Finding return from Newton's Formula

Question

I have Newton's formula

BMV =  CF1    +    CF2    +   CF3   + .... + CFn   + EMV
      -----.       -----      -----          -----
     (1+r)^t1    (1+r)^t2   (1+r)^t3        (1+r)^tn

BMV -> Beginning Market Value,

EMV -> Ending Market Value,

CF -> Cash Flows,

t -> Time Period

r -> Return

I have the values of BMV, EMV, CFn, tn. How to evaluate 'r' here?

Answer 1

You can write your equation as

$$B-E=\sum_{i=1}^n \frac{c_i}{R^{t_i}}$$

with $R=1+r$. Clearing denominators gives

$$(B-E) R^T=\sum_{i=1}^n c_i R^{T-t_i}$$

where $T=\sum_{i=1}^n t_i$. This is now a polynomial equation that can probably be readily solved numerically; at the end you can subtract $1$ to get back to $r$.