Question

A. Suppose the opportunity cost of capital is 5% and you have just won a $750,000 lottery that entitles you to $75,000 at the end of each year for the next 10 years.

1. What is the minimum lump sum cash payment you would be willing to take now in lieu of the IO-year annuity?

2. What is the minimum lump sum you would be willing to accept at the end of the 10 years in lieu of the annuity?

Answer 1

Answer 1)

Calculation of minimum lump sum cash payment that should be received now in lieu of 10 years annuity

The minimum amount that should be received now in lieu of 10 year annuity will be equal to the present value of annuity, i.e., $ 579,130.

Answer 2)

Calculation of minimum lump sum cash payment that should be received at the end of 10 years in lieu of 10 years annuity

The minimum amount that should be received 10 years in lieu of 10 year annuity can be calculated as follows:

Lump sum amount to be received at the end of 10 years = $ 579,130/ Present value factor at 5% for 10 years

                                                                                                        = $ 579,130/ 0.61391

                                                                                                         = $ 943,347

Therefore the lump sum amount to be received at the end of 10 years from now in lieu of 10 year annuity is $ 943,347.

Working Note:

Calculation of Present value of annuity of $ 75,000 at 5% for 10 years

Present value of annuity = $ 75,000 X Present value of annuity factor at 5% for 10 years

                                              = $ 75,000 X 7.72173

                                              = $ 579,130