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# Re: st: Solving equations iteratively

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Solving equations iteratively Date Wed, 5 May 2010 12:34:26 -0400

```See e.g.
http://www.stata.com/statalist/archive/2010-04/msg01113.html

On Wed, May 5, 2010 at 6:50 AM, David Scheuer <david.scheuer@gmx.de> wrote:
> Hello everybody
>
> I am stuck in a problem. In order to rebuild cost of capital models, which determine cost of capital implied as the internal rate of return from a valuation model, I need to solve equations iteratively.
>
> For instance, this is the first (of 30) row in my dataset and I want to find r_CT in every row by solving the following equation.
>
> p_0 = 27.09  bv_0 = 18.02  eps_1 = 2.72  eps_2 = 2.94  eps_3 = 3.32 eps_4 = 3.96  eps_5 = 3.24  bv_1 = 19.38 bv_2 = 20.85  bv_3 = 22.51  bv_4 = 24.49 g_CT = .0125  r_CT = .
>
> p_0=bv_0+(eps_1-r_CT*bv_0)/(1+r_CT)+(eps_2-r_CT*bv_1)/(1+r_CT)^2+(eps_3-r_CT*bv_2)/(1+r_CT)^3+(eps_4-r_CT*bv_3)/(1+r_CT)^4+((eps_5-r_CT*bv_4)*(1+g_CT))/((r_CT-g_CT)*(1+r_CT)^4
> ,
> where only r_CT is an unknown variable. I know that it should be between 0 and 1 because it is an interest rate.
>
> I guess I have to write a program in mata but I am not quite familiar with the syntax yet.
>
> Thanks a lot for any suggestion. I would appreciate it very much.
>
> Have a nice day
> David

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```