# A company forecasts the free cash flows in millions shown below. The weighted average cost of...

## Question:

A company forecasts the free cash flows in millions shown below. The weighted average cost of capital is 13%, and the FCFs are expected to continue growing at a 5% rate after Year 3. Assuming that the ROIC is expected to remain constant in Year 3 and beyond, What is the Year 0 value of operations, in millions?

Year 1 | FCF | $15 |
---|---|---|

Year 2 | FCF | $10 |

Year 3 | FCF | $40 |

## DCF Approach to Firm Valuation:

The discounted cash flow (DCF) approach is a method of firm valuation. This approach starts with estimating free cash flows a firm is expected to generate in the future. Given an appropriate discount rate, the DCF approach calculates the value of a firm as the discounted present value of free cash flows.

## Answer and Explanation:

The value of the firm is $412.67 millions.

According to the discounted cash flow approach, the value of the firm is the discounted present value of future free cash flows. The appropriate discount rate is 13%. At this discount rate, the present value of the free cash flows in the future is:

- {eq}\displaystyle \frac{15}{(1 + 13\%)} + \frac{10}{(1 + 13\%)^2} + \frac{40}{(1 + 13\%)^3} + \sum_{t=4}^{\infty}{\frac{40*(1 + 5\%)^{t-3}}{(1 + 13\%)^t}}\\ = 13.27 + 7.83 + 27.72 + \displaystyle \frac{40*(1 + 5\%)}{(13\% - 5\%)(1 + 13\%)^3}\\ = 48.82 + 363.85\\ = 412.67 {/eq}

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from Accounting 102: Intro to Managerial Accounting

Chapter 8 / Lesson 4