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 $7.1 million. The cash flows are expected to grow at 7 percent for the next five years before leveling off to 4 percent for the indefinite future. The cost of capital for Schultz and Arras is 11 percent and 9 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Please go step by step in detail, thank you in advance!

Answer 1

The maximum price per share Schultz should pay for Arras is $ 47.74 / share.

Working notes ÷

Share price = value of equity /no. of shares

Value of equity = Value of company - value of debt

Value of firm = present value of future cash flows

The cash flows each year will be:

Year 1: $7,100,000(1 + .07) = $7,597,000

Year 2: $7,597,000(1 + .07) = $8,128,790

Year 3: $8,128,790(1 + .07) = $8,697,805

Year 4: $8,697,805(1 + .07) = $9,306,651

Year 5: $9,306,651(1 + .07) = $9,958,117

Year 6: $9,958,117(1 + .04) = $10,356,442

Since the cash flows begin a perpetual growth rate, we can calculate the terminal value in year 5

We are valuing Arras, we need to use the cost of capital for that company i.e. 9%

. So, the terminal value is:

TV5= CF6/ (WACC– g)

TV5= $10,356,442/(0.09 – 0.04)

TV5= $207,128,840

Now we can discount the cash flows for the first 5 years and  the terminal value ÷

Value of firm

= $[7,597,000 /(1.09)¹ + 8,128,790/(1.09)²  + 8,697,805/(1.09)³ + 9,306,651/(1.09)⁴ + (9,958,117+ 207,128,840)/(1.09)⁵]

= $[7,597,000 × 0.917 + 8,128,790 × 0.842 + 8,697,805 × 0.772 + 9,306,651 × 0.708 + 217,086,957 × 0.650

= $168,221,227

The value of the equity = $(168,221,227 – 25,000,000 ) =$143,221,227

Share price = $143,221,227/3,000,000

Share price = $ 47.74 / share

The maximum price per share Schultz should pay for Arras is $ 47.74 / share.

NOTE÷

1. As nothing said in the question for rounding off ,the figures for annuity factor are rounded to 3 decimals. So there may be a little bit difference in the value of company. And the final answer is rounded to 2 decimals

1. If calculation is made with financial calculator then the value of company is $ 168,212,559.75

value of equity =$(168,212,559.75 - 25,000,000)

=$143,212,559.75

Share price = 143,212,559.75/ 3,000,000

=$ 47.738

= $ 47.74 / share

The final answer i.e. price per share is same =

$ 47.74/share in both the calculations.