Carhart Towers Inc. is considering a proposed project. The company estimates that if it invests in the project today, the project's estimated NPV is $10 million, but there remains a lot of uncertainty about the project's profitability.
As an alternative to making the investment today, the company is considering waiting a year. In particular, it is considering spending some money today to collect additional information, which would enable the firm to make a better assessment of the project's value one year from now. Carhart believes that if it waits a year, there is a 50 percent chance the information collected will be positive and the project's expected NPV one year from now (not including the cost of obtaining the information) will be $25 million. There is also a 50 percent chance the information collected will be negative and the project's expected NPV one year from now (not including the cost of obtaining the information) will be -$12 million.
If the company chooses to collect additional information, the costs of collecting this information will be incurred today. Moreover, if the company chooses to wait a year, it has the option to invest or not invest in the project after receiving the information about the project's prospects. Assume that all cash flows are discounted at 11 percent. What is the maximum amount of money the company would be willing to spend to collect this information?
A) $1.009 million
B) $1.261 million
C) $1.502 million
D) $1.793 million
E) $2.500 million

Question

Quizplus · Accepted Answer

To find the maximum amount Carhart Towers Inc. would be willing to spend on collecting information, we first calculate the expected NPV if the company waits a year to decide, taking into account the probabilities of positive and negative outcomes and the discount rate. The expected NPV one year from now, not including the cost of obtaining the information, is calculated as follows: (0.5 * $25 million) + (0.5 * -$12 million) = $6.5 million. To find its present value, we discount it by 11%, resulting in $6.5 million / (1 + 0.11) = $5.855 million. The current NPV without additional information is $10 million. Therefore, the maximum amount the company would be willing to pay for the information is the difference between the present value of the expected NPV if it waits ($5.855 million) and the current NPV ($10 million), which is $10 million - $5.855 million = $4.145 million. However, this calculation does not align with the provided options, indicating a mistake in the explanation process. The correct approach involves recognizing the option to not proceed with the project if the information is negative, which wasn't accounted for correctly. The correct calculation should focus on the value of the option to wait and make a decision based on the information, which involves calculating the expected value of the project after obtaining the information and comparing it to the current NPV, then determining the maximum cost of information from that comparison. Given the mistake in the initial explanation, let's correct the approach:The correct expected NPV when considering the option to abandon the project in case of negative information is: (0.5 * $25 million / (1 + 0.11)) + (0.5 * $0 / (1 + 0.11)) = $11.261 million / (1 + 0.11) = $10.144 million. The difference between this value and the project's current NPV ($10 million) gives the maximum amount the company should be willing to pay for the information. However, the calculation provided does not directly lead to any of the options given, indicating a need to correctly apply the option valuation method to determine the maximum amount the company would be willing to spend on collecting the information, which involves correctly calculating the expected value of waiting and making the investment decision based on the new information.