Bond Valuation: Solving for C

[ash44]

Hi, I'm trying to revise for my finals and I know how to calculate bonds, but have no idea how to calculate the coupon rate. I am not great at maths, but understand the fundamentals of financial mathematics. I honestly just want to get a decent grade, my major doesn't involve any maths. This is a junior elective, I understand annuities and single cash flow calculations.

The question: Outback Corporation has bonds on the market with ten and a half years to maturity, a YTM of 6.9%, compounded semi-annually, and a current price
of $1,070. The bonds have a face value of $1,000 and make half-yearly payments. What is the semi-annual coupon payment? What must the coupon rate be on Outback’s bonds?

What I have:
coupon payments = 21 (10.5x2), per period yield = 6.9/2 = 3.45%, face value =$1000, sale price = $1070.
I know pv (coupon) + pv (single cash flow) gives me the answer, but I can't really rearrange formulas that well and i'm hoping someone rearranges it for me so I can solve. I have been memorising all my formulas in every way possible, since my algebra knowledge is very limited and I do not have time to learn algebra before my exam and because I will no longer do maths at university after this subject (lacking foundation so its way too difficult for me).

Thank you for your time.

Ash

 

[Deleted member 4993]

Hi, I'm trying to revise for my finals and I know how to calculate bonds, but have no idea how to calculate the coupon rate. I am not great at maths, but understand the fundamentals of financial mathematics. I honestly just want to get a decent grade, my major doesn't involve any maths. This is a junior elective, I understand annuities and single cash flow calculations.

The question: Outback Corporation has bonds on the market with ten and a half years to maturity, a YTM of 6.9%, compounded semi-annually, and a current price
of $1,070. The bonds have a face value of $1,000 and make half-yearly payments. What is the semi-annual coupon payment? What must the coupon rate be on Outback’s bonds?

What I have:
coupon payments = 21 (10.5x2), per period yield = 6.9/2 = 3.45%, face value =$1000, sale price = $1070.
I know pv (coupon) + pv (single cash flow) gives me the answer, but I can't really rearrange formulas that well and i'm hoping someone rearranges it for me so I can solve. I have been memorising all my formulas in every way possible, since my algebra knowledge is very limited and I do not have time to learn algebra before my exam and because I will no longer do maths at university after this subject (lacking foundation so its way too difficult for me).

Thank you for your time.

Ash

Where is the formula that needs re-arranging?

 

[ash44]

\(\displaystyle \mbox{Bond value }\, =\, \dfrac{C}{r}\, \left(1\, -\, \dfrac{1}{(1\, +\, r)^n}\right)\, +\, \dfrac{FV}{(1\, +\, r)^n}\)

\(\displaystyle $1,070\, =\, \dfrac{C}{0.0345}\, \left(1\, -\, \dfrac{1}{(1\, +\, 0.0345)^{21}}\right)\, +\, \dfrac{1,000}{(1\, +\, 0.0345)^{21}}\)

\(\displaystyle C\, =\, $39.24\)

 

[ash44]

Let a=1070, b=1000, u=.0345, v = (1.0345)^21

Equation becomes:
a = C/u(1 - 1/v) + b/v

C/u(1 - 1/v) = a - b/v

Can you solve that for C?

Thanks, still a little confused though

1070-1000/(1,0345)^21 = 34.3
1000/(1.0345)^21 = 490.5

490.5+34.3=524.8

So how do they get 39.24 as C?

 

[stapel]

Thanks, still a little confused though

1070-1000/(1,0345)^21 = 34.3
1000/(1.0345)^21 = 490.5

490.5+34.3=524.8

So how do they get 39.24 as C?

How did you go from this:

. . . . .\(\displaystyle $1,070\, =\, \dfrac{C}{0.0345}\, \left(1\, -\, \dfrac{1}{(1\, +\, 0.0345)^{21}}\right)\, +\, \dfrac{1,000}{(1\, +\, 0.0345)^{21}}\)

...which leads to this:

. . . . .\(\displaystyle $1,070\, -\, \dfrac{1,000}{1.0345^{21}}\, =\, \dfrac{C}{0.0345}\, \left(1\, -\, \dfrac{1}{(1\, +\, 0.0345)^{21}}\right)\)

...to this?

. . . . .\(\displaystyle $1,070\, -\, \dfrac{1,000}{1.0345^{21}}\, =\, 34.3\)

Please reply showing all of your steps, including how you justified the removal of the variable. Thank you!

 

[ash44]

In all honestly I have no idea how to solve for C. I barely know how to rearrange so the brackets, indices, etc. make it way too confusing...

 

[stapel]

In all honestly I have no idea how to solve for C.

Then why did they allow you to register for your current class? A placement test would have told them that you weren't yet ready for it, instead of setting you up to fail! :shock:

Unfortunately, there is no reasonable way for us here to try to figure out all the gaps in your background knowledge and then provide the weeks or months of personalized instruction that you seek. Please seriously consider hiring a qualified local tutor and setting aside a few hours a day over the next few weeks for intensive private lessons. Good luck!