You are provided the following information about a company Shoes4You:• Current stock price: $35• Shares outstanding: 1,000,000• Past year earnings: $4,000,000• Net book value: $28,000,000• Past year free cash flow: $8,000,000• Dividend payout ratio: 20%• Cost of equity capital: 11%• Expected dividend growth rate: 3%The justified forward P/E ratio for Shoes4You is closest to:
Wait…i’m a bit confused. Why wouldn’t the answer be the second choice (3)? I thought the formula for the justified P/E was dividend payout ratio/r-g. I wasn’t aware you were actually supposed to calculate the P/E using current price/ EPS for the justified P/E.
Based on the information we are provided, we can use the
Gordon growth model (which is the same model used in the text for this
P0 = D1 / (r – g)
The justified P/E ratio based on this model is:
P0 / E1 = (D1 / E1) / (r – g) = p / (r – g)
p is the dividend payout ratio (20%)
r is the cost of equity capital (11%)
g is the expected dividend growth
We then have:
P0 / E1 = 0.2 / (0.11 – 0.03) = 2.5
The P/E ratio is Price/Earnings Per Share. The stock
price is $35. Earnings per share are $4,000,000 / 1,000,000 = $4. The P/E ratio
then is $35/$4 = $8.75.
I apologize for the confusion. I marked 9 as the final answer when it should have been 3.
The justified forward P/E ratio is the P/E ratio calculated using forecasted earnings, i.e. P0 / E1 in this case. We make use of the dividend discount model for valuing the price of a stock.
The last paragraph of the solution calculates what the regular P/E ratio would have been. It’s not what the question is asking for.
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