Question

Using Excel. What is the present value of the following series of cash payments: $8,000 per year for four consecutive years starting one year from today, followed by annual cash payments that increase by 2% per year in perpetuity (i.e. cash payment in year 5 is $8,000*1.02, cash payment in year 6 is $8,000*1.022, etc.)? Assume the appropriate discount rate is 5%/year.

Answer 1

Growing Perptuity is a series of payments that occurs periodically which continues to grow indefinitely at a specified rate.

Hence PV is a geometric series, PV = [D/(1+r)] + [D(1+g)/(1+r)^2] + ....

On simplifying the formula for PV, we get

PV = D / (1+r) - (1+g)

where, D is the dividend per year

r = discount rate

g = growth rate

PV = 8000 / (1+0.05) - (1+0.02)

= 8000/0.03

=266,666.666