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 $7.6 million. The cash flows are expected to grow at 5 percent for the next five years before leveling off to 2 percent for the indefinite future. The cost of capital for Schultz and Arras is 9 percent and 7 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))

Answer 1

Current cash flow from assets = CF0 = $7.6 million = $7600000

Growth rate of cash flow from assets for first five years = g =5%

Cash flow from assets in year 1 = CF1 = CF0 (1+g) = 7600000 x (1+5%) = 7600000 x 1.05 = 7980000

Cash flow from assets in year 2 = CF2 = CF0 (1+g)² = 7600000 x (1+5%)² = 7600000 x (1.05)² = 8379000

Cash flow from assets in year 3 = CF3 = CF0 (1+g)³ = 7600000 x (1+5%)³ = 7600000 x (1.05)³ = 8797950

Cash flow from assets in year 4 = CF4 = CF0 (1+g)⁴ = 7600000 x (1+5%)⁴ = 7600000 x (1.05)⁴ = 9237847.50

Cash flow from assets in year 5 = CF5 = CF0 (1+g)⁵ = 7600000 x (1+5%)⁵ = 7600000 x (1.05)⁵ = 9699739.875

Growth rate of cash flow from assets after year 5 = g1 = 2%

In Discounted cash flow analysis we always use cost of capital of the target company as discount rate to reflect risk of the investment.

Discount rate = r = Cost of capital of Arras = 7%

According to constant growth rate model

V5 = Terminal value of Arras at end of year 5 = [CF5(1+g2)] / (r-g) = [96699739.875 (1+2%)] / (7% - 2%)

= [96699739.875 x 1.02] / 5% = 9893734.6725 / 5% = 197874693.45

Value of Arras company = Sum of present value of cash flow from assets from year 1 to year 5 + Present value of Terminal value of Arras at end of year 5 = 7980000 / (1+7%) + 8379000 / (1+7%)² + 8797950 / (1+7%)³ + 9237847.50 / (1+7%)⁴ + 9699739.875 / (1+7%)⁵ + 197874693.45 / (1+7%)⁵ = 7457943.9252 + 7318543.1042 + 7181747.9059 + 7047509.6273 + 6915780.4754 + 141081921.6994 = 177003446.7374

Value of Equity = Value of Array company - Value of debt = 177003446.7374 - 25000000 = 152003446.7374

Maximum price of share of Array = Value of Equity / Shares outstanding = 152003446.7374 / 3000000 = 50.6678 = $50.67 (rounded to two decimal places)

Maximum price of share of Array that should be paid = $50.67