Question

CPP is interested in comparing if they should maintain the current lighting fixtures in Building 9 that has a life-cycle cost (NPV) of $50,000 or invest in new, indirect lighting fixtures in Building 9. The cost for the new fixture is $12,000 with savings of $1,000/year. A rebate will be granted after two years of operation for $1,500. Study period is 15 years. The university uses an annual rate of return of 4%. Calculate the life-cycle cost (i.e. NPV) for the new fixtures and advise if CPP should change the current fixture to the new ones.

Answer 1

NPV of current lighting fixtures = $50,000

Rate of Return = 4%

Study period = 15 years

Cost of new fixture = $12,000

Saving per year = $1,000

Rebate after 2 years = $1,500

Present value of saving in year 1 = [1,000 / (1 + 0.04)^¹]

Present value of saving in year 1 = [1,000 / (1 + 0.04)^²]

Present value of saving in year 1 = [1,000 / (1 + 0.04)^³]

and so on....

This forms a G.P. whose sum is = [1,000 / (1 + 0.04)^¹] + [1,000 / (1 + 0.04)^²] + [1,000 / (1 + 0.04)^³] + ........... + [1,000 / (1 + 0.04)^¹⁵]

Sum of G.P. = [a * (1 - r^ⁿ) / (1 - r)]

a = [1,000 / (1 + 0.04)^¹]

r (ratio of two consecutive terms) = (1 / 1.04) = 0.961

n = 15

Sum of series = [1,000 / (1 + 0.04)^¹] * (1 - 0.961^¹⁵) / (1 - 0.961) = 11,118.39

Present value of subsidy which is given after 2 years = [1,500 / (1 + 0.04)^²] = 1,386.83

Net present value of new fixture = -12,000 + 11,118.39 + 1,386.83 = 505.22

As net present value of keeping the current lighting fixture is more than building new fixture, they should keep current fixture.