Question

Here is the ORIGINAL data of the Sport Hotel project: 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 TWO things: the worth of the hotel, should the city be awarded the franchise, is not $8 million but some unknown smaller number; and the probability of getting the franchise is NOT 50% but is upgraded to 80%. 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?

Answer 1

Let W be the the new worth of the hotel when the franchise is granted, so that the NPV of the Sporthotel project to be equal to exactly zero

NPV of the hotel = Probability that franchise is granted x the worth of the hotel, should the city be awarded the franchise + Probability that franchise is not granted x the worth of the hotel, if the city is not awarded the franchise - total cost of the hotel = 80% x W + (1 - 80%) x 2,000,000 - 5,000,000 = 0.80W + 0.20 x 2,000,000 - 5,000,000 = 0.80W - 4,600,000

Setting this to zero,

0.80W - 4,600,000 = 0

Hence, W = 4,600,000 / 0.8 = $  5,750,000 = $ 5.75 mn = $ 6 mn (rounded off to the nearest integer)

Please enter your answer as per requirement.

• If it's in $, enter 5,750,000 as your answer
• If it's in $ mn with two places of decimal, enter 5.75
• If it's in $ mn with integer as answer, enter 6
• If it's a multiple choice question, please choose: The value of the hotel should the city be awarded the franchise = $ 6 million