Question

A promise to pay 12,000 per year, paid monthly (m = 12).  If the payments begin in 5 years (first payment end of month one in year 6).  Payments will increase with the rate of inflation estimated at 2.40% and will continue forever. Using monthly compounding for the entire problem, if you require 7.20% (APR) to make this investment, what is the fair value today?

Answer 1

APR = 7.2% per annum

Monthly required return = 7.2%/12 = .60%

Yearly Inflation = 2.4%

Monthly Growth = 2.4%/12 = .20%

Value at Year End 5 = Cash Flow at month end / (Monthly required return - Monthly Growth)

Value at Year End 5 = 1000 / (.40%)

Value at Year End 5 = 250,000

Present Value today = Value at year End 5 / (1+required return%)^n

= 250,000 / (1.072)^5

=176,590