Question

projected life of 12 years is offered for sale. If annual net cash flows are expected to be roughly $ 500,000 determine the appropriate purchase price for the property when interest is 12%: (a) compounded annually, and (b) compounded continuously.

Answer 1

Property price (rate annually compounded)	#
Annuity of payments = PMT =	$500,000.00
Rate =	12.0000%
Number of payments = N =	12
Present Value or Price = (PMT x ((1-((1+R)^-N)) / R)
Price or PV = (500000*((1-((1+12%)^-12))/12%)
Price or PV =	$3,097,187.1

Property price (rate continuously compounded)	#
Annuity of payments = PMT =	$500,000.00
Rate = e^(12%) - 1 = 2.7182818^(12%)-1 =	12.749685%
Number of payments = N =	12
Present Value or Price = (PMT x ((1-((1+R)^-N)) / R)
Price or PV = (500000*((1-((1+12.749685%)^-12))/12.749685%)
Price or PV =	$2,992,514.1

# Continuously compounded rate is calculated using exponential value of “e” which is approximately = 2.7182818. T