Question

A town in Wyoming wants to drill a geothermal well to provide district heating steam and hot water for its businesses and residences. After government subsides, the capital investment for the well is $1,600,000. Assuming end-of-year annual dollars savings in steam and hot water equal to 4 % of the investment cost of the well, and assuming the residual value of the well after 72 years is zero, determine the internal rate of return (as a percent) for this situation. The MARR of the town is 3% per year (Enter your answer as a number without the % sign.)

Answer 1

Answer:

here we determine internal rate of return by trial and error method. we find the rate where the npv become zero

initial investment = $1600000

annual saving = $1600000*4% = $64000

first we assume i = 4%

pv = -1600000 + $64000 ( P/A 4% 72 years)

​​​​​​= -1600000 + $64000 ( 23.516)

= -1600000 + 1505024

= -94976

here npv negative so we try with lower rate i = 3%

npv = -1600000 + $64000 ( P/A 3% 72 years)

= -1600000 + 64000 (29.365)

= -1600000 + 1879360

= 279360

so rate of return between 3% and 4%. but we get exactly by interpolation formula

3 + 279360 / 279360+94976 *1

3 + 0.7463

3.7463

so the internal rate of return is 3.70