The free cash flows (in millions) shown below are forecast by Simmons Inc.If the weighted average cost of capital is 13% and the free cash flows are expected to continue growing at the same rate after Year 3 as from Year 2 to Year 3, what is the Year 0 value of operations, in millions? $$\begin{array} { l c c c }
\text { Year: } & 1 & 2 & 3 \
\hline \text { Free cash flow: } & - \$ 20 & \$ 42 & \$ 45
\end{array}$$

Question

The free cash flows (in millions) shown below are forecast by Simmons Inc.If the weighted average cost of capital is 13% and the free cash flows are expected to continue growing at the same rate after Year 3 as from Year 2 to Year 3, what is the Year 0 value of operations, in millions? $$\begin{array} { l c c c } 
\text { Year: } & 1 & 2 & 3 \
\hline  \text { Free cash flow: } & - \$ 20 & \$ 42 & \$ 45
\end{array}$$

Quizplus · Accepted Answer

The growth rate from Year 2 to Year 3 is calculated as $\frac{45 - 42}{42} = \frac{3}{42} = 0.0714$ or 7.14%. The terminal value at the end of Year 3, using the perpetuity growth formula, is $\frac{45 \times (1 + 0.0714)}{0.13 - 0.0714} = \frac{45 \times 1.0714}{0.0586} = 821.4286$. The present value of the free cash flows and the terminal value is calculated as: $-20 + \frac{42}{(1 + 0.13)} + \frac{45}{(1 + 0.13)^2} + \frac{821.4286}{(1 + 0.13)^3} = -20 + 37.1681 + 35.3982 + 564.4737 = 617.04$.

The Free Cash Flows (In Millions) Shown Below Are Forecast Year: 123 Free cash flow: −$20$42$45\begin{array} { l c c c } \text { Year: } & 1 & 2 & 3 \\\hline \text { Free cash flow: } & - \$ 20 & \$ 42 & \$ 45\end{array} Year: Free cash flow: ​1−$20​2$42​3$45​​

The Free Cash Flows (In Millions) Shown Below Are Forecast $\begin{array} { l c c c } \text { Year: } & 1 & 2 & 3 \\\hline \text { Free cash flow: } & - \$ 20 & \$ 42 & \$ 45\end{array}$