Question

In: Finance

Assume you have $1 million now, and you have just retired from your job. This would...

Assume you have $1 million now, and you have just retired from your job. This would be your initial wealth, W₀.
You expect to live for 20 years, and you want to have the same level of consumption for each of the 20 years, after adjusting for inflation. That is, you want to keep the same purchasing power of consumption for all 20 years. In the equation, this means that C_t will be constant in real dollars over the rest of your lifetime.
You also wish to leave the purchasing power equivalent of $100,000 today to your kids at the end of the 20 years as a bequest (or to pay them to take care of you). In real dollars, of course, since there is no inflation in real dollars, you will need to have $100,000 to give them at the end of the 20 years.
You expect real interest rates to stay at 5% per year. So, your savings account will earn 5% in real dollars over the next 20 years.
The Omar example in the textbook shows Omar’s human capital through labour earnings, but our assignment problem does not have any labour earnings. You have already earned your retirement savings of $1 million.
The assignment problems will ask you to apply the formula to calculate the level of consumption that fits the intertemporal budget constraint, given assumptions about initial wealth and a planned bequest.

5.1

a. Calculate the present value of your bequest of $100,000 in real dollars. (1 mark)

b. Determine the constant value of consumption that equates the value of your initial wealth on the right side of the equation with the total of consumption and your bequest.

Hint: To do this, you need to recognize that the equation contains an annuity for future consumption. The bequest is a single lump sum value, and the initial wealth is already stated at present value. The present value of labour income is zero.

Use this information to determine

i. the present value of consumption for all 20 years.

ii. use that value to determine the annual consumption for each of the 20 years. This part is very similar to the last question on Assignment 1.

Expert Solution

Answer 5.a. For the PV of $100,000 we will use the formula where FV= future value= $100,000, r= interest rate = 5%, and n= number of years= 20

Substituting the values in the equation, we get

PV= $37,688.95

Answer 5.b.The constant annual consumption is the annuity. Thus to calculate the annuity we will have to use the EXCEL function of PMT. To use this just type =PMT and click on the PMT function from the drop down menu.

Now input rate=0.05, nper=20, PV=-1000000 and FV=100000

The PMT= $77,218.33

Thus the constant annual consumption of $77,218.33 can be made for 20 years and have a remainder of $100,000 at the end of the 20 years for kids. I am also attatching a before and after pic of the excel spreadsheet for calculating this

jeff jeffy answered 5 months ago

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