You are valuing a bank. The bank currently has assets of $310 per share. Five years from now (that is, at the end of five years), you expect their assets per share to be $490. After Year 5, you expect their assets per share to grow at 4 percent per year forever. The bank has an ROA of 1.2 percent and an ROE of 11.0 percent. The bank's cost of equity is 10.0 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:
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.
Step-by-step explanation:
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Answer:
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 Equity = $9.5/13
Substitute:
13 $9.5/Equity
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 = 8.2%
= 0.082
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