What is the present value of a $1,000 perpetuity growing at 2% annually with a 10% discount rate?

To calculate the present value of a perpetuity that grows at a constant rate, you can use the Gordon Growth Model, which is expressed as:

[ PV = \frac{C}{r - g} ]

where:

• PV is the present value,

• C is the cash flow of the perpetuity,

• r is the discount rate, and

• g is the growth rate.

In this scenario:

• The cash flow ( C ) is $1,000.

• The growth rate ( g ) is 2% (or 0.02 as a decimal).

• The discount rate ( r ) is 10% (or 0.10 as a decimal).

Plugging these values into the formula gives:

[ PV = \frac{1000}{0.10 - 0.02} ]

This simplifies to:

[ PV = \frac{1000}{0.08} ]

[ PV = 12500 ]

Thus, the present value of this growing perpetuity is $12,500. This method accurately accounts for the fact that future cash flows will increase over time due to the growth factor, making the investment more valuable today as compared to a non-growing perpetuity.