Question

Your company operates a steel plant. On average, revenues from the plant are $30 million per year. All of the plants costs are variable costs and are consistently 80% of revenues, including energy costs associated with powering the plant, which represent one quarter of the plant’s costs, or an average of $6 million per year. Suppose the plant has an asset beta of 1.25, the risk-free rate is 4%, and the market risk premium is 5%. The tax rate is 40%, and there are no other costs. a. Estimate the value of the plant today assuming no growth. b. Suppose you enter a long-term contract which will supply all of the plant’s energy needs for a fixed cost of $3 million per year (before tax). What is the value of the plant if you take this contract? c. How would taking the contract in (b) change the plant’s cost of capital? Explain

Answer 1

The tax rate is t = 40% = 0.4

Risk Free Rate = 4%  

market risk premium = 5%

Beta = 1.25

Cost of Equity ( r) = Risk Free Rate + Beta * market risk premium = 4% + 1.25 * 5% = 10.25%

Ans : a.

Value of the Plant with no growth V(0)

Free Cash Flow to the Firm = (Revenue - Cost) * ( 1 - tax Rate )  

Revenue =  $30 million

Cost =  80% of revenues = 80% * 30 = $ 24 Million

Free Cash Flow to the Firm = ( 30 -  24 ) * ( 1 - 0.4) = 6 * 0.6 = $ 3.6 Million

Value of the firm = Free Cash Flow to the Firm / Cost of Equity ( r) = $ 3.6 Million /  10.25% = $ 35.12  Million

the value of the plant today assuming no growth $ 35.12 Million (Ans)

Ans : b.

Now As per New contract plant’s energy cost =  $3 million

Earlier Energy Cost = $6 million

Total cost without considering energy cost = Total Cost -  Earlier Energy Cost = 24 - 6 = $ 18 million

Free Cash Flow to the Firm not considering energy cost = (Revenue - Cost) * ( 1 - tax Rate )

=  ( 30 - 18 ) * ( 1 - 0.4) = 12 * 0.6 = $ 7.2 Million

Energy cost after tax = Energy Cost as per contract * ( 1 - tax rate) = 3 * (1 – 0.40) = 1.80 Million

Cost of capital (For Energy Cost) = Risk free rate = 3%

Value V1 =( Free Cash Flow to the Firm not considering energy cost / Cost of Equity ) - ( Net Savings in Energy cost after tax / Risk free rate)

= ( 7.2 / 10.25% ) - ( 1.80 / 3%) = 70.24 - 60 = $ 12.04 Million

value of the plant as per new contract = $ 12.04  Million (Ans)

Ans : c.

After Considering Energy contract Free Cash flow of the Firm = Free Cash Flow to the Firm not considering energy cost - Energy cost after tax = $ 7.2 Million - $ 1.80 Million = $ 5.4 Million

Cost of Capital = Free Cash Flow / value of the plant =   5.4 /  12.04 = 0.4485 =44.85%

New cost of capital 44.85% (Ans)