Question

Cost of Solar PV System is $1 per watt, Size is 20 kW, Interest rate is 4%, Energy saved is 18000 kWh per year, Cost of electricity is $0.12/kWh

How long will it take to recover the investment, assuming no other cash flows?

How long will it take to recover the investment if you apply the 30% tax credit?

Answer 1

we will use pv table for finding present value annuity factor

Cost of pv system = $1 per watt

Size = 20 kw (1 kw = 1000 w)

so , cost = 20 kw *1000 w * $1/watt = $20,000

cost of electricity saved each year = 0.12 * 18000 = 2160

1 Assuming no other cash flows

Equation is :-

Cost of pv system = saving in cost each year * PVAF @ 4%

20000 = 2160 * PVAF

PVAF = 9.259

Observing the PVAF Table , we will notice in 4% coloumn that 9.259 (close to 9.385) pvaf come at 12 years.

(use link for pvaf table = http://www.cimaglobal.com/Documents/Student%20docs/2010%20syllabus%20docs/P1/P1-performance-operations-tables-2010-syllabus.pdf?utm_source=referrer&utm_medium=banner&utm_campaign=p1samples)

so , 12 years will take to recover.

2 If 30 % tax credit applied .

there are 2 cases :- case 1 tax credit applied only on energy cost saved

case 2 tax credit applied on energy cost saved and on cost in form of depreciation tax shield

( since depreciation figures are missing we will go for case 1 )

After tax credit net cost saved = 0.12*18000*(1- tax rate)

= 0.12*18000*0.7

= 1512

so equation is :-

cost = cost saved * PVAF

20000 = 1512*PVAF

PVAF = 13.22 (OR Almost equal to 13.13 given in pvaf table )

so from observing in pvaf table , answer is 19 years.

(Note:-

1 If we would have done with case 2 , then answer would be 12 years i.e same as 1 st question .)

2 refer link for pvaf table (http://www.cimaglobal.com/Documents/Student%20docs/2010%20syllabus%20docs/P1/P1-performance-operations-tables-2010-syllabus.pdf?utm_source=referrer&utm_medium=banner&utm_campaign=p1samples)