1. Mr. Smith has received a large inheritance. He wants to invest enough of the inheritance today to live off of for the next twenty years. He is planning on the following expenditures for the next twenty years:

at the end of each of the first five years (t = 1,2,3,4,5), $50,000 per year

at the end of each of the next ten years (t = 6,7,8,9,10,11,12,13,14,15), $75,000 per year

at the end of each of the next three years (t = 16,17,18) $25,000 per year

at the end of each of years 19 and 20, $85,000 per year.

Also at the end of year 20, Mr. Smith wishes to make a one-time payment of $100,000 to his nephew for graduate school.

A. Based on these planned expenditures, how much must Mr. Smith invest today to be able to cover these costs. Assume that he can invest at a rate of 7% per year.

2. Ms. Landis is the president of Modern Manufacturing. Her company has developed a new 3D printer for use in the construction industry. She has received three offers to purchase this 3D printer technology, as follows:

• a payment of $500,000 now, followed by annual payments of $120,000 at the end of years 6 through 15.
• a payment of $900,000 today
• a series of semiannual payments of $80,000 spread over the next 10 years. The first payment will be received today and the remaining payments will come at the beginning of each semiannual period.

A. Using a required rate of return of 12% per year, calculate the present value of each of the three offers.