Banner Corporation will not pay dividends until year 3, whereby it is expected to pay $5 in dividends. Dividends are then expected to grow at 20%, 10% and 5% in years 4, 5 and 6.
Afterwards, dividend growth will stabilize to 2% consistently. If the rate of return is 10%, determine
The stock price now.

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of all the dividends in years 3 to infinity, using the dividend discount model.

PV of dividends = ($5 / (1+0.10)^3) + ($5 * 1.20 / (1+0.10)^4) + ($5 * 1.20 * 1.10 / (1+0.10)^5) + ($5 * 1.20 * 1.10 * 1.05 / (1+0.10)^6) + ($5 * 1.20 * 1.10 * 1.05 * (1+0.02) / (0.10-0.02) * (1/(1+0.10)^6))

PV of dividends = $13.69

Next, we can calculate the expected stock price in year 6, using the formula:

P6 = D7 / (r-g) 
where D7 is the dividend in year 7, r is the required rate of return and g is the growth rate.

D7 = $5 * 1.20 * 1.10 * 1.05 * 1.02 = $7.13
r = 0.10
g = 0.02

P6 = $7.13 / (0.10-0.02) = $101.86

Finally, we can calculate the present value of the stock price in year 6, using the discount factor of year 6:

PV of stock price in year 6 = $101.86 / (1+0.10)^6 = $54.77

Therefore, the stock price now is the sum of the present value of all the dividends and the present value of the stock price in year 6:

Stock price now = PV of dividends + PV of stock price in year 6 
Stock price now = $13.69 + $54.77 = $68.46

However, we need to take into account that the question asks for the stock price without dividends, so we need to subtract the dividends that are expected to be paid in years 3 to 6:

Total dividends in years 3 to 6 = $5 * (1+1.20+1.20*1.10+1.20*1.10*1.05) = $24.25
PV of dividends in years 3 to 6 = $24.25 / (1+0.10)^3 = $19.18

Stock price without dividends = Stock price now - PV of dividends in years 3 to 6 
Stock price without dividends = $68.46 - $19.18 = $49.28

Therefore, the best choice is B) $65.77, as it is closest to the calculated value of $49.28 when rounded to the nearest cent.

Banner Corporation Will Not Pay Dividends Until Year 3, Whereby