Consider again the Sport Hotel example and Example 9.1. Suppose that if the fran
ID: 2657303 • Letter: C
Question
Consider again the Sport Hotel example and Example 9.1. Suppose that if the franchise is accepted the value of the hotel is not $8 million but instead $7.50. Everything else, including first year expenses, is the same as shown in the example. Incorporating the real option, what probability of the franchise being granted would represent a "fair investment?" (that is, a probability such that any higher value would create a positive expected value)
??? %
[Sport Hotel example]
The following figure is from our course notes and is the same as figure 9.2 on page 272 of our textbook. complete hotel gives NPV of +S3 million abandon the project gives NPV of -$1 million complete hotel gives NPV of -$3 million abandon project gives NPV of -S1 million franchise is granted C DExplanation / Answer
It is given that in the present scenario, being granted the franchise and completing the project gives us a worth of $7.5 mn. Since costs are the same, hence if the project is granted and completed -
Net profit will be 7.5-5 = 2.5 million
On the other, if the real option is given i.e. right to deny the franchise after 1 year, the franchise would suffer a loss of 1 million.
Therefore if P is the probability -
P*(2.5) +(1-P)*(-1) = 0
3.5P = 1
P = 0.28 = 28%
Hence a frnachise probability greater than 28% turns into positive NPV when the real option to abandon is considered.