The dollar-weighted rate of return is the internal rate of return (IRR) of the cash flows.

• At $t=0$: Buy 1 share for $40 $\rightarrow CF_0 = -40$
• At $t=1$: Receive $4 dividend, buy 1 share for $42 $\rightarrow CF_1 = 4 - 42 = -38$
• At $t=2$: Receive $8 dividend (2 shares $\times$ $4), sell 2 shares for $43 each ($86) $\rightarrow CF_2 = 8 + 86 = 94$

Equation: $-40 - \frac{38}{1+r} + \frac{94}{(1+r)^2} = 0$

Let $x = \frac{1}{1+r}$: $94x^2 - 38x - 40 = 0$

Using the quadratic formula: $x = \frac{38 + \sqrt{(-38)^2 - 4(94)(-40)}}{2(94)} = \frac{38 + \sqrt{1444 + 15040}}{188} = \frac{38 + \sqrt{16484}}{188} \approx \frac{166.39}{188} \approx 0.885$

Since $x = \frac{1}{1+r}$, we have $1+r = \frac{1}{0.885} \approx 1.13$. Therefore,$r \approx 13%$.