Question

You are the owner of a small earthwork construction firm and you own two scrapers. You are considering the purchase of a new scraper. Your current scraper earns you $23,000 per year and has a yearly maintenance cost of $4,100 that is increasing by $1,095 per year. The salvage value is $45,000 but that value is decreasing by $4,000 per year. You have paid off your current scraper. The first new model has a cost of $195,000, is capable of earning you $55,000 per year, and has a yearly maintenance cost of $5,100, which increases by $740 every year thereafter. The salvage value for this machine is $180,000, which decreases by $18,000 every year thereafter. The second model has a cost of $170,000, is capable of earning $45,000 per year, and has a yearly maintenance cost of $4,000 that increases by $950 per year thereafter. The salvage value for this machine is $158,000, which decreases in value by $14,000 each year thereafter. If you plan to have whatever scraper you purchase for a 6-year period, which investment is optimal? Assume a 4% APR compounded yearly.

please solve with explenation

Answer 1

Evaluation: NPV for Current Scrapper NPV for First Model Scrapper NPV for First Second Scrapper $105,139.91 $128,456.32 $102,594.36 NPV for First Model Scrapper is the highest among other alternatives. So, firm should choose First Model Scrapper. Assumptions: Given salvage value is at the end of first year. And the same is decreased by respective year's reduction for rest of 5 years. Workings:

NPV for Current Scrapper Year Initial cost 3 4 6 $0 $23,000 ($5,195) $23,000 ($6,290) $23,000 $23,000 $23,000 $23,000 Earnings Maintenance cost ($7,385) ($8,480) ($9,575) [Being increased by $1,095 each year] $25,000 [$45,000 - ($4,000 x 5 years)] ($4,100) Salvage value Net Cash Flow (NCF) Discount Factor @ 4% (DF) Discounted Cash Flow (NCF) x (DF) $14,520 $0 $18,900 $17,805 $16,710 $15,615 $38,425 1.0000 0.9615 0.8890 0.9246 0.8548 0.8219 0.7903 $0.00 $18,173.08 $16,461.72 $14,855.13 $13,347.77 $11,934.38 $30,367.84 $105,139.91 [Sum of discounted cash flow from year-0 thru 6] Net Present Value (NPV)

NPV for First Model Scrapper Year Initial cost 2 3 ($195,000) $55,000 ($5,840) $55,000 $55,000 Earnings Maintenance cost $55,000 $55,000 $55,000 ($8,800) [Being increased by $740 each year] $90,000 [$180,000 - ($18,000o x 5 years)] $136,200 ($5,100) ($6,580) ($7,320) ($8,060) Salvage value Net Cash Flow (NCF) ($195,000) $49,900 $47,680 $46,940 $49,160 $48,420 Discount Factor @ 4% (DF) 1.0000 0.9615 0.9246 0.8890 0.7903 0.8548 0.8219 Discounted Cash Flow (NCF) x (DF) ($195,000.00) $47,980.77 $45,451.18 $43,045.20 $40,757.06 $38,581.26 $107,640.84 Net Present Value (NPV) $128,456.32 [Sum of discounted cash flow from year-0 thru 6] NPV for First Second Scrapper Year Initial cost ($170,000) Earnings Maintenance cost Salvage value Net Cash Flow (NCF) Discount Factor @ 4% (DF) Discounted Cash Flow (NCF) x (DF) $45,000 $45.000 $45,000 $45,000 $45,000 $45,000 ($8,750) [Being increased by $950 each year] $88,000 [$158,000 - ($14,000 x 5 years)] ($4,950) ($4,000) ($5,900) ($6,850) ($7,800) ($170,000) $40,050 $41,000 $39,100 $38,150 $37,200 $124,250 1.0000 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 ($170,000.00) $39,423.08 $37,028.48 $34,759.76 $32,610.78 $30,575.69 $98,196.58 Net Present Value (NPV) $102,594.36 [Sum of discounted cash flow from year-0 thru 6]