Question

It is the beginning of September, and you have been offered the following deal to go heli-skiing. If you pick the first week in January and pay for your vacation now, you can get a week of heli-skiing for $1,700. However, if you cannot ski because the helicopters cannot fly due to bad weather, there is no snow, or you get sick, you do not get a refund. There is a 50% probability that you will not be able to ski. If you wait until the last minute and go only if you know that the conditions are perfect and you are well, the vacation will cost you $5,300. You estimate that the pleasure you get from heli-skiing is worth $7,200 per week to you (if you had to pay more than that, you would choose not to go). If your cost of capital is 13% per year, should you book ahead or wait?  

Answer 1

Cost of Capital is 13%p.a which will be our discounting rate. so the discounting rate per month will be 1.0833333% (13/12)   or .010833333

Lets construct the Cash flows for the booking.. The booking amount paid will be a cash Outflow. The value of Pleasure given in $ terms per week would be considered as the inflow. Accordingly,

The initial Booking amount paid of 1,700 is not refundable- and hence it is a definite Outflow- not requiring any probability adjustment.

The probability of whether going or not for the SKi is 50% and hence the Inflow( Pleasure of ski)- is adjusted for 50% and we take the adjusted cash flow of 3,600 ( 7,200 X 50%)

Discounting rate at the rate of 1,083333% for 4 months (sept to Dec) is applied to arrive at the DF .

since we will be booking only when conditions are fine and a final decision has been made about the trip- both the cash outflows (booking amount) and inflows(pleasure of ski) are definitive- not requiring any probability adjustment.( in other words 100% probable)

Discounting rate at the rate of 1,083333% for 4 months is applied to arrive at the DF .

As seen from the above the NPV of booking at the last minute is Higher ($1,819.85) when compared against the NPV of booking now ($1,748.14) by   $ 71.71 (1,819.85-1,748.14)

Hence it is recommended TO WAIT.