Question

You are valuing a bank. The bank currently has assets of $320 per share. Five years from now (that is, at the end of five years), you expect their assets per share to be $460. After Year 5, you expect their assets per share to grow at 3 percent per year forever. The bank has an ROA of 2.0 percent and an ROE of 11.5 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.

$

Answer 1

ROA = Net Income / Assets

Net Income = ROA * Assets

Current Net Income = $320 * 0.02 = $6.4

Net Income at the end of 5 years = $460 * 0.02 = $9.2

ROE = Net Income / Equity

Equity = Net Income/ROE

Current Equity = $6.4/0.115 = $55.65

Equity at the end of 5 years = $9.2/0.115 = $80

CAGR (Growth) in 5 years = ($ 460 / $ 320)^1/5 - 1
= 1.0753 - 1 = 0.0753, or 7.53%

V = FCFE(0) x (1+g) / (r - g)
= [$55.65 * (1 + 0.0753)] / [0.11 - 0.0753]

= $59.84 / 0.0347 = $1,723.55

Terminal Value = [{FCFE(5) x (1+g)} / (r - g)] * (1 + r)^-5

= [{$80 * (1 + 0.0753)} / (0.11 - 0.0753)] * (1 + 0.11)^-5

= [$86.02 / 0.0347] * 0.5935

= $2,477.60 * 0.5935 = $1,470.34

Total Value = V + Terminal Value

= $1,723.55 + $1,470.34 = $3,193.89