A municipality is considering an investment in a small-scale energy system that will cost $6.5 million to install, and then generate a net annuity of $400,000/year for 25 years, with a salvage value at the end of $1 million. (a) Calculate the net worth of the project using simple payback.

Question

A municipality is considering an investment in a small-scale energy system that will cost $6.5 million to install, and then generate a net annuity of $400,000/year for 25 years, with a salvage value at the end of $1 million. (a) Calculate the net worth of the project using simple payback. (b) Suppose they set the MARR at 5%, what is the net present worth of the project by this approach?

Accepted Answer

(a) The net worth of the project by the simple payback method is the total value of the annuities, plus the salvage value, minus the initial cost of the project, or

25 × ($400,000) + $1,000,000 − $6,500,000 = $4,500,000

(b) Using discounting, the following factors are needed: (P/A, 5%, 25) = 14.09 and (P/F, 5%, 25) = 0.295.

The NPV is then

14.09 × ($400,000) + 0.295 × ($1,000,000) − $6,500,000 = −$567,119 EU

Thus the project is not viable at an MARR of 5%.

Discussion

The comparison of simple payback and present worth analysis using discounting illustrates the potential effect of even a relatively low MARR on financial viability over a long period such as 25 years. In this case, a project in which returns from annuity and salvage value exceed initial costs by 69% using simple payback, is not viable when discounting is taken into account. This effect can be large on renewable energy projects, where the initial capital cost is often high per unit of productive capacity, relative to the annual output, so that these projects are likely to have a long payback period.

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