Respuesta :
Answer:
Following are the solution to this question:
Explanation:
Calculating the value of the first investment:
First amount = $ 104 000
Overhead annual expense = $ 64 000
So after 4 years the cumulative costs are estimated at a rate of 25 percent for the first 4 years, for the first year of AOC for three years, for the second year of AOC for two years etc., depending on the cost initially incurred. The net cost would then be:
[tex]C=104000(1+0.25)^4+64000(1+0.25)^3+64000(1+0.25)^2+64000(1+0.25)^1+64000\\\\[/tex]
[tex]=104000(1.25)^4+64000(1.25)^3+64000(1.25)^2+64000(1.25)^1+64000\\\\=104000(2.44140625)+64000(1.953125)+64000(1.5625)+64000(1.25)+64000\\\\=253,906.25+125,000+100,000+80,000+64000\\\\= 622,906.25[/tex]
Calculating the value of the second investment:
The AOC second investment will be x, then:
[tex]622,906.25=165000(1+0.25)^4+x(1+0.25)^3+x(1+0.25)^2+x(1+0.25)+x \\\\622,906.25=402832.0313+x(1.25)^3+x(1.25)^2+x(1.25)+x\\\\220074.219=x[(1.25)^3+(1.25)^2+(1.25)+1]\\\\220074.219=x[5.765625]\\\\x= \frac{220074.219}{5.765625} \\\\ x= 38170.0542[/tex]
