Question

C.T. All Ltd., a manufacturer of customized baseball souvenirs, is negotiating with the Grand Slam Company to purchase or to lease a machine that produces foam cushions for seating at baseball parks. The machine would cost $250,000. In five years the machine would have an estimated salvage value of $40,000. Its useful economic life is nine years. These machines have a CCA rate of 20 percent.

C.T. All can borrow funds at 13 1/3 percent from its Nearby Bank, and has a tax rate of 25 percent. The capital cost rate on this machine is 9 percent, and C.T. All’s cost of capital is 15 percent. Lease payments would be at the beginning of each year, and tax savings would occur at the end of each year. Lease payments would be $64,645.

We note that of all the cash flows, the salvage value has the greatest uncertainty. We recognize this by discounting the salvage value at a higher discount rate—the cost of capital.

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

PV cost           $

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

PV cost           $

b. Should C.T. All Ltd. lease or borrow to purchase the machine?

• Lease

• Borrow/Purchase

Please provide correct answers. thanks.

Answer 1

(a - 1) The present value of the lease option calculation should consider several factors:

• 5 years of annual lease expenses of $65,545.
• The tax savings (shield) associated with the annual lease expense, which is 25% of the annual lease expense.
• The discount rate calculation, which should be equal to the interest rate on the lease. In this case, the machine cost of $250,000, and 5 annual payments of $65,645 give an imputed interest rate of 9.82% (we can determine this using the Excel IRR function on the series of cash flows: -$250,000, $65,645 $65,645, $65,645, $65,645, $65,645. A discount rate of 9.82% makes present value of these cash flows equal to zero).
• No salvage value, as the operating lease means that the machine returns to the lessor at the end of the five-year term.

Our model must account for the fact that the lease payments occur at the beginning of the year, while the tax savings come at the end of the year. Thus, we show our first lease payment in year 0, which is equivalent to the beginning of year 1 (and is thus discounted with a factor of 1.0000). The last lease payment occurs at the end of year 4 (effectively the beginning of year 5). The tax savings are shown in years 1 - 5, and discounted as year-end cash flows.

Operating Lease	0	1	2	3	4	5
Annual Lease Expense	$(65,645)	$(65,645)	$(65,645)	$(65,645)	$(65,645)
Tax Shield		$16,411	$16,411	$16,411	$16,411	$16,411
Net Cash Flow	$(65,645)	$(49,234)	$(49,234)	$(49,234)	$(49,234)	$16,411
Discount Factor @ 9.82%	1.0000	0.9106	0.8292	0.7550	0.6875	0.6260
PV of Net Cash Flow	$(65,645)	$(44,831)	$(40,823)	$(37,172)	$(33,848)	$10,274
Sum PV	$(212,046

The present value cost of the lease option is $212,046

(a-2)

Our borrow / purchase option models the same 5-year period of possession of the machine, but also must account for ownership of the machine, and with it the assumption that it will be sold for salvage value after five years. Thus our purchase model must consider a different set of cash flows:

• $250,000 purchase outflow in year 0
• Depreciation tax savings in years 1 - 5. The CCA rate of 20% means that a depreciation expense equal to 20% of the undepreciated (net book) value of the machine will result in annual tax savings of 25% of the deprecation expense. We ignore the salvage value in our depreciation expense calculation.
• A discount factor of 13.33% for the annual operating cash flows
• A higher discount factor of 15% on the salvage cash flow at the end of year 5.

The cash flow model is presented below:

Purchase	0	1	2	3	4	5	Salvage
Capex	$(250,000)
Salvage							$40,000
Depreciation Expense		$50,000	$40,000	$32,000	$25,600	$20,480
Depreciation Tax Shield		$12,500	$10,000	$8,000	$6,400	$5,120
Net Cash Flow	$(250,000)	$12,500	$10,000	$8,000	$6,400	$5,120	$40,000
Discount Factor	1.0000	0.8824	0.7785	0.6870	0.6061	0.5348	0.4972
PV of Net Cash Flow	$(250,000)	$11,029	$7,785	$5,496	$3,879	$2,738	$19,887
Sum of PV Costs	$(199,185)

The present value cost of borrow/purchase option is $199,185.

(b)

Under these sets of assumptions (operating lease, or purchase with salvage), the most economical decision is to purchase. However, we should note that the purchase option is favored because of the salvage value of the equipment, which offers nearly a $20,000 benefit in present value terms. If we adjust the purchase model to remove the effect of the salvage cash flow, the operating lease becomes the better economic decision.

We should also note, however, that the purchase option might also incur a tax benefit on the sale of the machine after year 5. The accumulated depreciation over 5 years is $168.080, leaving a book value of $81,920 after year 5 ($250,000 - $168,080 = $81,920). If the salvage value in a sale is $40,000, the loss on the sale of $41,920 will offer an additional tax benefit to C.T. All