Question

Phoenix Motor Corporation has pulled off a miraculous recovery. Four years ago, it was near bankruptcy. Now , Collins Ndhlovu, the charismatic leader, a corporate folk hero, may run for president. Phoenix has just announced a $1 per share dividend, the first since the crisis hit. Analysts expect an increase to a “normal” $3 as the company completes its recovery over the next three years. After that, dividend growth is expected to settle down to a moderate long-term growth rate of 6%. Phoenix’ stock is selling at $50 per share. What is the expected long-run rate of return from buying the stock at this price? Assume that dividends of $1, $2, and $3 for years 1, 2, 3. A little trial and error (or a numerical calculator search) will be necessary to find r.

Answer 1

Price of the share = PV of the expected dividends = PV of dividends for years 1, 2 and 3 + PV of terminal value of dividends:
We have
50 = 1/(1+r)+2/(1+r)^2+3/(1+r)^3+3*1.06/((r-0.06)*(1+r)^3))
The value of r has to be found by trial and error so
that the value of RHS = 50.
Using r = 10%
= 1/(1.10)+2/(1.10)^2+3/(1.10)^3+3*1.06/((0.10-0.06)*(1.10)^3)) =	64.55
Using r = 11%
= 1/(1.11)+2/(1.11)^2+3/(1.11)^3+3*1.06/((0.11-0.06)*(1.11)^3)) =	51.22
Using r = 12%
= 1/(1.12)+2/(1.12)^2+3/(1.12)^3+3*1.06/((0.12-0.06)*(1.12)^3)) =	42.35
The value of r would be between 11% and 12%.
r = 11+(51.22-50)/(51.22-42.35) =	11.14%	(Answer)