Question

Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

$ millions	2020	2021	2022	2023	2024
Net Income	1.0	2.5	4.2	4.7	5.0
Investment	1.0	1.5	1.7	1.9	1.9
Free Cash Flow	0	1.0	2.5	2.8	3.1

Phoenix’s recovery will be complete by 2024, and there will be no further growth in net income or free cash flow. a) Calculate the PV of free cash flow, assuming a cost of equity of 10%. b) Assume that Phoenix has 12 million shares outstanding. What is the price per share?

Answer 1

a. The PV is computed as shown below:

= Free cash flow in 2020 / (1 + cost of equity) + Free cash flow in 2021 / (1 + cost of equity)² + Free cash flow in 2022 / (1 + cost of equity)³ + Free cash flow in 2023 / (1 + cost of equity)⁴ + Free cash flow in 2024 / (1 + cost of equity)⁵ + 1 / (1 + cost of equity)⁵ x [ (Free cash flow in 2024 / cost of equity) ]

= $ 0 million / 1.10 + $ 1 million / 1.10² + $ 2.5 million / 1.10³ + $ 2.8 million / 1.10⁴ + $ 3.1 million / 1.10⁵ + 1 / 1.10⁵ x [ ($ 3.1 million / 0.10) ]

= $ 0 million / 1.10 + $ 1 million / 1.10² + $ 2.5 million / 1.10³ + $ 2.8 million / 1.10⁴ + $ 3.1 million / 1.10⁵ + 31 million / 1.10⁵

= $ 0 million / 1.10 + $ 1 million / 1.10² + $ 2.5 million / 1.10³ + $ 2.8 million / 1.10⁴ + $ 34.1 million / 1.10⁵

= $ 25.79058807 million $ 25.79 million Approximately

b. The price per share is computed as shown below:

= Price computed in part a above / Number of shares outstanding

= $ 25.79058807 million / 12 million shares

= $ 2.15 Approximately

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