Question

Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios​ (you get to​ choose):

1.$8,750 per year at the end of each of the next five years

2.$47,450 ​(lump sum) now

3.$98,650 ​(lump sum) five years from now

Requirements

1.Calculate the present value of each scenario using a 6% discount rate. Which scenario yields the highest present value?

2.would your preference change if you used a 10% discount rate?

Answer 1

Requirement 1

Year Option 1 Receipt Discounting factor Present value 1 $8,750.00 0.943396226 $ 8,254.72 2 $8,750.00 0.88999644 $ 7,787.47 3 $8,750.00 0.839619283 $ 7,346.67 4 $8,750.00 0.792093663 $ 6,930.82 5 $8,750.00 0.747258173 $ 6,538.51 Total $ 36,858.18

Option 2 present value = $47,450

Option 3 present value = $98,650 x 0.7472 = $73,717

Option 3 has highest present value

Requirement 1

Option 1 Year Receipt Discounting factor Present value 1 $8,750.00 0.909090909 $ 7,954.55 2 $8,750.00 0.826446281 $ 7,231.40 3 $8,750.00 0.751314801 $ 6,574.00 4 $8,750.00 0.683013455 $ 5,976.37 5 $8,750.00 0.620921323 $ 5,433.06 Total $ 33,169.38

Option 2 present value = $47,450

Option 3 present value = $98,650 x 0.6209 = $61,254

Option 3 has highest present value