Question

# Alex is a new intern in an investment bank. She is trying to value a firm...

Alex is a new intern in an investment bank. She is trying to value a firm using non-constant growth model. Firm's free cash flow in current year is \$10m. FCF will grow by 12%, 10%, and 8% in years 1, 2, and 3, respectively. Alex assumes WACC=10%, uses the wrong formulas and finds that firm value is \$108.33m. Alex's manager says the actual WACC of firm should be 12% and want Alex to re-calculate correct firm value. What is the correct firm value?

Firms value = present value of future cash flows

Present value year 1 cash flow = 10,000,000(1.12) / ( 1 + 0.12)1

Present value year 1 cash flow = 11,200,000 / 1.12

Present value year 1 cash flow = 10,000,000

Present value of year 2 cash flow = 11,200,000(1.1) / (1.12)2

Present value of year 2 cash flow = 12,320,000 / (1.12)2

Present value of year 2 cash flow = 9,821,428.571

Present value of year 3 cash flow = 12,320,000(1.08) / (1.12)3

Present value of year 3 cash flow = 13,305,600 / (1.12)3

Present value of year 3 cash flow = 9,470,663.265

Correct firm value = 9,470,663.265 + 9,821,428.571 + 10,000,000

Correct firm value = 29,292,091.84

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