Question

5. Real options

Darnell and Eleanor are going to see a play this weekend and want to buy tickets before they sell out. They want to go the same night that their friends are going, but they haven't been able to reach them to find out whether they have tickets for Friday or Saturday night. If they purchase tickets for the same night that their friends did, they will get a utility of 15. If they choose the wrong night and end up going without their friends, they will only get a utility of 5.

The numbers in the following table reflect the utility Darnell and Eleanor get under each of the described outcomes.

Options	Day Friends See Play
	Saturday	Friday
(1) Buy Friday tickets	5	15
(2) Buy Saturday tickets	15	5

If the probability that their friends have tickets for Saturday night is 50%, then the expected value of utility from buying tickets for Friday is , and the expected value of utility from buying tickets for Saturday is .

Now, suppose Darnell and Eleanor consider a third option: pay nominal fee for a Friday night ticket that can be converted into a Saturday ticket. If Darnell and Eleanor can choose to buy tickets for Friday night, knowing they have the option to convert their ticket date, they now will get a utility of 15, regardless of whether their friends have tickets for Friday or Saturday night, since they have the option to convert the date of their ticket.

The value of utility from buying tickets for Friday (with the option to convert to changing their ticket date) is

; therefore, the value of the real option is

.

Suppose, instead, that if they end up going alone Friday night, it won't actually bother them much. That is, they will get a utility of 10 (rather than 5) if their friends have tickets for Saturday night and they bought nonconvertible tickets for Friday. This the variability of their outcomes and, thus, the value of the real option to convert their ticket date.

Please show your work and provide detailed explanation to your answers.

Answer 1

Let us first calculate the expected utility on Friday & Saturday.

Given that the friends having ticket of Saturday has a probability of 50%,

Probability of a Friday ticket = 1 - 50% = 50%.

If friends have same day ticket, then their utility is 15 otherwise 5.

Probability of both the outcomes is 50%.

Hence, expected utility = (5 * 50%) + (15 * 50%) = 2.5 + 7.5 = 10

Therefore the expected utility is 10 on each day.

Now, as they have a third option of paying a nominal fee to get 15 utility,

The value of real option will be = new utility - expected utility = 15 - 10 = 5

Now, in the new case if they get a utility of 10 instead of 5 if their friends don't come,

Expected utility = (10 * 50%) + (15 * 50%) = 5 + 7.5 = 12.5

So, the value of real option will be = new utility - expected utility = 15 - 12.5 = 2.5