Question

1. An alternate solar power system has a guaranteed service life of 25 years, an initial cost of $8000 and the same estimated saving of $600 per year for the home electrical power bill. Find the approximate IRR (i*) to nearest whole percent.
2. Same solar power system as in question 1. The homeowner decides to sell the house when the system has an expected remaining service life of 15 years. The initial investment of $8000 is considered a sunk cost that can not be recovered. How much equivalent value would this solar system add to the normal (without the system) appraised value of the house at this time with a 5% MARR

Answer 1

a) initial cost = 8000

annual savings = 600

t = 25 years

Let i be rate of return, then at rate of return PW=0

PW at i% = -8000 + 600*(P/A, i%,25)

Equating this to zero,

(P/A,i%,25) = 8000/600 = 13.3333

Using trail and error method

At i = 5%, (P/A,i%,25) = 14.093944

At i = 6%, (P/A,i%,25) = 12.783356

Using interpolation

i = 0.05 + [(14.093944-13.333333)/(14.093944-12.783356)] * (0.06-0.05)

i = 0.05 + 0.0058035

i = 0.0558 = 5.58% (Approx)

b) MARR = 5%

Present value of annual saving of 600 for 15 years = 600* (P/A,5%,15)

= 600 * 10.37965

= 6227.79

Value added to house = 6228 (rounding off)