5.2 Intertemporal Budget Constraint with Nominal Cash Flows (7 marks)

Using the same information as stated in 5.1 and adding the assumption that inflation is expected to be 3% per year over the next 20 years, translate all of the values (i.e., the bequest, the initial wealth, and the consumption, into nominal dollars (i.e., actual dollars rather than purchasing power).

The trickiest part is the fact that the consumption amount will no longer be constant, because inflation will require that you spend 3% more each year to maintain the same consumption. So, if you spent $1 last year to buy a chocolate bar, the same chocolate bar will cost you $1.03 at the end of year 1, $1.0609 at the end of year 2 (i.e., 1.0609 = 1.03 x 1.03 = 1.03^2), and so on.

a. The present value of your bequest will be the same as in part 5.1a, because the present value of the nominal amount must be the same as the real amount at time 0. But in 20 years, the real amount of $100,000 will not be the same as the nominal amount. Calculate the nominal amount you will need to have 20 years from now to satisfy the bequest for your kids. (2 marks)

Hint: One way to visualize how to do this is to realize that $100,000 of purchasing power is no different than the price of 100,000 $1 chocolate bars today. All you need to do is determine how much youd have to pay to buy the same chocolate bars 20 years in the future.

b. Calculate the actual amount of consumption, in nominal dollars, for each of the 20 years, using the stated assumptions. This requires you to calculate 20 numbers, so you might want to use an Excel spreadsheet, such as the one provided with this assignment (5.2 template). (4 marks)