Question

Which cash flow has the greatest present value if your discount rate is 9.5%?

A) A lump sum payment of $10,000 today

B) A lump sum payment of $25,000 at the end of 10 years

C) A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter

D) A perpetual stream of annual parents of $1,000 starting in one year

Answer 1

1)

Present value of 1st option = $10,000

3)

Present value of 2nd option = Future value / (1 + r)ⁿ

Present value of 2nd option = 25,000 / (1 + 0.095)¹⁰

Present value of 2nd option = 25,000 / 2.478228

Present value of 2nd option = $10,087.85

3)

Present value of 3rd option = Cash flow 1 / Required rate - growth rate

Present value of 3rd option = 500 / 0.095 - 0.05

Present value of 3rd option = 500 / 0.045

Present value of 3rd option = $11,111.11

4)

'A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter' will have the highest present value.

Present value = Cash flow / required rate

Present value = 1,000 / 0.095

Present value = $10,526.32

5)

C) A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter will have the highest present value