Question

3. Analysis of an expansion project Companies invest in expansion projects with the expectation of increasing the earnings of its business. Consider the case of Garida Co.: Garida 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 Unit sales 4,800 5,100 5,000 5,120 Sales price $22.33 $23.45 $23.85 $24.45 Variable cost per unit $9.45 $10.85 $11.95 $12.00 Fixed operating costs except depreciation $32,500 $33,450 $34,950 $34,875 Accelerated depreciation rate 33% 45% 15% 7%

This project will require an investment of $15,000 in new equipment. The equipment will have no salvage value at the end of the project’s four-year life. Garida 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.

Determine what the project’s net present value (NPV) would be when using accelerated depreciation.

$49,386

$51,533

$42,944

$34,355

Now determine what the project’s NPV would be when using straight-line depreciation.     

Using the      depreciation method will result in the highest NPV for the project.

No other firm would take on this project if Garida turns it down. How much should Garida reduce the NPV of this project if it discovered that this project would reduce one of its division’s net after-tax cash flows by $300 for each year of the four-year project?

$559

$1,024

$931

$791

The project will require an initial investment of $15,000, but the project will also be using a company-owned truck that is not currently being used. This truck could be sold for $12,000, after taxes, if the project is rejected. What should Garida do to take this information into account?

Increase the amount of the initial investment by $12,000.

The company does not need to do anything with the value of the truck because the truck is a sunk cost.

Increase the NPV of the project by $12,000.

Answer 1

Net Present Value (NPV) using Accelerated Depreciation Method

Particulars	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	22.33	23.45	23.85	24.45
Variable Cost per unit	9.45	10.85	11.95	12.00
Contribution per unit	12.88	12.60	11.90	12.45
Number of units sold	4,800	5,100	5,000	5,120
Contribution Margin	61,824	64,260	59,500	63,744
Fixed Cost	32,500	33,450	34,950	34,875
Accelerated Depreciation Expenses	4,950	6,750	2,250	1,050
Earnings Before Tax	24,374	24,060	22,300	27,819
Tax at 40%	9,750	9,624	8,920	11,128
Earnings After Tax	14,624	14,436	13,380	16,691
Add: Depreciation Expenses	4,950	6,750	2,250	1,050
Annual Cash Inflow	19,574	21,186	15,630	17,741
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	17,635	17,195	11,428	11,686
Present Value of Annual Cash Inflows	57,944
Less: Initial Investment	15,000
Net Present Value	42,944

“NPV using Accelerated Depreciation = $42,944”

Net Present Value (NPV) using Straight Line Depreciation Method

Particulars	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	22.33	23.45	23.85	24.45
Variable Cost per unit	9.45	10.85	11.95	12.00
Contribution per unit	12.88	12.60	11.90	12.45
Number of units sold	4,800	5,100	5,000	5,120
Contribution Margin	61,824	64,260	59,500	63,744
Fixed Cost	32,500	33,450	34,950	34,875
Straight Line Depreciation Expenses	3,750	3,750	3,750	3,750
Earnings Before Tax	25,574	27,060	20,800	25,119
Tax at 40%	10,230	10,824	8,320	10,048
Earnings After Tax	15,344	16,236	12,480	15,071
Add: Depreciation Expenses	3,750	3,750	3,750	3,750
Annual Cash Inflow	19,094	19,986	16,230	18,821
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	17,202	16,221	11,867	12,399
Present Value of Annual Cash Inflows	57,689
Less: Initial Investment	15,000
Net Present Value	42,689

“NPV using Straight Line Depreciation = $42,689”

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 $300 each year

Particulars	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	22.33	23.45	23.85	24.45
Variable Cost per unit	9.45	10.85	11.95	12.00
Contribution per unit	12.88	12.60	11.90	12.45
Number of units sold	4,800	5,100	5,000	5,120
Contribution Margin	61,824	64,260	59,500	63,744
Fixed Cost	32,500	33,450	34,950	34,875
Straight Line Depreciation Expenses	3,750	3,750	3,750	3,750
Earnings Before Tax	25,574	27,060	20,800	25,119
Tax at 40%	10,230	10,824	8,320	10,048
Earnings After Tax	15,344	16,236	12,480	15,071
Add: Depreciation Expenses	3,750	3,750	3,750	3,750
Annual Cash Inflow	19,094	19,986	16,230	18,821
Less: Reduction in the After-tax cash inflow	300	300	300	300
Net Annual Cash Flow	18,794	19,686	15,930	18,521
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	16,932	15,978	11,648	12,201
Present Value of Annual Cash Inflows	56,758
Less: Initial Investment	15,000
Net Present Value	41,758

Therefore, the Reduction in the NPV = $931 [$42,689 - $41,758]

Garida should take the following information into account

Increase the amount of the initial investment by $12,000.

NOTE

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.