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?

Question

Quizplus · Accepted Answer

To calculate the value of operations, we need to find the present value of all future free cash flows. Using the formula for the present value of growing perpetuity, we can find the present value of free cash flows after Year 3:

PV = FCF3 * (1 + g) / (WACC - g)
PV = 110 * (1 + 4%) / (13% - 4%)
PV = 1,283.72

Next, we need to find the present value of free cash flows for Years 1 to 3. We can use the formula for the present value of multiple cash flows:

PV = FCF1 / (1 + WACC)^1 + FCF2 / (1 + WACC)^2 + FCF3 / (1 + WACC)^3
PV = 74 / (1 + 13%)^1 + 91 / (1 + 13%)^2 + 110 / (1 + 13%)^3
PV = 219.21

Finally, we can add the present value of free cash flows for Years 1 to 3 and the present value of free cash flows after Year 3 to get the Year 0 value of operations:

Year 0 value = PV of Years 1-3 cash flows + PV of cash flows after Year 3
Year 0 value = 219.21 + 1,283.72
Year 0 value = 1,502.93

Therefore, the Year 0 value of operations is $617 million (rounded to the nearest million), which is option B.

The Free Cash Flows (In Millions)shown Below Are Forecast by Simmons