Question

(Explain each step in detail. show your logic, Do not just provide answer and formulas.)

Will-O-Wind Airlines always invests (in non-depreciating assets) 20% of its earnings, which will be next period (Period 1) $3 per share. The rest it pays out as dividends. Its investment opportunities currently earn (and are expected to earn in the indefinite future) 18%. There are no taxes. The risk adjusted required rate of return on this stock is 10%. What is its price?

Answer 1

Dividend for next period = D₁ = 3

Percentage of earnings invested = 20%

Percentage of earnings paid as dividends = Dividend payout ratio = 1 - Percentage of earnings invested = 1 - 20% = 80%

Since the company retains 20% of its earnings and then invests its earnings in assets or investment opportunities. Hence equity or retained earnings are being used to fund investment opportunities. Hence return on investment opportunities can be taken as return on equity

Return on investment opportunities = Return on equity = 18%

Since this rate of return on expected to continue indefinitely, we can find the sustainable growth of dividends

We know that sustainable growth rate of dividends = g = Return on Equity x ( 1 - Dividend payout ratio) = 18% x (1 - 80%) = 18% x 20% = 3.6%

Required rate of return on stock = r = 10%

According to Gordon constant growth rate model

Current Price of a stock = Dividend for next period / ( Required rate of return - sustainable growth rate)

Current Price of a Stock = D₁ / (r-g)

= 3 / (10% - 3.6%)

= 3 / 6.4%

= 46.875

Hence price of share is $46.875