Chapter 4 The Value of Common Stocks 103
bre44380_ch04_076-104.indd 103 09/30/15 12:46 PM
Phoenix’s recovery will be complete by 2021, and there will be no further growth in free
cash flow.a. Calculate the PV of free cash flow, assuming a cost of equity of 9%.
b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
c. If the 2016 net income is $1 million, what is Phoenix’s P/E ratio? How do you expect that
P/E ratio to change from 2017 to 2021?
d. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the
years from 2017 to 2021.
CHALLENGE
- Constant-growth DCF formula The constant-growth DCF formula:
P 0 =DIV 1
_____r − gis sometimes written as:P 0 =ROE(1 − b) BVPS
________________
r − b ROEwhere BVPS is book equity value per share, b is the plowback ratio, and ROE is the ratio of
earnings per share to BVPS. Use this equation to show how the price-to-book ratio varies as
ROE changes. What is price-to-book when ROE = r?- DCF valuation Portfolio managers are frequently paid a proportion of the funds under
management. Suppose you manage a $100 million equity portfolio offering a dividend yield
(DIV 1 /P 0 ) of 5%. Dividends and portfolio value are expected to grow at a constant rate. Your
annual fee for managing this portfolio is .5% of portfolio value and is calculated at the end
of each year. Assuming that you will continue to manage the portfolio from now to eternity,
what is the present value of the management contract? How would the contract value change
if you invested in stocks with a 4% yield? - Valuing free cash flow Construct a new version of Table 4.7, assuming that the concatena-
tor division grows at 20%, 12%, and 6%, instead of 12%, 9%, and 6%. You will get negative
early free cash flows.
a. Recalculate the PV of free cash flow. What does your revised PV say about the division’s
PVGO?
b. Suppose the division is the public corporation Concatco, with no other resources. Thus
it will have to issue stock to cover the negative free cash flows. Does the need to issue
shares change your valuation? Explain. (Hint: Suppose first that Concatco’s existing
stockholders buy all of the newly issued shares. What is the value of the company to
these stockholders? Now suppose instead that all the shares are issued to new stockhold-
ers, so that existing stockholders don’t have to contribute any cash. Does the value of the
company to the existing stockholders change, assuming that the new shares are sold at a
fa i r pr ice?)
The major stock exchanges have wonderful websites. Start with the NYSE (www.nyse.com) and
Nasdaq (www.nasdaq.com). Make sure you know how trading takes place on these exchanges.
● ● ● ● ●FINANCE ON
THE WEB