Final answer:
Upon calculating the cost of buying and the cost of leasing the machine, including tax shields from interest and depreciation, the total cost of buying is $30,875, while leasing costs $31,000. Therefore, it is more economical for the business to buy the machine.
Step-by-step explanation:
The question relates to making a financial decision on whether to buy or lease a machine for business purposes, considering factors such as the cost of purchase, the terms of the loan, the depreciation rate, the residual value after five years, lease costs, and the tax rate.
To tackle this problem, we must calculate the total cost of buying and leasing, including tax considerations and compare to determine the more economical option for the business.
Firstly, calculating the cost of buying: The machine costs $35,000 financed by a loan at a 10% interest rate (interest-only payments), with principal repayment at the end of year 5.
Yearly depreciation is $6,000, and the tax rate is 35%, so the tax shield from depreciation is $6,000 x 35% = $2,100. Annual interest is $35,000 x 10% = $3,500, and the tax shield from the interest is $3,500 x 35% = $1,225. The cost of buying after tax savings would be:
Interest cost for five years: $3,500 x 5 = $17,500.
Interest tax shield: $1,225 x 5 = $6,125.
Depreciation tax shield: $2,100 x 5 = $10,500.
Final payment (principal amount): $35,000.
Minus residual value: -$5,000.
Total cost of buying = $17,500 + $35,000 - $6,125 - $10,500 - $5,000 = $30,875.
Secondly, the cost of leasing for five years is $8,000 per year. The tax shield is $8,000 x 35% = $2,800. Thus, the cost of leasing after tax is:
Lease payments over five years: $8,000 x 5 = $40,000.
Minus lease payment tax shield: -$2,800 x 5 = -$14,000.
Plus cost of acquiring machine at end of lease: +$5,000.
Total cost of leasing = $40,000 - $14,000 + $5,000 = $31,000.
Comparing both options, the total cost of buying is $30,875, while the total cost of leasing is slightly higher at $31,000. Therefore, buying the machine is the cheaper option over the long term for the business.