WIND ENERGY SYSTEMS - Cd3wd

Chapter 8—Economics 8–13
A n
1+e a
A n
(1+e a) 2
✻
✻
A n
(1+e a) 3
✻
An
1+e a) 4
✻
✲
❄
P v
Figure 4: Present value of uniform series of payments when apparent escalation is equal to
inflation rate.
back with one hundred deflating dollars each year for 20 years is actually gaining the difference of the
present values. He borrows $746.94 and pays back the equivalent of $444.52, so he gains $302.42.
Nowwewanttodeterminethepresentvalueofanuniformly escalating series of payments.
These might be for a fixed amount of fuel or energy each year, with the cost increasing at the
apparent escalation rate e a . Each years payment is higher than the previous years payment
by the factor 1 + e a . The series is shown in Fig. 5. The present value of this series is given by:
P v =
n∑
j=1
( )
A n (1 + e a ) j
1+ea n
(1 + i) j = A n (1 + e a )
1+i − 1
e a − i
(16)
A n (1 + e a )
✻
❄
P v
A n (1 + e a ) 2 A n (1 + e a ) 3 A n (1 + e a ) 4
✻
✻
✻
✲
Figure 5: Present value of a series of annual payments increasing at the apparent escalation
rate e a .
Example
You are considering adding some insulation in your home which should save you 1200 kWh of
electricity per year. If electricity costs $0.05 per kWh with an apparent escalation rate of 8 percent,
what is the present value of 20 years of payments for this electricity? Assume interest rates are 12
percent.
The Year 0 cost, A n , of 1200 kWh is 1200(0.05) = $60. When we substitute this in Eq. 16 we get:
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001