You are valuing a bank. The bank currently has assets of $325 per share. Five years from now (that is, at the end of five years), you expect their assets per share to be $485. After Year 5, you expect their assets per share to grow at 3.25 percent per year forever. The bank has an ROA of 1.4 percent and an ROE of 12.5 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 and Explanation:

To calculate free cash flow to equity

Calculate net income given return on assets 2% and assets $475

Return on assets = Net income / Assets

Substitute:

= 2 % = Net income / $ 475

=$ 475 x 0.02 = $ 9.5

Calculate net income given return on assets 2% and assets $320

Return on Assets = Net income / Assets

Return on assets = 2 % = Net income / $ 320

=$ 320 x 0.02 = $ 6.4

Given return on equity =13

Return on equity = Net income / Equity

Substitute:

13 = $ 9.5 / Equity

Equity = $ 9.5 / 13

Equity = $ 0.73 ( at end of 5 years)

Therefore free cash flow to equity in year 0=

13 = $ 6.4 / Equity

= $ 6.4 / 13

= $ 0.49

To calculate to total value of stock = beginning value given by FCFE(0)*(1+g)/(r-g) + terminal value, we find

Compounded annual growth rate in 5 years = ($ 475 / $ 320)1/5 - 1

= 0.082

= 8.2 %

Beginning value= FCFE(0) x (1+g) / (r - g)

= 0.49 x ( 1+ 0.082 ) / (0.12 - 0.082)

= 0.49 x 1.082 / 0.038

= $ 13.95

Terminal value = $ 0.73 x (1+ 0.04) / ( 0.12 - 0.04) x (1.12)5

= $5.42

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