"A share pays dividends annually and the next dividend payment is due in 3 months time and is expected to be 5 cents per share. It is expected that future dividends will grow at a rate of 4% p.a. compound and that inflation will be 1.5% p.a. The current price of the share assuming dividends are held in perpetuity is 200 cents. Calculate the annual real yield to an investor purchasing the share."
This was my initial attempt at this question:
I found the value of the perpetuity $t= \frac{3}{12}$ by using the formula for a multiplicative perpetuity paid in advance: $$(C\ddot{a})^{r}_{{\infty}\rceil} = \frac{(1+i)}{i-r}$$ and set $r = 0.04 +0.015 = 0.055)$
I then discounted back this value to $t=0$ using the discount function $v^{0.25} = \frac{1}{(1+i)^{0.25}}$ and put this equation equal to 200 in order to find $i$
i.e
$$200 = v^{0.25}(5\frac{(1+i)}{(i-0.055)})$$
I would then use interpolation to find an estimate for $i$ the annual real yield
However I was uncertain if this was correct as the growth and inflation rates were given per annum and I began my perpetuity at $t = \frac{3}{12}$