Question

You are hoping to set up a fund for your family to pay out $75,000 per year indefinitely. If current interest rates are 8% how much will you need to deposit today? Suppose, you want to see the payout grow by 5% to cover any unforeseen costs, by how much does your deposit need to increase to develop the sustaining fund?

Answer 1

Answer;

Cash flow for perpetuity;

Present value of investment = cash flow / interest rate or yield,

Cash flow for perpetuity = $75,000 per year

Interest rate = 8%

Present value of investment = $75000/8%

= $937,500

Part 2 cash flow with growing perpetuity

Presents value of investment with growing perpetuity = cash flow + growth / (interest rate - growth)

Cash flow at t0 = 75000

Growth = 5%

Interest rate = 8%

Present value of investment = 75000 + 5%/(8%-5%)

= 78750/ 3%

= $2,625,000

So,increase fund by $2,625,000 - $937,500 =$1,687,500

Alternatively if investor want one time growth

Cash flow for perpetuity = $75000 + 5% = $78,750

Rate of interest = 8 %

Present value of investment = 78,750/8%

= 984,375

Increase fund by $984,375 - $937,500 = $46,875