Question

Wet for the Summer, Inc., manufactures filters for swimming pools. The company is deciding whether to implement a new technology in its pool filters. One year from now the company will know whether the new technology is accepted in the market. If the demand for the new filters is high, the present value of the cash flows in one year will be $14.3 million. Conversely, if the demand is low, the value of the cash flows in one year will be $8 million. The value of the project today under these assumptions is $12.9 million, and the risk-free rate is 6 percent. Suppose that in one year, if the demand for the new technology is low, the company can sell the technology for $9.4 million. What is the value of the option to abandon?

Answer 1

$131,283

Step-by-step explanation:

Upstate Price = Present Value of Cash Flows if Demand is High / Value of Project = $14.3 million / $12.9 million = 1.10853

Downstate Price = Present Value of Cash Flows if Demand is Low / Value of Project = $8 million / $12.9 million = 0.62016

Now, the computation of Probability of Demand being High

Risk Free Rate = (Probability of Rise) * (U-1) + (1 - Probability of Rise) * (d-1)

0.06 = (Probability of Rise) * (1.10853 - 1) + (1 - Probability of Rise) * (0.62016 - 1)

0.06 = (Probability of Rise) * 0.10853 + (1 - Probability of Rise)*(-0.37984)

0.06 = 0.10853 Probability of Rise + 0.37984 Probability of Rise - 0.37984

0.06 + 0.37984 = 0.10853 Probability of Rise + 0.37984 Probability of Rise

0.43984 = 0.10853 + 0.37984 Probability of Rise

0.43984 = 0.48837 Probability of Rise

Probability of Rise = 0.43984 / 0.48837

Probability of Rise = 0.9006286217417122

Probability of Rise = 0.9006

Probability of Fall = 1 - 0.9006

Probability of Fall = 0.0994

Value of the option to abandon = Probability of Fall * (Selling Price - Cash Flow if Demand is Low)/(1 + Risk Free rate)

Value of the option to abandon = 0.0994 * ($9,400,000-$8,000,000) / (1 + 0.06)

Value of the option to abandon = 0.0994 * $1,400,000/1.06

Value of the option to abandon = $139,160 / 1.06

Value of the option to abandon = $131283.0188679245

Value of the option to abandon = $131,283