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 $29 million. If the demand is low, the value of the cash flows in one year will be $24.5 million. The value of the project today under these assumptions is $27.7 million and the risk-free rate is 3 percent. Suppose that, in one year, if the demand for the new technology is low, the company can sell the technology for $25.8 million.

What is the value of the option to abandon? Use the two-state model to value the real option. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.) Value of the option to abandon = ?

Answer 1

Answer: In one year, the company will abandon the technology if the demand is low since the value of abandonment is higher than the value of continuing operations. Since the company is selling the technology in this case, the option is a put option. The value of the put option in one year if demand is low will be:

Value of put with low demand = 25,800,000 –24,500,000

Value of put with low demand = $1300,000

Also, if demand is high, the company will not sell the technology, so the put will expire worthless. We can value the put with the binomial model.

In one year, the percentage gain on the project if the demand is high will be:

Percentage increase with high demand = ($29,000,000 –27,700,000) / $27,700,000

Percentage increase with high demand = 4.693%

And the percentage decrease in the value of the technology with low demand is:

Percentage decrease with high demand = ($24,500,000 –27,700,000) / $27,700,000

Percentage decrease with high demand = –.1155, or –11.55%

Now we can find the risk-neutral probability of a rise in the value of the technology as:

Risk-free rate = (ProbabilityRise)(ReturnRise) + (ProbabilityFall)(ReturnFall)

Risk-free rate = (ProbabilityRise)(ReturnRise) + (1 –ProbabilityRise)(ReturnFall)

.03 = (ProbabilityRise)(.04693) + (1 –ProbabilityRise)(–.1155)

0.03=0.04693 ProbabilityRise-0.1155+0.1155 Probability Rise

0.03+0.1155=0.16243 Probability Rise

ProbabilityRise= .8957

So, a probability of a fall is:

ProbabilityFall= 1 –ProbabilityRise

ProbabilityFall= 1 –.8957

ProbabilityFall= .1043

Using these risk-neutral probabilities, we can determine the expected payoff of the real option at expiration. With high demand, the option is worthless since the technology will not be sold, and the value of the technology with low demand is the $1300,000 we calculated previously.

So, the value of the option to abandon is:

Value of option to abandon = [(.8957)(0) + (.1043)($1300,000)] / (1 + .03)

Value of option to abandon = $131640.78