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	2.1	3.1	5.4	5.90	6.2
Investment	2.1	2.1	2.3	2.5	2.5
Free cash flow	0	1.0	3.1	3.4	3.7

  
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 8%. (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

b. Assume that Phoenix has 12 million shares outstanding. What is the price per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Confirm that the expected rate of return on Phoenix stock is exactly 8% in each of the years from 2020 to 2024. (Hint: First, calculate the PV of all future cash flows starting in each year. Round your answer to 2 decimal places.)

Answer 1

Part A:

PV of Cash flows = Sum [ Cash Flow * PVF(r%, n) ]

PVF(r%, n) = 1 / ( 1 + r )^n
r = Int Rate per period
n = No. of periods

Year	Cash Flow	PVF @8%	PV of CFs
1	$ 1,000,000.00	0.9259	$     925,925.93
2	$ 3,100,000.00	0.8573	$ 2,657,750.34
3	$ 3,400,000.00	0.7938	$ 2,699,029.62
4	$ 3,700,000.00	0.7350	$ 2,719,610.46
PV of CFs			$ 9,002,316.34

Part B:

Price per share = PV of Cash Flows / No. of shares

= $  9,002,316.34 / 12000000

= $ 0.75

Part C:

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows or Rate of growth is expected from project/ Investment. At IRR, NPV of Project/ Investment will be Zero. It assumes that intermediary Cfs are reinvested at IRR only.

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be accepted / Rejected
IRR < Cost of Capital - Project will be erejected

Year	CF	PVF @8 %	Disc CF	PVF @9 %	Disc CF
0	$ -9,002,316.34	1.0000	$ -9,002,316.34	1.0000	$ -9,002,316.34
1	$ 1,000,000.00	0.9259	$      925,925.93	0.9174	$      917,431.19
2	$ 3,100,000.00	0.8573	$ 2,657,750.34	0.8417	$ 2,609,207.98
3	$ 3,400,000.00	0.7938	$ 2,699,029.62	0.7722	$ 2,625,423.83
4	$ 3,700,000.00	0.7350	$ 2,719,610.46	0.7084	$ 2,621,173.28
NPV			$                  0.00		$    -229,080.06

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 8 % + [ 0 / ( 0 - ( -229080.06) ) ] * 1 %
= 8 % + [ 0 / ( 229080.06) ] * 1 %
= 8 % + [ 0 ] * 1 %
= 8 % + 0 %
= 8 %

Thus it gives 8% Ret each year from 2020 to 2024