Solve Equation

[MAC1430]

Hi everyone,

I need to calculate cost of capital based on the model looks like below:

All the variables in this model are known, except the discount rate .

I’m entering a dead end to find useful code to solve the equation above, where only   is the unknown.

If you know a solution to this problem, please comment, it is very much appreciated.

Thank you very much.

[FreelanceReinh · Accepted solution]

Hi @MAC1430,

I think you can use the SOLVE function in PROC FCMP:

/* Define function DISCRATE */

proc fcmp outlib=work.funcs.test;
function rhs(t, B[*], a, g, e[*], c);
  s=B[t];
  do tau=1 to 5;
    s = s + a*e[t+tau]/(1+g+c)**tau;
  end;
  s = s + a*e[t+5]*(1+g)/(c*(1+g+c)**5);
  return(s);
endfunc;
function discrate(t, P[*], B[*], a, g, e[*]);
  r=g+solve("RHS", {.}, P[t], t, B, a, g, e, .);
  return(r);
endfunc;
run;

/* Make function available */

options cmplib=work.funcs;

/* Apply function DISCRATE to arbitrary sample data */

data test;
array p[3] (175 180 190);
array b[3] (  2   3   4);
array e[8] (. 1.1 0.8 0.9 1.2 1.0 0.7 0.6);
a=0.5772;
g=0.0123;
do t=1 to 3;
  dr=discrate(t,p,b,a,g,e);
  output;
end;
run;

EDIT:  Took the second fraction out of the sum (t=1, ..., 5), as this seems more plausible mathematically (without knowing the background or source of the formula).

[Ksharp]

Do you have SAS/IML? Calling @Rick_SAS 

[Rick_SAS]

For more information about how to use the SOLVE function and PROC FCMP, see "Find the root of a function by using the SAS DATA step."

The same article provides links to other root-finding methods in SAS. As @Ksharp points out, the easiest way to solve this equation is to use the FROOT function in SAS/IML, if you have a license for SAS/IML.