Question

Suppose there is a growing perpetuity in which you receive $10 at year 4, and the amount you receive grows at 3% from date 4 onward (to infinity). Assume currently the interest rate is 5%. The present value of this growing perpetuity (that is the value at date 0) is $____.

0 year	1 year	2 year	3 year	4 year	5 year	6 year
				$10	$10*(1+3%)	$10*(1+3%)^2

Answer 1

The present value of a growing perpetuity when the cash flow starts from year 1 is given by the formula:

PV_t-1 = C_t/(r - g)

r = interest rate = 5%

g = growth rate = 3%

Since, in this case, the cash flow starts from year 4, so using the above formula we will get the value at t = 3

Value of the perpetuity at t =3 is:

Value at t:3 = V_t=3 = C₄/(r - g) = 10/(5% - 3%) = 10/2% = 500

Now, we will have to discount the value at t =3 to get the present value of the perpetuity at t = 0

Present value of the perpetuity [t = 0] = V_t=3/(1+r)³ = 500/(1.05)³ = 431.918799265738

The present value of this growing perpetuity (that is the value at date 0) is $431.92

Answer -> $431.92 (Rounded to two decimal places)