Question

insert R510D USB Use the following information to answer questions 4.5 and 6. MARR-20% Initial Cost Benefits O&M Costs Alternative #1 $270,000 S100,000 in year I; $125,000 in year 2 remainingyearsincrease by 10%morethanthe previousyear S20,000 in year increasing by $1,000 per year Salvage $55,000 Life (in years) The Net Present Worth of Alternative #1, over the given lifespan. is closest to a) $332,673 b)S171963 c) $163,320 d) $219,958 e) $231,87 fS157,112 333) , 10% 20,6 2017 2 74 386 32,0179
The right answer is B I don’t know what I’m doing wrong

Answer 1

The net present worth can be determined using the following mathematical expression

Net present worth = - 270,000 + 100000(P/F,20%,1) + 125000(P/G, 10%,20%,6)(p/F,20%,2) - 20000(P/A,20%,7) -1000(P/G,20%,6) + 55000(P/F,20%,7)

= - 270000 + 100000*0.8333 +

$\large NPW = - 270,000 +100,000*0.8333+\frac{125,000}{1.2*0.1}*[1-(\frac{1.1}{1.2})^6] -20,000*7.2091 -1000*8.255 + 55,000*0.2791$

NPW = - 270,000+83,333 + 423654 - 72091 - 8255 + 15350

NPW = $ 17,991

Answer is B. $ 171,963.

Since I have rounded off the values so exact answer I am not getting.

Here when we have growth rate that is g% then the value can be calculated as follows

$\large PVIGA(10\% ,20\% ,7)= \frac{125,000}{1.2*(0.2-0.1)}*[1-(\frac{1+0.1}{1+0.2})^6]$

Since growth started from second year.

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