Question

7. Analysis of an expansion project Companies invest in expansion projects with the expectation of increasing the earnings of its business Consider the case of Yeatman Co.: Yeatman Co. is considering an investment that will have the following sales, variable costs, and fixed operating costs: Year 1 Year 2 Year 3 Year 4 5,820 $42.57 $43.55 $44.76$46.79 $22.83 $22.97 $23.45 $23.87 Fixed operating costs except depreciation $66,750 $68,950 $69,690 $68,900 7% 5,500 5,200 Unit sales Sales price Variable cost per unit 5,700 Accelerated depreciation rate 33% 45% 15% This project will require an investment of $25,000 in new equipment. The equipment will have no salvage value at the end of the project's four-year life. Yeatman pays a constant tax rate of 40%, and it has a weighted average cost of capital (WACC) of 11%. Determine what the project's net present value (NPV) would be when using accelerated depreciation. O $65,279 O $87,038 O $72,532 O $83,412

Answer 1

NPV using Accelerated Depreciation

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	42.57	43.55	44.76	46.79
Variable Cost per unit	22.83	22.97	23.45	23.87
Contribution per unit	19.74	20.58	21.31	22.92
Number of units sold	5,500.00	5,200.00	5,700.00	5,820.00
Contribution Margin	1,08,570.00	1,07,016.00	1,21,467.00	1,33,394.40
Fixed Cost	66,750.00	68,950.00	69,690.00	68,900.00
Accelerated Depreciation Expenses	8,250.00	11,250.00	3,750.00	1,750.00
Earnings Before Tax	33,570.00	26,816.00	48,027.00	62,744.40
Tax at 40%	13,428.00	10,726.40	19,210.80	25,097.76
Earnings After Tax	20,142.00	16,089.60	28,816.20	37,646.64
Add: Depreciation Expenses	8,250.00	11,250.00	3,750.00	1,750.00
Annual Cash Inflow	28,392.00	27,339.60	32,566.20	39,396.64
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	25,578	22,189	23,812	25,952
Present Value of Annual Cash Inflows	$97,532
Less: Initial Investment	$25,000
Net Present Value	$72,532

“NPV using Accelerated Depreciation = $72,532”

NPV using Straight Line Depreciation

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	42.57	43.55	44.76	46.79
Variable Cost per unit	22.83	22.97	23.45	23.87
Contribution per unit	19.74	20.58	21.31	22.92
Number of units sold	5,500.00	5,200.00	5,700.00	5,820.00
Contribution Margin	1,08,570.00	1,07,016.00	1,21,467.00	1,33,394.40
Fixed Cost	66,750.00	68,950.00	69,690.00	68,900.00
Straight Line Depreciation Expenses	6,250.00	6,250.00	6,250.00	6,250.00
Earnings Before Tax	35,570.00	31,816.00	45,527.00	58,244.40
Tax at 40%	14,228.00	12,726.40	18,210.80	23,297.76
Earnings After Tax	21,342.00	19,089.60	27,316.20	34,946.64
Add: Depreciation Expenses	6,250.00	6,250.00	6,250.00	6,250.00
Annual Cash Inflow	27,592.00	25,339.60	33,566.20	41,196.64
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	24,858	20,566	24,543	27,138
Present Value of Annual Cash Inflows	$97,105
Less: Initial Investment	$25,000
Net Present Value	$72,105

“NPV using Straight Line Depreciation = $72,105”

Using the “Accelerated” Depreciation method will result in the highest NPV for the Project

Reduction in the NPV of the Project if the after-tax cash flow reduced by $400 each year

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	42.57	43.55	44.76	46.79
Variable Cost per unit	22.83	22.97	23.45	23.87
Contribution per unit	19.74	20.58	21.31	22.92
Number of units sold	5,500.00	5,200.00	5,700.00	5,820.00
Contribution Margin	1,08,570.00	1,07,016.00	1,21,467.00	1,33,394.40
Fixed Cost	66,750.00	68,950.00	69,690.00	68,900.00
Straight Line Depreciation Expenses	6,250.00	6,250.00	6,250.00	6,250.00
Earnings Before Tax	35,570.00	31,816.00	45,527.00	58,244.40
Tax at 40%	14,228.00	12,726.40	18,210.80	23,297.76
Earnings After Tax	21,342.00	19,089.60	27,316.20	34,946.64
Add: Depreciation Expenses	6,250.00	6,250.00	6,250.00	6,250.00
Annual Cash Inflow	27,592.00	25,339.60	33,566.20	41,196.64
Less: Reduction in the After-tax cash inflow	400.00	400.00	400.00	400.00
Net Annual Cash Flow	27,192.00	24,939.60	33,166.20	40,796.64
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	24,497	20,242	24,251	26,874
Present Value of Annual Cash Inflows	$ 95,864
Less: Initial Investment	$25,000
Net Present Value	$70,864

Therefore, the Reduction in the NPV = $1,241 ($72,105 - $70,864)

If the company requires Initial Investment of $25,000, then “It will increase the amount of Initial Investment by $25,000”