Question

You have just won the lottery and will receive a lump sum payment of $22.53 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that will earn 4.81 percent. If you make equal annual withdrawals for the next 25 years, how much can you withdraw each year starting exactly one year from now?

Fancy Cat Products has a project that will cost $250,100 today and will generate monthly cash flows of $5,445 for the next 62 months. What is the rate of return of this project when expressed as an APR?

Answer 1

Formula for PV of annuity can be used to compute periodic cash withdrawal as:

PV = P x [1 – (1+r)-n]/r

P = PV/ [1 – (1+r)-n]/r

PV = Present value of fund = $ 22,300,000

P = Periodic cash withdrawal

r = Rate per period = 0.0481 p.a.

n = Number of periods = 25

P = $ 22,530,000/ [1 – (1+0.0481)-25]/0.0481

   = $ 22,530,000/ [1 – (1.0481)-25]/0.0481

   = $ 22,530,000/ [(1 – 0.308981142995874)/0.0481]

   = $ 22,5300,000/ (0.691018857004126/0.0481)

   = $ 22,530,000/ 14.3662964034122

   = $ 1,568,253.87471811 or $ 1,568,253.87

Annually $ 1,568,253.87 can be withdrawn from the fund for 25 years.

Excel formula for monthly rate of return:

Monthly rate of return = RATE(nper,pmt,pv)

nper = Number pf periods = 62

pmt = Monthly payment = $ 5,445

pv = Present value = - $ 250,100

Monthly rate of return = RATE(62,5445,-250100)

                                    = 1.01 %

APR = Monthly rate of return x 12 = 1.01 x 12 = 12.10 %

Rate of return of the project is 12.10 %