Kumquat Farms Ltd. has decided to acquire a kumquat picking machine. The cost of

Question

Kumquat Farms Ltd. has decided to acquire a kumquat picking machine. The cost of the picking machine is $45,000, and it has an economic life of 10 years. At the end of seven years, the market (salvage) value is estimated to be $11,000. Seven years is the time horizon for analysis.

The owner of Kumquat Farms Ltd. has discussed this acquisition with his financial services conglomerate. It has agreed to lend him the purchase price at 10 percent per year, payable in equal blended payments at the end of each year, for seven years.

An alternative method of financing the equipment would be to lease it from the local leasing store. Annual lease payments, payable at the beginning of each of the next seven years, would be $7,750. This would be considered an operating lease.

The equipment has a CCA of 20 percent. The benefits of any tax shields are realized at the end of each year. The company’s tax rate is 25 percent. Kumquat Farms’ cost of capital is 16 percent.

a.1 Calculate PV cost of lease alternative. (Do not round intermediate calculations. Round the final answer to nearest whole dollar. Input the answer as positive value.)

a.2 Calculate PV cost of borrowing/purchase alternative. (Do not round intermediate calculations. Round the final answer to nearest whole dollar. Input the answer as positive value.)

Kumquat Farms Ltd. has decided to acquire a kumquat picking machine. The cost of the picking machine is $45,000, and it has an economic life of 10 years. At the end of seven years, the market (salvage) value is estimated to be $11,000. Seven years is the time horizon for analysis.

Explanation / Answer

Calculation of PV of lease alternative Year Lease payments Discount factor @ 16% Present Values 0 -$7,750 1 -$7,750.00 1 -$7,750 0.862068966 -$6,681.03 2 -$7,750 0.743162901 -$5,759.51 3 -$7,750 0.640657674 -$4,965.10 4 -$7,750 0.552291098 -$4,280.26 5 -$7,750 0.476113015 -$3,689.88 6 -$7,750 0.410442255 -$3,180.93 PV of Lease Alternatives -$36,306.70 PV of lease alternative $36,306.70 Calculation of PV of borrowing / purchase alternative Year 0 1 2 3 4 5 6 7 PV Purchase of machine -$45,000.00 Borrowings $45,000.00 Loan payment -$9,243.00 -$9,243.00 -$9,243.00 -$9,243.00 -$9,243.00 -$9,243.00 -$9,243.00 Tax shield on Depreciation $2,250.00 $1,800.00 $1,440.00 $1,152.00 $921.60 $737.28 $589.82 Tax shield on Interest exp. $1,125.00 $1,006.00 $876.00 $732.00 $575.00 $401.00 $210.00 After Tax salvage value $10,609.30 Net Cash flow $0.00 -$5,868.00 -$6,437.00 -$6,927.00 -$7,359.00 -$7,746.40 -$8,104.72 $2,166.12 Discount factor @ 16%            1.000000         0.862069            0.743163    0.640658    0.552291    0.476113    0.410442    0.353830 Present Values $0.00 -$5,058.62 -$4,783.74 -$4,437.84 -$4,064.31 -$3,688.16 -$3,326.52 $766.44 -$24,592.75 PV of borrowing / purchase alternative $24,592.75 Kumquat Farms Ltd. buy the picking machine as it has less PV compared to leasing option. Workings Using present value of annuity formula , we can calculate the yearly loan payment amount PV of annuity = P * {[1 - (1+r)^-n]/r} PV of annuity = Loan amount = 45000 P = Yearly loan payment = ? r = rate of interest per annum = 10% n = no.of years = 7 45000 = P * {[1 - (1+0.10)^-7]/0.10} 45000 = P * 4.868419 P = Yearly loan payment = $9243.25 Loan Repayment schedule & tax shield on Interest Year Loan payment Principal Interest Loan balance Tax shield @ 25% on Interest 0 $45,000 1 $9,243 $4,743 $4,500 $40,257 $1,125 2 $9,243 $5,218 $4,026 $35,039 $1,006 3 $9,243 $5,739 $3,504 $29,300 $876 4 $9,243 $6,313 $2,930 $22,987 $732 5 $9,243 $6,945 $2,299 $16,042 $575 6 $9,243 $7,639 $1,604 $8,403 $401 7 $9,243 $8,403 $840 -$0 $210 Calculation of depreciation using CCA 20% and tax shield Year Depreciable Value Depreciation @ 20% Tax shield @ 25% 1                    45,000.00             9,000.00          2,250.00 2                    36,000.00             7,200.00          1,800.00 3                    28,800.00             5,760.00          1,440.00 4                    23,040.00             4,608.00          1,152.00 5                    18,432.00             3,686.40              921.60 6                    14,745.60             2,949.12              737.28 7                    11,796.48             2,359.30              589.82 Calculation of after tax salvage value of machine Sale value $11,000.00 Less : Book Value $9,437.18 Gain on Machine $1,562.82 Tax @ 25% $390.70 After tax Salvage value $10,609.30 (Sale value - Tax )

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