The answer for option 2 should be -$1,453,892 do not solve it by excel and sprea

Question

The answer for option 2 should be -$1,453,892

do not solve it by excel and spread sheet

Leonard, a company that manufactures explosion- proof motors, is considering two alternatives for ex- panding its international export capacity. Option 1 requires equipment purchases of $900,000 now and $560,000 two years from now, with annual M&O; costs of $79,000 in years 1 through 10. Option 2 involves subcontracting some of the production at costs of $280,000 per year beginning now through the end of year 10. Neither option will have a sig- nificant salvage value. Use a present worth analysis to determine which option is more attractive at the company's MARR of 20% per year. (Note: Check out the spreadsheet exercises for new options that Leonard has been offered recently.) 9

Explanation / Answer

Option 1:

-900000-79000/1.2-(79000+560000)/1.2^2.........-79000/1.2^10

=-900000-79000/1.2-(79000+560000)/1.2^2-79000/1.2^3*(1-1/1.2^8)/(1-1/1.2)

=-1620094

Option 2:

Total 11 cash flows, first cash flow now that is year 0 and then 10 cash flows in the year 1-10..

-280000-280000/1.2^1-280000/1.2^2..........-280000/1.2^10

=-(280000+280000/1.2^1+280000/1.2^2..........+280000/1.2^10)

As the above is a geometric progression whose number of terms is n=11, common ratio as 1/1.2 and first term as 280000. Sum of a Geomteric progression with first term as a, common ratio as r and number of terms as n is a*(1-r^n)/(1-r)

Hence, the above sum=-280000*(1-1/1.2^11)/(1-1/1.2)

=-1453892

So, option 2 is less costly and hence more attractive

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