Question

Schultz Industries is considering the purchase of Arras Manufacturing. Arras is currently a supplier for Schultz, and the acquisition would allow Schultz to better control its material supply. The current cash flow from assets for Arras is $8 million. The cash flows are expected to grow at 9 percent for the next five years before leveling off to 6 percent for the indefinite future. The cost of capital for Schultz and Arras is 13 percent and 11 percent, respectively. Arras currently has 3 million shares of stock outstanding and $25 million in debt outstanding.

What is the maximum price per share Schultz should pay for Arras?

Answer 1

Maximum Price per share to be paid by Schultz for Arras

Maximum Price per share Schultz should pay for Arras = [Value of the firm – Value of Debt] / Number of common shares outstanding

Value of the firm = Present Value of Annual Cash flows + Present Value of Terminal Flow

Present Value of Annual Cash flows

Year	Annual Cash flow ($)	Present Value factor at 11%	Present Value of Annual Cash flow ($)
1	87,20,000 [CF0 x 109%]	0.90090090	78,55,856
2	95,04,800 [CF1x 109%]	0.81162243	77,14,309
3	1,03,60,232 [CF2 x 109%]	0.73119138	75,75,312
4	1,12,92,653 [CF3 x 109%]	0.65873097	74,38,820
5	1,23,08,992 [CF4 x 109%]	0.59345133	73,04,787
TOTAL			3,78,89,085

Present Value of Terminal Flow

Terminal Flow = CF5(1 + g) / (Ke – g)

= $1,23,08,992(1 + 0.06) / (0.11 – 0.06)

= $1,30,47,531 / 0.05

= $26,09,50,623

Present Value of Terminal Flow

Present Value of Terminal Flow = Terminal Flow x [PVIF 11%, 5 Year]

= $26,09,50,623 x 0.59345133

= $15,48,61,493

Total Value of the Firm

Total Value of the Firm = Present Value of Annual Cash flows + Present Value of Terminal Flow

= $3,78,89,085 + $15,48,61,493

= $19,27,50,578

Maximum Price per share Schultz should pay for Arras = [Value of the firm – Value of Debt] / Number of common shares outstanding

= [$19,27,50,578 - $250,00,000] / 30,00,000 common shares outstanding

= $16,77,50,578 / 30,00,000 common shares outstanding

= $55.92 per share

“Therefore, the maximum Price per share Schultz should pay for Arras will be $55.92”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.