Answer :
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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