Question

Companies invest in expansion projects with the expectation of increasing the earnings of its business.

Consider the case of McFann Co.:

McFann 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	4,200	4,100	4,300	4,400
Sales price	$29.82	$30.00	$30.31	$33.19
Variable cost per unit	$12.15	$13.45	$14.02	$14.55
Fixed operating costs except depreciation	$41,000	$41,670	$41,890	$40,100
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. McFann 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.

$56,964

$49,534

$44,581

$59,441

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 McFann turns it down. How much should McFann 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 $500 for each year of the four-year project?

$1,163

$1,551

$1,706

$1,318

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 $18,000, after taxes, if the project is rejected. What should McFann do to take this information into account?

Increase the amount of the initial investment by $18,000.

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 $18,000.

Answer 1

NPV using Accelerated Depreciation

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	29.82	30.00	30.31	33.19
Variable Cost per unit	12.15	13.45	14.02	14.55
Contribution per unit	17.67	16.55	16.29	18.64
Number of units sold	4,200	4,100	4,300	4,400
Contribution Margin	74,214	67,855	70,047	82,016
Fixed Cost	41,000	41,670	41,890	40,100
Accelerated Depreciation Expenses [Initial Investment x Accelerated Depreciation Rate]	4,950	6,750	2,250	1,050
Earnings Before Tax	28,264	19,435	25,907	40,866
Tax at 40%	11,306	7,774	10,363	16,346
Earnings After Tax	16,958	11,661	15,544	24,520
Add: Depreciation Expenses	4,950	6,750	2,250	1,050
Annual Cash Inflow	21,908	18,411	17,794	25,570
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	19,737	14,943	13,011	16,843
Present Value of Annual Cash Inflows	64,534
Less: Initial Investment	15,000
Net Present Value	49,534

“NPV using Accelerated Depreciation = $49,534”

NPV using Straight Line Depreciation

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	29.82	30.00	30.31	33.19
Variable Cost per unit	12.15	13.45	14.02	14.55
Contribution per unit	17.67	16.55	16.29	18.64
Number of units sold	4,200	4,100	4,300	4,400
Contribution Margin	74,214	67,855	70,047	82,016
Fixed Cost	41,000	41,670	41,890	40,100
Straight Line Depreciation Expenses [Initial Investment / 4 Years]	3,750	3,750	3,750	3,750
Earnings Before Tax	29,464	22,435	24,407	38,166
Tax at 40%	11,786	8,974	9,763	15,266
Earnings After Tax	17,678	13,461	14,644	22,900
Add: Depreciation Expenses	3,750	3,750	3,750	3,750
Annual Cash Inflow	21,428	17,211	18,394	26,650
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	19,305	13,969	13,450	17,555
Present Value of Annual Cash Inflows	64,279
Less: Initial Investment	15,000
Net Present Value	49,279

“NPV using Straight Line Depreciation = $49,279”

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 $500 each year

	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	29.82	30.00	30.31	33.19
Variable Cost per unit	12.15	13.45	14.02	14.55
Contribution per unit	17.67	16.55	16.29	18.64
Number of units sold	4,200	4,100	4,300	4,400
Contribution Margin	74,214	67,855	70,047	82,016
Fixed Cost	41,000	41,670	41,890	40,100
Straight Line Depreciation Expenses	3,750	3,750	3,750	3,750
Earnings Before Tax	29,464	22,435	24,407	38,166
Tax at 40%	11,786	8,974	9,763	15,266
Earnings After Tax	17,678	13,461	14,644	22,900
Add: Depreciation Expenses	3,750	3,750	3,750	3,750
Annual Cash Inflow	21,428	17,211	18,394	26,650
Less: Reduction in the After-tax cash inflow	500	500	500	500
Net Annual Cash Flow	20,928	16,711	17,894	26,150
Present Value Factor at 11%	0.90090	0.81162	0.73119	0.65873
Present Value of Annual Cash Inflows	18,855	13,563	13,084	17,226
Present Value of Annual Cash Inflows	62,728
Less: Initial Investment	15,000
Net Present Value	47,728

Therefore, the Reduction in the NPV = $1,551 [$49,279 - $47,728]

McFann should take the following information into account while evaluating the project

Increase the amount of the initial investment by $18,000.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.