Question

You are valuing a bank. The bank currently has assets of $315 per share. Five years from now (that is, at the end of five years), you expect their assets per share to be $500. After Year 5, you expect their assets per share to grow at 3 percent per year forever. The bank has an ROA of 1.6 percent and an ROE of 12.5 percent. The bank's cost of equity is 11.0 percent. What is the value of the bank's stock? Use the free cash flow to equity model to value this stock. Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

ROA = Net income / Assets
1.6% = Net income / $315
Net income = $315 x 0.016 = $5.04

ROA = Net income / Assets
1.6% = Net income / $500

Net income = $500 x 0.016 = $8

ROE = Net income / Equity
12.5 = Net income / Equity
12.5 = $8 / Equity
Equity = $8 / 12.5
Equity = $0.64 ( at end of 5 years)

12.5 = $5.04 / Equity
Equity = $5.04 / 12.5
Equity = $0.4032 ( FCFE in year zero FCFE(0))

CAGR (Growth) in 5 years = ($500 / $315)^1/5 - 1
= (1.587)^0.2 - 1
= 1.0968 -1
= 0.0968
Annual Growth rate = 9.68%

V = FCFE(0) x (1+g) / (r - g)
V = 0.4032 x ( 1+ 0.0968 ) / (0.11 - 0.0968)
V = 0.4422 / 0.0132 = $33.53

Terminal value = $0.64 x (1+ 0.03) / ( 0.11 - 0.03) x (1.11)⁵
= $0.6592 / 0.1348
= $4.89

Total value = V + Terminal value = $33.53 + $4.89 = $38.42