Question

Alternative A and Alternative B are being considered for recovering aluminum from garbage. Alternative A – has a capital cost of $100,000, a first year maintenance cost of $15,000, with maintenance increasing by $500 per year for each year after the first. Alternative B - has a capital cost of $120,000, a first year maintenance cost of $17,000, with maintenance increasing by $1,000 per year after the first. Revenues from the sale of aluminum are $20,000 in the first year, increasing $2,000 per year for each year after the first. Life of both alternatives is 10 years. There is no salvage value. The before-tax MARR is 10%. Using present worth analysis, determine which alternative is preferred.
a.) The present worth of alternative A
b.) The present worth of alternative B

Answer 1

a)

Let's first calculate the present worth of alternative A.

The net annual revenue of alternative A for the 10 years will be as follows,

Year 1 = $20,000 - $15,000

Year 1 = $5,000

And revenue each increases by $2,000 and the cost of alternative A increase by $500 each year. So each year the net revenue will increase by an amount of

= $2,000 - $5,00

= $1,500.

So net revenue in year 2,

= net revenue in year 1 + $1,500

= $5,000 + $1,500

Year 2 = $6,500

And for year 3,

Year 3 = net revenue in year 2 + $1,500

Year 3 = $8,000

And for year 4,

Year 4 = net revenue in year 3 + $1,500

Year 4 = $8,000 + $1,500

Year 4 = $9,500

And in year 5,

Year 5 = net revenue in year 4 + $1,500

Year 5 = $9,500 + $1,500

Year 5 = $11,000

And for year 6,

Year 6 = net revenue in year 5 + $1,500

Year 6 = $11,000 + $1,500

Year 6 = $12,500

And for year 7,

Year 7 = net revenue in year 6 + $1,500

Year 7 = $12,500 + $1,500

Year 7 = $14,000

And for year 8,

Year 8 = net revenue in year 7 + $1,500

Year 8 = $14,000 + $1,500

Year 8 = $15,500

For year 9,

Year 9 = net revenue in year 8 + $1,500

Year 9 = $15,500 + $1,500

Year 9 = $17,000

And for year 10,

Year 10 = net revenue in year 9 + $1,500

Year 10 = $17,000 + $1,500

Year 10 = $18,500.

Now in order to calculate the present worth of this we need to discount this cash flow with MARR of 10% or 0.1

= $5,000/(1+0.1) + $6,500/(1+0.1)^2 + $8,000/(1+0.1)^3 + $9,500/(1+0.1)^4 + $11,000/(1+0.1)^5 + $12,500/(1+0.1)^6 + $14,000/(1+0.1)^7 + $15,500/(1+0.1)^8 + $17,000/(1+0.1)^9 + $18,500/(1+0.1)^10

= $4545.45 + $5,371.90 + $6,010.51 + $6,488.62 + $6,830.13 + $7,055.91 + $7,184.21 + $7,230.86 + $7,209.65 + $7,132.55

= $65,059.79

So the present worth of alternative A is equal to $65,059.79.

We are only asked to calculate the present worth of alternative A so we don't need to subtract the capital cost of alternative A.

b)

Now let's calculate the present worth of alternative B.

Again let's calculate the net annual revenue for alternative B.

Notice that requires annual maintenance cost of $17,000 which increases increase year by $1,000 and generates a revenue of $20,000 which increases by $2,000 each year.

So the increase in the annual net revenue of alternative B is equal to,

= $2,000 - $1,000

= $1,000.

Net revenue in year 1,

= $20,000 - $17,000

= $3,000

Net revenue in year 2,

Year 2 = net revenue in year 1 + $1,000

Year 2 = $3,000 + $1,000

Year 2 = $4,000

Net revenue in year 3,

Year 3 = net revenue in year 2 + $1,000

Year = $4,000 + $1,000

Year = $5,000

Net revenue in year 4,

Year 4 = net revenue in year 3 + $1,000

Year 4 = $5,000 + $1,000

Year 4 = $6,000

Net revenue in year 5,

Year 5 = net revenue in year 4 + $1,000

Year 5 = $6,000 + $1,000

Year 5 = $7,000

Net revenue in year 6,

Year 6 = net revenue in year 5 + $1,000

Year 6 = $7,000 + $1,000

Year 6 = $8,000

Net revenue in year 7,

Year 7 = net revenue in year 6 + $1,000

Year 7 = $8,000 + $1,000

Year 7 = $9,000

Net revenue in year 8,

Year 8 = net revenue in year 7 + $1,000

Year 8 = $9,000 + $1,000

Year 8 = $10,000

Net revenue in year 9,

Year 9 = revenue in year 8 + $1,000

Year 9 = $10,000 + $1,000

Year 9 = $11,000

Net revenue in year 10,

Year 10 = net revenue in year 9 + $1,000

Year 10 = $11,000 + 1,000

Year 10 = $12,000.

Now let's calculate the present worth by discounting the net revenues by 10% MARR.

= $3,000/(1+0.1) + $4,000/(1+0.1)^2 + $5,000/(1+0.1)^3 + $6,000/(1+0.1)^4 + $7,000/(1+0.1)^5 + $8,000/(1+0.1)^6 + $9,000/(1+0.1)^7 + $10,000/(1+0.1)^8 + $11,000/(1+0.1)^9 + $12,000/(1+0.1)^10

= $2,727.27 + $3,305.78 + $3,756.57 + $4098.08 + $4,346.44 + $4,515.79 + $4,618.42 + $4,665.07 + $4,665.07 + $4,626.51

= $41,325.

So the present worth of alternative B is equal to $41,325.

Again we are only asked to calculate the present worth not the net present worth of the alternative so don't need to subtract the capital cost here.

I hope I was able to help you, thank you.