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 $475. After Year 5, you expect their assets per share to grow at 4 percent per year forever. The bank has an ROA of 2.0 percent and an ROE of 13.0 percent. The bank's cost of equity is 12.0 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

Answer:-

ROA = Net income / Assets
ROA = 2 % = Net income / $ 475

Net income = $ 475 x 0.02 = $ 9.5

ROA = Net income / Assets
ROA = 2 % = Net income / $ 320

Net income =$ 320 x 0.02 = $ 6.4

ROE = Net income / Equity
ROE = 13 = Net income / Equity
13 = $ 9.5 / Equity
Equity = $ 9.5 / 13
Equity = $ 0.73 ( at end of 5 years)

13 = $ 6.4 / Equity
Equity = $ 6.4 / 13
Equity = $ 0.49 ( FCFE in year zero FCFE(0))

CAGR (Growth) in 5 years = ($ 475 / $ 320)^1/5 - 1
= (1.484)^0.2 - 1
= 1.082 -1
= 0.082
Annual Growth rate = 8.2 %

V = FCFE(0) x (1+g) / (r - g)
V = 0.49 x ( 1+ 0.082 ) / (0.12 - 0.082)
V = 0.49 x 1.082 / 0.038
V = 0.53 / 0.038 = $ 13.95

Terminal value = $ 0.73 x (1+ 0.04) / ( 0.12 - 0.04) x (1.12)⁵
= $ 0.73 x 1.04 / 0.08 x 1.76
= $ 0.759 / 0.14
= $ 5.42

Total value = V + Terminal value = $ 13.95 + $ 5.42 = $ 19.37