a. Calculate the landfill project’s internal rate of return to the nearest whole

Question

a. Calculate the landfill project’s internal rate of return to the nearest whole percent.

Jefferson County's Board of Representatives Is considering the purchase of a site for a new sanitary landfill. The purchase price for the site is $190,000 and preparatory work will cost $69,900. The landfill would be usable for 10 years. The board hired a consultant, who estlmated that the new landfill would cost the county $46,000 per year less to operate than the county's current landfill. The current landfill also will ast 10 more years. For a landfill project, Jefferson County can borrow money from the federal government at a subsldized rate. The county's hurdle rate is only 8 percent for this project. Use Appendix A for your reference. (Use appropriate factorfs) from the tables provided.)

Explanation / Answer

Savings in operating costs per year = $46000

Initial investment = $190000 + $69900 = $259900

NPV at 10%:

NPV = $46000 x PVIFA (10%, 10) -$259900 = $46000 x 6.14456 - $259900 = $22750

NPV at 20%:

NPV = $46000 x PVIFA (20%, 10) -$259900 = $46000 x 4.19247 - $259900 = -$67046

IRR is the discount rate at which NPV is zero

Rate

NPV

10%

22750

R

0

20%

-67046

By interpolation we get

R = 10% + 10% * ((0-22750)/(-67046-22750) = 13%

As hurdle rate is 8%, and IRR is 12.53%, the project should be accepted.

Rate

NPV

10%

22750

R

0

20%

-67046

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