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 $8.4 million. The cash flows are expected to grow at 8 percent for the next five years before leveling off to 5 percent for the indefinite future. The cost of capital for Schultz and Arras is 12 percent and 10 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 final answer to 2 decimal places. (e. g., 32.16))

$58.57

Explanation:

First, we need to determine the  future cash flow of the company from Year 1 till the growth becomes level off at a constant perpetual rate. As shown below:

Year 1         8,400,000 x (1 + 0.08)  =  9,072,000

Year 2        9,072,000 x (1 + 0.08)  =  9,797,760

Year 3        9,797,760 x (1 + 0.08)  =  10,581,581

Year 4        10,581,581 x (1 + 0.08)  =  11,428,107

Year 5        11,428,107 x (1 + 0.08)  =  12,342,356

Year 6        12,342,356 x (1 + 0.05)  =  12,959,474

Next, we need to calculate the terminal value as after Year 5 the growth has become constant for the indefinite future. We need the cost of capital of Arras as the value being determined is for Arras Manufacturing and not Schultz. Calculation shown as follows:

12,959,474 / (0.1 - 0.05) = $259,189,480

Now, we discount the cash flow of both the first 5 years and terminal value at present time value. As done below:

V0 = 9,072,000 / (1 + 0.1) + 9,797,760 / (1 + 0.1)^2 + 10,581,581 / (1 + 0.1)^3 + 11,428,107 / (1 + 0.1)^4 + (12,342,356 + 259,189,480) / (1 + 0.1)^5

V0 = 8,247,273 + 8,097,322 + 7,950,098 + 7,805,551 + 168,599,907

V0 = 200,700,151

Lastly, we deduct the above discounted value given with the outstanding debt to calculate the market value of equity and then divide it by the total number of shares to calculate the maximum price per share.

Market Value of Equity = 200,700,151 - 25,000,000 = 175,700,151

Share price = $58.57 per share

Hence the maximum price per share Schultz should pay for Arras is $58.57

answer; maintain a safe following distance;