Question

6-45. (Calculating the present value of a growing perpetulty) A pension plan pays €30,000 at the end of Year 1 and then grows at the rate of 3 percent per year indefi- nitely. What is the present value if the rate of interest to discount the cash flow is 7 percent?

Answer 1

Solution :

Calculation of present value of a growing perpetuity:

The formula for calculating the present value of a growing perpetuity is

= CF₁ / ( r – g )

Where

CF₁ = First payment of the growing perpetuity ; g = Growth rate of the perpetuity ;

r = Interest rate or discount rate

As per the information given in the question we have

First payment of the growing perpetuity = CF₁ = € 30,000

Growth rate of the perpetuity = g = 3 % = 0.03

Interest rate or discount rate = r = 7 % = 0.07

Applying the above values in the formula we have

= € 30,000 / ( 0.07 – 0.03 )

= € 30,000 / 0.04

= € 750,000

Thus the present value of the growing perpetuity = € 750,000