1,000 \times \frac{r}{1}} \right) \cdot \frac{{1 - \frac{1}{{\left( {1 + \tfrac{{.068}}{1}} \right)^{\left( {16 \times 1} \right)} }}}}{{\tfrac{{.068}}{1}}} \hfill \\ \end{gathered}\)
Now solve for r.

 

[Denis]

Re: Corporate Finance: Find Coupon Rate

Very picturesque, Sir Jonah. Hungover? Your .08's should be .068 :twisted:

 

[jonah]

Re: Corporate Finance: Find Coupon Rate

Hungover?

Sleepy and dead tired actually.
Edited/Corrected for momoanzu's benefit.

 

[jimm1909]

Re: Corporate Finance: Find Coupon Rate

Perhaps Jonah will ride in and make that easier for you to "see"

Glad to chip in, Sir Denis.
I prefer to use r as the coupon rate myself, so
\(\displaystyle \begin{gathered} 1,051 = 1,000\left( {1 + \tfrac{{.068}}{1}} \right)^{ - \left( {16 \times 1} \right)} + \left( {1,000 \times \frac{r}{1}} \right) \cdot \frac{{1 - \left( {1 + \tfrac{{.068}}{1}} \right)^{ - \left( {16 \times 1} \right)} }}{{\tfrac{{.068}}{1}}} \hfill \\ \Leftrightarrow \hfill \\ 1,051 = \frac{{1,000}}{{\left( {1 + \tfrac{{.068}}{1}} \right)^{\left( {16 \times 1} \right)} }} + \left( {1,000 \times \frac{r}{1}} \right) \cdot \frac{{1 - \frac{1}{{\left( {1 + \tfrac{{.068}}{1}} \right)^{\left( {16 \times 1} \right)} }}}}{{\tfrac{{.068}}{1}}} \hfill \\ \end{gathered}\)
Now solve for r.

Awesome thanks for the responses and explanations. Glad I found this forum this will really help me do well on my finals.

Thanks again,

-Jim

 

[Deleted member 4993]

This post has been viwed ~1100 times - I wonder why? Too many key words (like coupon, bond, etc.) for the "bots"??