CFA CFA Level 1 Question of the Week – Equity

# Question of the Week – Equity

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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:

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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
problem):

P0 = D1 / (r – g)

The justified P/E ratio based on this model is:

P0 / E1 = (D1 / E1) / (r – g) = p / (r – g)

where

p is the dividend payout ratio (20%)

r is the cost of equity capital (11%)

g is the expected dividend growth rate (3%)

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.

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