I can buy a car today for $5000 and at the end of one year will be able to sell it for $4400. The car yields services which I would be willing to give up if offered a lump sum of $1100 today. I believe that inflation will be 10% during the year and I currently earn a 15% rate of return on my investments. I should buy the car? True or false?

I'm having difficulty deciding how to approach this question any guidance would be much appreciated

Buying the car creates for you a cost today, and a cash inflow in one year. The "today" cost is the net of two amounts: the purchase cost, and the dollar value of the benefit you expect from owning the car for one year. (The "benefit" has been expressed in terms of its lump-sum indifference amount, which is equivalent to giving you its 'present value'.)

Now you need to discount the cash inflow (one year hence) and compare its PV against this net "today" cost of the car. If the former exceeds the latter, then buying the car is a good deal.

For discounting the cash inflow you have two choices: (a) Discount that nominal cash flow by your nominal discount rate, or (b) First determine both the real (i.e. inflation-adjusted) cash flow and the real discount rate (using the given inflation expectation), and then discount the real CF by the real rate.

Tip: You'll get the same answer either way. Still, do it both ways just for grins---and to see the equivalency first-hand. Then you'll understand why in practice, present-val work is almost always done by discounting nominal flows at nominal rates, rather than going the extra steps to inflation-adjust everything in sight (flows, rates), only to get back to exactly the same answer. Besides, nominal rates are frequently known in advance, whereas inflation rates can only be predicted ex ante.