What is the present value per share of High Tech stock using the discounted cash flow approach if the terminal value of High Tech is based on using the constant growth model to determine terminal value?

Kinetic Corporation is considering acquiring High Tech Systems. Jim Smith, the vice
president of finance at Kinetic, has been assigned the task of estimating a fair acquisition price
for High Tech. Smith is aware of several approaches that could be used for this purpose. He
plans to estimate the acquisition price based on each of these approaches, and has collected or
estimated the necessary financial data.
High Tech has 10 million shares of common stock outstanding and no debt. Smith has
estimated that the post-merger free cash flows from High Tech, in millions of dollars, would
be 15, 17, 20, and 23 at the end of the following four years. After Year 4, he projects the free
cash flow to grow at a constant rate of 6.5 percent a year. He determines that the appropriate
rate for discounting these estimated cash flows is 11 percent. He also estimates that after four
years High Tech would be worth 23 times its free cash flow at the end of the fourth year.
Smith has determined that three companies—Alpha, Neutron, and Techno—are comparable to High Tech. He has also identified three recent takeover transactions—Quadrant,
ProTech, and Automator—that are similar to the takeover of High Tech under consideration.
He believes that price-to-earnings, price-to-sales, and price-to-book value per share of these
companies could be used to estimate the value of High Tech. The relevant data for the three
comparable companies and for High Tech are as follows:
Valuation Variables Alpha Neutron Techno High Tech
Current stock price ($) 44.00 23.00 51.00 31.00
Earnings/share ($) 3.01 1.68 2.52 1.98
Sales/share ($) 20.16 14.22 18.15 17.23
Book value/share ($) 15.16 7.18 11.15 10.02
The relevant data for the three recently acquired companies are given below:
Valuation Variables Quadrant ProTech Automator
Stock price pre-takeover ($) 24.90 43.20 29.00
Acquisition stock price ($) 28.00 52.00 34.50
Earnings/share ($) 1.40 2.10 2.35
Sales/share ($) 10.58 20.41 15.93
Book value/share ($) 8.29 10.14 9.17
While discussing his analysis with a colleague, Smith makes two comments. Smith’s first
comment is: “If there were a pre-announcement run-up in Quadrant’s price because of
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speculation, the takeover premium should be computed based on the price prior to the runup.” His second comment is: “Because the comparable transaction approach is based on the
acquisition price, the takeover premium is implicitly recognized in this approach.
A. $39.38.
B. $40.56.
C. $41.57.

Answer: C. $41.57.