From the data given, we know that Prairie Home Stores (PHS) has a current book value of $80,000,000. With 400,000 outstanding shares, the book equity per share is $200.

There are two possible paths for future performance to consider. The first, a constant growth scenario, assumes that PHS will continue on its current trajectory of paying out 2/3 of its earnings as dividends, and retaining the other 2/3 to grow the business. In this scenario, we will continue the company’s growth rate of 5%, with no change in plowback or dividends. In this scenario, price per share is determined by the current dividends, divided by (r-g)

The value of the company will be equal to the present value of all future cash flows ( i.e. dividend payments) that investors expect to receive.

Constant growth scenario:

EPS 2013 = $ 12,000,000 / 400,000 shares = $ 30.00

Book equity per share in 2013 = $80,000,000 / 400,000 shares = $200.00 per share Dividends paid out per share in 2013 = $ 8,000,000 / 400,000 shares = $ 20.00 per share Payout ratio in 2013 = $ 20.00 (DIV2013) / $ 30 (EPS 2013) = 0.67 Plowback ratio 2013 = $10.00 (RE per share 2013) / $ 30.00 (EPS 2013) = 0.33 Sustainable growth rate = 0.15 (rate of return) x 0.33 (plowback ratio) = 5 % Price per share 2012 = DIV2013/(r-g) = $20/(11%-5% ) = $ 333.33 $ 333.33 price per share x 400,000 shares = $ 133,333,333 - value of the company in 2012

P/E ratio = $ 333.33( price per share) / 30 (EPS) = 11.11

Rapid Growth Scenario:

Since Price = DIV / r-g, and there are no dividends paid in the years 2013 – 2016, we can calculate the value of the company in 2016 and discount it to obtain the Present value in 2012. EPS 2017 = $21,000,000 / 400,000 shares = $52.50

Book equity per share 2017 = $139,900,000 / 400,000 shares = $349.75 Dividends paid out per share 2017 = $14,000,000 / 400,000 shares = $35.00 Payout ratio in 2017 = $ 35.00 (DIV per share 2017) / $ 52.50 (EPS 2017) = 0.67 Plowback ratio in 2017 = $ 17.50 (RE in 2017) / 52.50 (EPS in 2017) = 0.33 Sustainable growth rate = 0.15 (rate of return) x 0.33 (plowback ratio) = 5 % Price per share in 2016= $35.00 (DIV 2017) / 0.06 (r - g)= $583.33 Let’s discount it to 2012 value:

Financial calculator:

FV = 583.33

N = 4, I/Yr = 11%

PV = 384.25 – price per share in 2012

384.25 x 400,000 shares = 153,700,000 – value of the company in 2012 under rapid growth

Conclusion:

Rapid growth scenario promises higher stock price, so it should be chosen. PVGO between the previous example and this one:

153,700,000 – 133,333,333 = 20,366,667

Under both scenarios, current price per share is more than $200.

Now here’s my calculations:

Constant growth scenario:

Assuming a 15% required return:

P0 = DIV1 / (r-g) = $20 / (.15 - .05) = $20/.1 = $200

Assuming an 11% required return, we’ll have:

P0 = DIV1 / (r-g) = $20 / (.11 - .05) = $20/.06 = $333.33

In the constant growth scenario, the stock is valued at $200 if we assume a 15% expected return, and $333.33 if we assume 11% expected return.

Now, in the rapid growth scenario, things get even more exciting.

I think that 2017/2020 is the horizon year, because it’s AFTER that point when the growth goes down to 5%. In paragraph 6, the problem states “...would require reinvestment of all of Prairie Home’s earnings from 2016 to 2019. After that the company could resume its normal dividend payout and growth.”

your book’s years:20122013201420152016201720182019 my book’s years:20152016201720182019202020212022

year #01234567

earnings growth from previous year---4.6%15%15%15%15%5%5% dividend0000$35$36.75$38.59

todayH

NB: neither book shows 2019 or 2022, but we know that the beginning of...