Question

Here is the ORIGINAL data of the Sporthotel problem: 1. Projected outflows First year (Purchase Right, Land, and Permits) $1,000,000 Second Year (Construct building shell $2,000,000 Third Year: (Finish interior and furnishings) $2,000,000 TOTAL $5,000,000 2. Projected inflows If the franchise is granted hotel will be worth: $8,000,000 when it opened If the franchise is denied hotel will be worth: $2,000,000 when it opened. The probability of the city being awarded the franchise is 50%. Suppose that everything is the same as in that problem except one thing: the worth of the hotel, should the city be awarded the franchise, is not $8 million but some unknown smaller number. What must the new worth of the hotel when the franchise is granted be in order for the NPV of the Sporthotel project to be equal to exactly zero?

_____ million?

Answer 1

You have not provided any discount rate. So I am assuming that everything is in PV terms.

You will get to know about the decision of the hotel after 1st year when all the Permits & Rights are purchased. So if the franchise is denied hotel, you won't go ahead and construct anything because the benefits are lesser than the costs.

Hence NPV = -1000000 + 0.5*(Worth of Hotel - 3000000) + 0.5*Worth of Second option

Worth of Second Option = 0

Now, for NPV to be zero

1000000 = 0.5*(Worth of Hotel - 3000000)

Worth of Hotel = $5,000,000

Ans is $5,000,000