Question

Widget Corp. is expected to generate a free cash flow (FCF) of $1,835.00 million this year (FCF₁ = $1,835.00 million), and the FCF is expected to grow at a rate of 21.40% over the following two years (FCF₂ and FCF₃). After the third year, however, the FCF is expected to grow at a constant rate of 2.82% per year, which will last forever (FCF₄). Assume the firm has no nonoperating assets. If Widget Corp.’s weighted average cost of capital (WACC) is 8.46%, what is the current total firm value of Widget Corp.? (Note: Round all intermediate calculations to two decimal places.) $44,347.57 million $53,217.08 million $55,008.09 million $5,705.25 million

Answer 1

The current total firm value of Widget Corp. is $39,643.09 million.

Step-by-step explanation:

To calculate the current total firm value of Widget Corp., we need to find the present value of its future free cash flows. The formula for calculating the present value of a growing perpetuity is FCF / (WACC - g), where FCF is the free cash flow, WACC is the weighted average cost of capital, and g is the growth rate. Let's break down the calculation:

Year 1: Present value of FCF₁ = FCF₁ / (1 + WACC) = $1,835.00 million / (1 + 0.0846) = $1,692.49 million

Year 2: Present value of FCF₂ = FCF₂ / (1 + WACC)² = $1,835.00 million * (1 + 0.2140) / (1 + 0.0846)² = $1,835.00 million * 1.2140 / 1.0766 = $2,058.87 million

Year 3: Present value of FCF₃ = FCF₃ / (1 + WACC)³ = $1,835.00 million * (1 + 0.2140)² / (1 + 0.0846)³ = $1,835.00 million * 1.2140² / 1.0766³ = $2,268.86 million

After Year 3: Present value of perpetual cash flows = FCF₄ / (WACC - g) = $1,835.00 million * (1 + 0.0282) / (0.0846 - 0.0282) = $1,835.00 million * 1.0282 / 0.0564 = $33,623.87 million

Finally, we sum up the present values of the free cash flows:

Total firm value = Present value of FCF₁ + Present value of FCF₂ + Present value of FCF₃ + Present value of perpetual cash flows = $1,692.49 million + $2,058.87 million + $2,268.86 million + $33,623.87 million = $39,643.09 million

Therefore, the current total firm value of Widget Corp. is $39,643.09 million.

Answer 2

$44,347.57 million

Step-by-step explanation:

Present value of FCFFs

=1835/1.0846 + 1835*1.214/1.0846^2 + 1835*1.214^2/1.0846^3 + 1835*1.214^2*1.0282/(8.46%-2.82%)*1/1.0846^3

=44347.55450420 million