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 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 Unit sales 3,000 3,250 3,300 3,400 Sales price $17.25 $17.33 $17.45 $18.24 Variable cost per unit $8.88 $8.92 $9.03 $9.06 Fixed operating costs except depreciation $12,500 $13,000 $13,220 $13,250 Accelerated depreciation rate 33% 45% 15% 7% 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. Determine what the project’s net present value (NPV) would be when using accelerated depreciation. $10,468 $8,374 $12,562 $9,421 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 Yeatman turns it down. How much should Yeatman 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? $931 $559 $698 $1,024 The project will require an initial investment of $25,000, but the project will also be using a company-owned truck that is not currently being used. This truck could be sold for $14,000, after taxes, if the project is rejected. What should Yeatman do to take this information into account? Increase the amount of the initial investment by $14,000. 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 $14,000.

Answer 1

NPV using Accelerated Depreciation

Particulars	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	17.25	17.33	17.45	18.24
Variable Cost per unit	8.88	8.92	9.03	9.06
Contribution per unit	8.37	8.41	8.42	9.18
Number of units sold	3,000	3,250	3,300	3,400
Contribution Margin	25,110	27,333	27,786	31,212
Fixed Cost	12,500	13,000	13,220	13,250
Accelerated Depreciation Expenses [Initial Investment Cost x Accelerated Depreciation Rate]	8,250	11,250	3,750	1,750
Earnings Before Tax	4,360	3,083	10,816	16,212
Tax at 40%	1,744	1,233	4,326	6,485
Earnings After Tax	2,616	1,850	6,490	9,727
Add: Depreciation Expenses	8,250	11,250	3,750	1,750
Annual Cash Inflow	10,866	13,100	10,240	11,477
Present Value Factor at 11%	0.9009	0.8116	0.7312	0.6587
Present Value of Annual Cash Inflows	9,789	10,632	7,487	7,560
Present Value of Annual Cash Inflows	35,468
Less: Initial Investment	25,000
Net Present Value	10,468

“NPV using Accelerated Depreciation = $10,468”

NPV using Straight Line Depreciation

Particulars	Year 1	Year 2	Year 3	Year 4
Sales Price per unit	17.25	17.33	17.45	18.24
Variable Cost per unit	8.88	8.92	9.03	9.06
Contribution per unit	8.37	8.41	8.42	9.18
Number of units sold	3,000	3,250	3,300	3,400
Contribution Margin	25,110	27,333	27,786	31,212
Fixed Cost	12,500	13,000	13,220	13,250
Straight Line Depreciation Expenses [Initial Investment Cost / 4 Years]	6,250	6,250	6,250	6,250
Earnings Before Tax	6,360	8,083	8,316	11,712
Tax at 40%	2,544	3,233	3,326	4,685
Earnings After Tax	3,816	4,850	4,990	7,027
Add: Depreciation Expenses	6,250	6,250	6,250	6,250
Annual Cash Inflow	10,066	11,100	11,240	13,277
Present Value Factor at 11%	0.9009	0.8116	0.7312	0.6587
Present Value of Annual Cash Inflows	9,068	9,009	8,218	8,746
Present Value of Annual Cash Inflows	35,042
Less: Initial Investment	25,000
Net Present Value	10,042

“NPV using Straight Line Depreciation = $10,042”

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	17.25	17.33	17.45	18.24
Variable Cost per unit	8.88	8.92	9.03	9.06
Contribution per unit	8.37	8.41	8.42	9.18
Number of units sold	3,000	3,250	3,300	3,400
Contribution Margin	25,110	27,333	27,786	31,212
Fixed Cost	12,500	13,000	13,220	13,250
Straight Line Depreciation Expenses	6,250	6,250	6,250	6,250
Earnings Before Tax	6,360	8,083	8,316	11,712
Tax at 40%	2,544	3,233	3,326	4,685
Earnings After Tax	3,816	4,850	4,990	7,027
Add: Depreciation Expenses	6,250	6,250	6,250	6,250
Annual Cash Inflow	10,066	11,100	11,240	13,277
Less: Reduction in the After-tax cash inflow	300	300	300	300
Net Annual Cash Flow	9,766	10,800	10,940	12,977
Present Value Factor at 11%	0.90090	0.81160	0.73120	0.65870
Present Value of Annual Cash Inflows	8,798	8,765	7,999	8,548
Present Value of Annual Cash Inflows	34,111
Less: Initial Investment	25,000
Net Present Value	9,111

Therefore, the Reduction in the NPV = $931 [$10,042 - $9,111]

Yeatman should take the following information into account

Increase the amount of the initial investment by $14,000.

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.