Question

Aliya works for an irrigation district that is considering two options for building new infrastructure to expand irrigation. The infrastructure won’t be built for 3 years (so, capital costs will be incurred in 2023). Option A is estimated to cost $5 million in 2020 dollars. It is anticipated that Option A infrastructure could be used for 5 years, then sold for $1 million (in 2028 dollars; this estimate does not need to be adjusted). Estimated additional revenues are $4.2 million per year, and estimated additional operating costs are $1 million per year (both in 2020 dollars). Option B is estimated to cost $8 million in 2020 dollars. Aliya anticipates that Option B could be used for 5 years, then sold for $0.5 million (also in 2028 dollars). Estimated additional revenues are $5.5 million per year, and estimated additional operating costs are $1.8 million per year (both in 2020 dollars). For both options: Capital cost annual inflation is estimated to be 3%. Future revenues and future operating costs are expected to rise at 2% per year. The combined federal and provincial incremental tax rate is 45%. Use a CCA depreciation rate of 45% and a discount rate of 10% (reflecting the MARR of the firm).

a) What is the gain or loss on disposal of Option A?

b) What is the gain or loss on disposal of Option B?

c) Determine the net present worth of the after-tax cash flow for each option, assuming 2023 is year 0.

d) Which option should Ying recommend, or should she recommend not to purchase either?

This is all the information I have, let me still know any specific information you need.

Answer 1

Given,

Evaluating option A

Step 1 : Initial Cashflows at year 2020

Investment in project = $5,000,000 as per 2020 dollars

capital cost annual inflation rate = 3%

Discounting rate = 10%

Investment amount as per 2023 dollars = Amount to invested in 2020 Inflation rate

$5,000,000 1.03 1.03 1.03 = $5,463,635

Present value of cashflows to be incurred in 2023 = $5,463,635 PvF(10%,3) = $5,000,000 0.751

= $4,103,190

Step 2 : Recurring cashflows and present value of cashflows

Yearly revenue = $4,200,000

Yearly operating cost = $ 1,000,000

CCA depriciation rate = 45%

Tax rate = 45%

Inflation rate in respect of revenue and expenditure = 2%

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Revenue	$4,200,000	$4,200,000	$4,200,000	$4,200,000	$4,200,000
Inflated Revenue	$4,546,215	$4,637,139	$4,729,882	$4,824,480	$4,920,969
Opearting costs	$1,000,000	$1,000,000	$1,000,000	$1,000,000	$1,000,000
Inflated operating costs	$1,082,432	$1,104,081	$1,126,163	$1,148,686	$1,171,660
Net opeating profit	$3,463,783	$3,533,058	$3,603,719	$3,675,794	$3,749,309
Depreciation	$2,250,000	$1,237,500	$680,625	$374,344	$205,889
Profit before tax	$1,213,783	$2,295,558	$2,923,094	$3,301,450	$3,543,420
Tax @45%	$543,202	$1,033,001	$1,315,392	$1,485,652	$1,594,539
Profit after tax	$670,581	$1,262,557	$1,607,702	$1,815,798	$1,948,881
Cashflow after tax[PAT + Depreciation	$2,920,581	$2,500,057	$2,288,327	$2,189,142	$2,154,770
PvF(10%,ny)	0.683	0.621	0.564	0.513	0.466
Present value of cashflows	$1,994,757	$1,552,535	$1,290,616	$1,123,030	$1,004,123

Step 3 : cashflows on disposal of infrastructure

Cashflows on sale = $1,000,000 as per 2028 dollars, so no need to inflate.

Book value = $5,000,000 - [$2,250,000+$1,237,500+$680,625+$374,344+$205,889] = $251642

Profit on sale = $1,000,000 - $251642 =$748358

Tax on sale = 336,761

Cashflow at end of project = $663,239

Present value of cashflow = $663239 0.466 = $309,069

NPV of the project = Present value of cashinflows - Present value of cashoutflows

= [$1,994,757+$1,552,535+$1,290,616+$1,123,030+$1,004,123+$309,069] - $4,103,190

= $2,170,940

Evaluating option B

Step 1 : Initial Cashflows at year 2020

Investment in project = $8,000,000 as per 2020 dollars

capital cost annual inflation rate = 3%

Discounting rate = 10%

Investment amount as per 2023 dollars = Amount to invested in 2020 Inflation rate

$8,000,000 1.03 1.03 1.03 = $8,741,816

Present value of cashflows to be incurred in 2023 = $8,741,816 PvF(10%,3) = $5,000,000 0.751

= $6,565,104

Step 2 : Recurring cashflows and present value of cashflows

Yearly revenue = $5,500,000

Yearly operating cost = $ 1,800,000

CCA depriciation rate = 45%

Tax rate = 45%

Inflation rate in respect of revenue and expenditure = 2%

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Revenue	$5,500,000	$5,500,000	$5,500,000	$5,500,000	$5,500,000
Inflated Revenue	$5,953,377	$6,072,444	$6,193,893	$6,317,771	$6,444,127
Opearting costs	$1,800,000	$1,800,000	$1,800,000	$1,800,000	$1,800,000
Inflated operating costs	$1,948,378	$1,987.345	$2,027,092	$2,067,634	$2,108,987
Net opeating profit	$4,004,999	$4,085,099	$4,166,801	$4,250,137	$4,335,140
Depreciation	$3,600,000	$1,980,000	$1,089,000	$598,950	$329,422
Profit before tax	$404,999	$2,105,099	$3,077,801	$3,651,187	$4,005,718
Tax @45%	$182,249	$947,294	$1,385,010	$1,643,034	$1,802,573
Profit after tax	$222,749	$1,157,804	$1,692,790	$2,008,153	$2,203,145
Cashflow after tax[PAT + Depreciation	$3,822,749	$3,137,804	$2,781,790	$2,604,103	$2,532,567
PvF(10%,ny)	0.683	0.621	0.564	0.513	0.466
Present value of cashflows	$2,610,937	$1,948,576	$1,568,929	$1,335,905	$1,180,176

Step 3 : cashflows on disposal of infrastructure

Cashflows on sale = $500,000 as per 2028 dollars, so no need to inflate.

Book value = $8,000,000 - [$3,600,000+$1,980,000+$1,089,000+$598,950+$329,422] = $402,628

Profit on sale = $500,000 - $402,628 =$97,372

Tax on sale = $97,372 0.45 = $43817

Cashflow at end of project = $500,000 - $43,817= $456,183

Present value of cashflow = $456183 0.466 = $212581

NPV of the project = Present value of cashinflows - Present value of cashoutflows

= [$2,610,937+$1,948,576+$1,568,929+$1,335,905+$1,180,176+$212581] - $6,565,104

= $2,292,000

Difference between NPV's

NPV as per option A = $2,170,940

NPV as per option B = $2,292,000

Difference = $121,060

Gain on disposal of option A = $121,060

Loss on disposal of option B = $121,060

Since NPV is higher as per option B, so it should be selected an the other is rejected.