The Solar Energy Company is producing electricity from a solar source by using a

ID: 2709983 • Letter: T

Question

The Solar Energy Company is producing electricity from a solar source by using a large array of solar cells and selling the power to the local utility company. Because these cells degrade over time, thereby resulting in lower conversion efficiency and power output, the cells must be replaced every four years, which results in a particular cash flow pattern that repeats itself as follows: n = 0, -$600,000; n = 1, $400,000; n = 2, $300,000; n = 3, $200,000; and n = 4, $100,000. Determine the annual equivalent cash flows at i = 10%.

Explanation / Answer

Formula for Annual Equivalent Cash Flow:

C = r (NPV) / 1 - (1 + r)-n

where,

C denotes Equivalent Annuity Cash Flow, NPV denotes Net Present Value, r denotes Rate Per Period, n denotes Number of Periods.

Year 0

Year 1

Year 2

Year 3

Year 4

Investment $

(600,000)

Cash Flow $

400,000

300,000

200,000

100,000

Discounting factor @10%

0.909

0.826

0.751

0.683

PV of cash flows $

830,135

363,636

247,934

150,263

68,301

NPV $

230,135

NPV =230,135 , r=10%, n=4

C= 0.10*230135/[1-(1.1)-4] =23013.50/0.3169= $72,620

So Annual equivalent cash flow is $72,620