Discrete Compounding: 10% Single Payment Uniform Series Compound Amount Factor T

Question

Discrete Compounding: 10% Single Payment Uniform Series Compound Amount Factor To FindF Given P FIP 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 Sinking Fund Factor To Find A GivenF AIF 1.0000 0.4762 0.3021 0.2155 0.1638 0.1296 0.1054 0.0874 0.0736 0.0627 Capital Recovery Factor To Find A Given P AIP 1.1000 0.5762 0.4021 0.3155 0.2638 0.2296 0.2054 0.1874 0.1736 0.1627 Compound Amount Factor To Find F Present Worth Factor To Find P GivenF PIF 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 Present Worth Factor To Find P Given Given FIA 1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 PIA 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 2 3 4 6 7 8 9 10

Explanation / Answer

Answer: a.

   Reduction in surveillance expense*(present worth factor for uniform series for 7yrs @ 10%)

+

(salvage*present worth factor single payment at 7th year @10%)

=

Installed cost of fuel cell

i.e. ($ 350 * 4.8684 ) + (salvage * 0.5132) = $ 2,300

$ 1,703.94 + (salvage * 0.5132) = $ 2,300

  (salvage * 0.5132) = $ 2,300 - $ 1,703.94

salvage = $ 596.06 / 0.5132 = $ 1161.46

Answer : b.

Reduction in surveillance expense*(present worth factor for uniform series for 7yrs @ IRR%) - installed cost = 0

  

Using hit and trial method to find IRR of fuel cell

At rate = 10%

($ 350 * 4.8684) - $ 2,300 = - $ 596.06

At rate 2%

($ 350 * 6.4720) - $ 2,300 = - $ 34.8

Using interpolation & extrapolation

(10% - IRR) / (10% - 2%) = (-$596.06 - 0 ) / {-$596.06 -  (- $ 34.8)}

(10% - IRR) / 8% = -$596.06/-$561.26

(10% - IRR) = 8.5%

IRR = 1.5%

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