Schultz Industries is considering the purchase of Arras Manufacturing. Arras is

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 $8.3 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?

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 $8.3 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?

Explanation / Answer

To calculate the maximum price per share, we need to find the market value of equity of the company. Market value of equity is the difference between the total market value of the company today and the value of debt. Total market value of the company is calculated by discounting all the cash flows expected in the near future, with the use of cost of capital for the company. Relevant formulas are:

Market Value of the Company = Cash Flow Year 1/(1+Cost of Capital)^1 + Cash Flow Year 2/(1+Cost of Capital)^2 + Cash Flow Year 3/(1+Cost of Capital)^3 + Cash Flow Year 4/(1+Cost of Capital)^4 + Cash Flow Year 5/(1+Cost of Capital)^5 + Terminal Value in Year 5/(1+Cost of Capital)^5

Value of Equity = Market Value of the Company - Value of Debt.

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Step 1: Calculate Cash Flows for the Year 1 to 6

Since, the cash flows for Year 1 to 5 will grow at the rate of 7% and after Year 5 at 4%, we get,

Cash Flow Year 1 = 8,300,000*(1+7%)^1

Cash Flow Year 2 = 8,300,000*(1+7%)^2

Cash Flow Year 3 = 8,300,000*(1+7%)^3

Cash Flow Year 4 = 8,300,000*(1+7%)^4

Cash Flow Year 5 = 8,300,000*(1+7%)^5

Cash Flow Year 6 = 8,300,000*(1+7%)^5*(1+4%)

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Step 2: Calculate Terminal Value Year 5

Since, the cash flows would grow at a perpetual growth rate of 4% from Year 5 onwards, we can calculate the terminal value in Year 5. We will use the cost of capital for Arras. The formula that would be used for calculating terminal value is:

TV5 = Cash Flow Year 6/(Cost of Capital - Perpetual Growth Rate)

TV5 = 8,300,000*(1+7%)^5*(1+4%)/(9% - 4%) = $242,136,530.79

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Step 3: Calculate Market Value Today and Value of Equity

Using the values calculated in step 1 and step 2 in the formula for market value, we get,

Market Value Today = 8,300,000*(1+7%)^1/(1+9%)^1 + 8,300,000*(1+7%)^2/(1+9%)^2 + 8,300,000*(1+7%)^3/(1+9%)^3 + 8,300,000*(1+7%)^4/(1+9%)^4 + 8,300,000*(1+7%)^5/(1+9%)^5 + 242,136,530.79/(1+9%)^5 = $196,642,851.54

_____________

Value of Equity = $196,642,851.54 - $25,000,000 = $171,642,851.54

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Step 4: Calculate Maximum Price Per Share

Using the value of equity calculated in step 3 and the number of common shares outstanding, we get,

Maximum Price Per Share = Value of Equity/Common Shares Outstanding = $171,642,851.54/3,000,000 = $57.21

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