Question

What is the present value of an investment that pays $200 every other year forever if the first cash flow occurs in two years? What is the value when the first cash flow occurs in one year? The opportunity cost of capital is 12% per year.

Answer 1

The formula to calculate the present value of perpetuity is as under,

Present value of Perpetuity = P/r

P = annuity = 200

r = opportunity cost of capital = 12%

Present value of Perpetuity = 200/12%

Present value of Perpetuity = 1666.67

Answer 1

Value of perpetuity at the end of 1st Year if cash flows occurs in two years = $1666.67

Present value if the first cash flow occurs in two year = Value of perpetuity at the end of 1st Year x discount factor of year 1 @ 12%

Present value if the first cash flow occurs in two year = $1666.67 x (1+0.12)^-1

Present value if the first cash flow occurs in two year = $1,488.10

Answer 2

Present value of perpetuity if cash flows occurs in one year = $1,666.67