To race or not to race? A very tough question to answer, I would say go Carter go, lets race. It might sound crazy to risk the Oil sponsorship, another engine failure and bad publicity on the national television, but if you work this as a business proposition by putting your business man hat on and put an expected value for both the options of racing and not racing, there isn’t much separating the both assuming the fact that a conservative estimate of sponsorship from Goodstone is worth as much as the Oil company Sponsorship ($500,000.00), so this bet is right on the money. More over the if they do end up finishing in the Top 5, Carters will endup the number one team in the circuit there by putting then in a position of picking up a bunch of more sponsorships in the coming year.
Expected Value Calculation
There are 3 possible out comes of the race – Race and can not complete the race due to Engine failure, Finish the race ending in Top Five and finally Finishing the Race and not ending in the top five. was a key question running thru the mind of John Carter, 1) Engine Failure – From the Historic data we know that we have about 29% chance of it happening and if it does happen Carter would loose the Oil Sponsorship Total Loss around 520000.00 2) Finishing the Race and ending in Top Five – 50% , Oil sponsorship retained plus a new sponsored 3) Finishing up the Race and not ending in Top Five – 21% Retain Oil Sponsorship $ 500,000.00 So the Total expected value for racing is roughly around 500,000.00 vs the expected Value of not racing 450,000. So as long as we are on the money we should go for it. Hence Carter should race.