Given that the purchase price of a machine is $1,000 and its market value at EOY four is $300, complete the table below [values (a) through (f)], using an opportunity cost of 5% per year. Compute the equivalent uniform CR amount, using information from the completed table.

Question

Year	Investment at Beginning of Year	Opportunity Cost of Interest (i = 5 %)	Loss in Value During Year	Capital Recovery Amount
1	$1,000	$50	(a)	$250
2	(b)	(c)	200	240
3	600	30	200	230
4	(d)	20	(e)	(f)

Accepted Answer

Year	Investment at Beginning of Year	Opportunity Cost of Interest (i = 5 %)	Loss in Value During Year	Capital Recovery Amount
1	$1,000	$50	$250-$50=$[latex]\underline{200}[/latex]	$250
2	1,000-200=[latex]\underline{800}[/latex]	800(0.05)=[latex]\underline{40}[/latex]	200	240
3	600	30	200	230
4	600-200=[latex]\underline{400}[/latex]	20	400-300=[latex]\underline{100}[/latex]	20+100=[latex]\underline{120}[/latex]

(a) Loss in Value = Capital Recovery Amount - Opportunity Cost

(b) Investment at [latex]BOY_{2} [/latex] = Investment at [latex]BOY_{1-} [/latex] Loss in Value during Year 1

(c) Opportunity Cost = Investment at BOY[latex]^{*}[/latex](0.05)

(d) Investment at [latex]BOY_{4}[/latex] = Investment at [latex]BOY_{3}[/latex] - Loss in Value during Year 3

(e) Loss in Value during Year 4 = Investment at [latex]BOY_{4} [/latex] - Salvage Value at [latex]EOY_{4} [/latex]

(f) Capital Recovery Amount = Opportunity Cost + Loss in Value during Year
PW(CR amount) = $250 (P/F, 5%, 1) + $240 (P/F, 5%, 2) + $230(P/F, 5%, 3) + $120 (P/F, 5%, 4)
= $753.18

AW(CR amount) = $753.18 (A/P, 5%, 4) = $212.40
Check: CR(5%) = $1,000 (A/P, 5%, 4) − $300 (A/F, 5%, 4) = $212.40

Question 5.R: Given that the purchase price of a machine is $1,000 and its...

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