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------------------------------------------------ Draw cash-flow diagrams showing all cash flows. Show the formulation of each step in the solution.

A manufacturing firm has recently purchased a new CNC lathe for $25,000. The estimated life of the lathe is ten years. The operating and maintenance cost of the lathe is expected to be $3,000 in the lathe's third year of operation, increasing by $150 per year thereafter. The lathe is expected to be overhauled at a cost of $5,000 in year five. The estimated salvage value of the lathe is $2,500. The manufacturing firm uses a Minimum Attractive Rate of Return (MARR) of 8% per year.

Compute the amount of income per year that the lathe must generate to justify its purchase.

Cash flow diagram is as follows (values in $). Arrows pointing towards the timeline are cash outflows (costs), while arrows pointing away from the timeline are cash inflows (annual income and salvage value).

Let annual income be R.

Refer the attached image for the flow chart.

Present value of costs ($) = 3,000 x P/F(8%, 3) + 3,150 x P/F(8%, 4) + (3,300 + 5,000) x P/F(8%, 5) + 3,450 x P/F(8%, 6) + 3,600 x P/F(8%, 7) + 3,750 x P/F(8%, 8) + 3,900 x P/F(8%, 9) + 4,050 x P/F(8%, 10)

= 3,000 x 0.7938 + 3,150 x 0.7350 + (3,300 + 5,000) x 0.6806 + 3,450 x 0.6302 + 3,600 x 0.5835 + 3,750 x 0.5403 + 3,900 x 0.5002 + 4,050 x 0.4632

= 2,381.4 + 2,315.25 + 8,300 x 0.6806 + 2,174.19 + 2,100.6 + 2,026.13 + 1,950.78 + 1,875.96

= 14,824.31 + 5,648.98

= 20,473.29

For equivalence,

Present value of income = Present value of costs

[tex]R x P/A(8%, 10) + 2,500 x P/F(8%, 10) = 20,473.29R x 6.7101 + 2,500 x 0.4632 = 20,473.29R x 6.7101 + 1,158 = 20,473.29R x 6.7101 = 19,315.29R = $2,878.54[/tex]

NOTE: All the P/F and P/A values are from the respective factor tables.

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