Question

please Derive/state and explain perpetuity formular /equation in financial management course with complete notation and terminology. Also mention the key assumptions made when deriving the equation.
b. provide a numerical example to illustrate the equation

Answer 1

Perpetuity is the equal amount of payment with periodic interval for indefinite time.

Formula to calculate the present value of perpetuity is following -

Present value of a perpetuity = C/ r

Where,

Periodic payment = C

Interest rate per period = r

The key assumptions made when deriving the perpetuity equation are -

• Equal amount of payments will be made for indefinite time period at regular interval
• Interest rate will remain constant

b. provide a numerical example to illustrate the equation

Assume that an amount of $100 is paid per year for indefinite time period and annual interest rate is 10 per annum

Therefore

Annual payment = C = $100

Interest rate per year = r = 10%

Therefore,

Present value of perpetuity = $100 /10% = $100/0.1 = $1,000

Therefore, present value of this perpetuity is $1,000