Help with using the solve function given parameters and three equations

Here is my code for an internal rate of return (IRR)

clear
clc
D1=45000;
g1=0.04;
n1=40; %years
D2=-60000;
g2=0.06;
n2=4; %years
D3=-30000;
g3=0.02;
n3=44; %years
syms i 
%Benefits: Positive Cash Flows
P1=D1*(((1-(1+g1)^(n1))*(1+i)^-(n1))/(i-g1));
%Costs: Negative Cash Flows
P2=D2*(((1-(1+g2)^(n2))*(1+i)^-(n2))/(i-g2));
%Costs: Opportunity Cost (Lost)
P3=D3*(((1-(1+g3)^(n1))*(1+i)^-(n3))/(i-g3));
i = solve(P1+P2+P3==0,i)

I should be getting an answer that is equal to 7.44%. Instead it is displaying a 42x1 matrix with random numbers. I am trying to get the three equations added together and set equal to zero in order to find i. Please help! I'm sure it's an easy fix.

Answer 1

[Star Strider]

It’s probably best not to use the Symbolic Toolbox for this. Using fzero with a slight restatement of your code will get you closer. Your code may have errors I can’t detect, so experiment with this approach:

D1=45000;
g1=0.04;
n1=40; %years
D2=-60000;
g2=0.06;
n2=4; %years
D3=-30000;
g3=0.02;
n3=44; %years
%Benefits: Positive Cash Flows
P1 = @(i) D1*(((1-(1+g1)^(n1))*(1+i)^(-n1))/(i-g1));
%Costs: Negative Cash Flows
P2 = @(i) D2*(((1-(1+g2)^(n2))*(1+i)^(-n2))/(i-g2));
%Costs: Opportunity Cost (Lost)
P3 = @(i) D3*(((1-(1+g3)^(n1))*(1+i)^(-n3))/(i-g3));
i = fzero(@(i) P1(i)+P2(i)+P3(i), 1)

i =
  -311.5344e-003

This is not the answer you’re expecting, but it beats getting the roots of a 42-degree polynomial!

[Alison Alexsy]

I modified my code a little bit to this

D1=45000;
D2=-60000;
D3=-30000;
g1=0.04;
g2=0.06;
g3=0.02;
n1=40; %years
n2=4; %years
n3=44; %years

syms i

P1=D1*((((1-(1+g1)^(n1))*(1+i)^(-n1))/(i-g1)));
P2=D2*((((1-(1+g2)^(n2))*(1+i)^(-n2))/(i-g2)));
P3=D3*((((1-(1+g3)^(n3))*(1+i)^(-n3))/(i-g3)));

i = solve(P1+P2+P3==0, i, 'ReturnConditions', true)

And it is is returning i =

             i: [1x1 sym]
    parameters: [1x1 sym]
    conditions: [1x1 sym]

No longer getting the long polynomial... but this still isn't correct

[Star Strider]

If it’s not giving you the correct output, check it against the equations you’re coding. We don’t have them, so we can’t check to see if you coded them correctly.

[Alison Alexsy]

This is what is looks like

[Star Strider]

Go back and check your code. When I coded it, I got:

D1=45000;
g1=0.04;
n1=40; %years
D2=-60000;
g2=0.06;
n2=4; %years
D3=-30000;
g3=0.02;
n3=44; %years
P1 = @(i) D1*((1-(1+g1)^n1*(1+i)^-n1)/(i-g1))/(1+i)^4;
P2 = @(i) D2*((1-(1+g2)^n2*(1+i)^-n2)/(i-g2));
P3 = @(i) D3*((1-(1+g3)^n3*(1+i)^-n3)/(i-g3));
int = fzero(@(i) P1(i)+P2(i)+P3(i), 1);
fprintf('\n\tInterest = %.4f%%\n', int*100)

  Interest = 7.4445%

Answer 2

[Walter Roberson]

With those powers of n1 and n3 being 40 and 44, it is not surprising that the solution is a polynomial of about that order. All of those values are mathematical solutions to the equations you set out.

Cutting short the explanations: use

syms i positive

[Alison Alexsy]

Warning: The solutions are parameterized by the symbols: z1.
To include parameters and conditions in the solution, specify
the 'ReturnConditions' option. 
> In solve>warnIfParams (line 500)
In solve (line 356)
In Rorys_IRR (line 24) 
Warning: The solutions are valid under the following
conditions: (825432267338751673*z1)/1477613924061677500 -
(2193686941466940022*z1^2)/369403481015419375 -
(13734013560400584693*z1^3)/369403481015419375 +
(41923794702955407671*z1^4)/211087703437382500 +
(257549755141161105337*z1^5)/52771925859345625 +
(4061174807376957043163*z1^6)/73880696203083875 +
(55327506*z1^7)/125 + (695322537*z1^8)/250 +
(3562007501*z1^9)/250 + (38235300389*z1^10)/625 +
(28053586184*z1^11)/125 + (89177740548*z1^12)/125 +
(248277101188*z1^13)/125 + (610428206384*z1^14)/125 +
(6670617103528*z1^15)/625 + (521092270449*z1^16)/25 +
(913130121501*z1^17)/25 + (1440471578286*z1^18)/25 +
(2050864725468*z1^19)/25 + (13201699314882*z1^20)/125 +
(3077916064938*z1^21)/25 + (3251507213136*z1^22)/25 +
(3113764464876*z1^23)/25 + (2702665018833*z1^24)/25 +
(53120895610653*z1^25)/625 + (7557143311314*z1^26)/125 +
(4855319480488*z1^27)/125 + (2811175743748*z1^28)/125 +
(1462482639044*z1^29)/125 + (3405514701264*z1^30)/625 +
(282645069928*z1^31)/125 + (207828929737*z1^32)/250 +
(67209878437*z1^33)/250 + (9473642763*z1^34)/125 +
(11508614754*z1^35)/625 + (474871579*z1^36)/125 +
(81566563*z1^37)/125 + (11349728*z1^38)/125 +
(1229154*z1^39)/125 + (972001*z1^40)/1250 + (1997*z1^41)/50 +
z1^42 - 991517786144719/147761392406167750 == 0 & 0 < z1.
To include parameters and conditions in the solution, specify
the 'ReturnConditions' option. 
> In solve>warnIfParams (line 507)
In solve (line 356)
In Rorys_IRR (line 24)

Is what it came back with

[Walter Roberson]

Use vpasolve() instead of solve()