Question

What is the value today of a money machine that will pay $4,319.00 per year for 24.00 years? Assume the first payment is made 2.00 years from today and the interest rate is 8.00%.

Answer 1

$ 42,105.28

Step-1:Present value of cash flow 1 year from today
Present Value	=-pv(rate,nper,pmt,fv)
	= $ 45,473.71
Where,
rate	=	Discount rate	=	8%
nper	=	Time	=	24
pmt	=	annual cash flow	=	$ 4,319.00
fv	=	Future Cash flow	=	0
Step-2:Calculation of value today
Value today	=	Value of cash flow in 1 years	*	Discount factor
	=	$ 45,473.71	*	0.9259259
	=	$ 42,105.28
Working:
Discount factor	=	(1+i)^-n		Where,
	=	(1+0.08)^-1		i	=	8%
	=	0.92592593		n	=	1
Note:
First payment of 24 years cash flow begins 2 year from now.
Present Value of cash flow found in step-1 is the present value of cash flow when cash flow begins 1 year from now.
So, in Step-2, Present Value is discounted for 1 year.