Advanced Chemical Industries is awaiting the verdict from a court case over whether it is liable for the clean-up of wastes on a disused factory site. If it is liable, this will result in a reduction of its free cash flow by $12 million per year for 10 years. If it is not liable, there will be no effect. On the close of trading the day before the announcement of the verdict, Advanced Chemicals was trading at $20 per share. Most investors calculate that there is a 100% chance that Advanced Chemicals will have a verdict returned against them. One investor, Jo, has performed extensive research into the outcome of the trial and estimates that there is no chance Advanced Chemicals will have a verdict returned against them. Given that Advanced Chemicals has 60 million shares outstanding and an equity cost of capital of 8% with no debt, Jo's estimate of the value of a share of Advanced Chemicals would be how much more than the market price?
A)$20.46
B)$20.68
C)$1.34
D)$20.96

Question

Quizplus · Accepted Answer

The market has priced in a 100% chance of a $12 million reduction in free cash flow for 10 years. The present value (PV) of this reduction can be calculated using the formula for the present value of an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the payment per period, r is the discount rate, and n is the number of periods. Here, P = $12 million, r = 8% (0.08), and n = 10 years. PV = $12 million * [(1 - (1 + 0.08)^-10) / 0.08] ≈ $12 million * 6.71008 ≈ $80.52 million. The total reduction in value is $80.52 million. With 60 million shares outstanding, this is a reduction of about $80.52 million / 60 million shares = $1.34 per share. Since Jo believes there will be no reduction, her estimate of the value of a share would be $1.34 more than the market price.

Advanced Chemical Industries Is Awaiting the Verdict from a Court