Chapter A, Problem 19P

Compute Net Present Value

Dungan Corporation is evaluating a proposal to purchase a new drill press to replace a less efficient machine presently in use. The cost of the new equipment at time 0, including delivery and installation, is $200,000. If it is purchased, Dungan will incur costs of $5,000 to remove the present equipment and revamp its facilities. This $5,000 is tax deductible at time 0.

Depreciation for tax purposes will be allowed as follows: year 1, $40,000; year 2, $70,000; and in each of years 3 through 5, $30,000 per year. The existing equipment has a book and tax value of $100,000 and a remaining useful life of 10 years. However, the existing equipment can be sold for only $40,000 and is being depreciated for book and tax purposes using the straightline method over its actual life.

Management has provided you with the following comparative manufacturing cost data:

The existing equipment is expected to have a salvage value equal to its removal costs at the end of 10 years. The new equipment is expected to have a salvage value of $60,000 at the end of 10 years, which will be taxable, and no removal costs. No changes in working capital are required with the purchase of the new equipment. The sales force does not expect any changes in the volume of sales over the next 10 years. The company’s cost of capital is 16 percent, and its tax rate is 40 percent.

Required

1. a.      Calculate the removal costs of the existing equipment net of tax effects.
2. b.      Compute the depreciation tax shield.
3. c.       Compute the forgone tax benefits of the old equipment.
4. d.      Calculate the cash inflow, net of taxes, from the sale of the new equipment in year 10.
5. e.       Calculate the tax benefit arising from the loss on the old equipment.
6. f.        Compute the annual differential cash flows arising from the investment in years 1 through 10.
7. g.      Compute the net present value of the project.

To determine

Compute the removal costs of the existing equipment net of tax effects.

Explanation of Solution

Net of tax:

Net of tax is the resultant amount that determines the final amount of the accounting period for the tax savings. The net of tax is determined by taking gross figures in the account.

Compute the equipment removal net of tax effects:

$\begin{array}{c}\text{Equipment removal net of tax effects = Cost of removal }\times \left(\text{1}-\text{Tax rate}\right)\\ =\$5,000\times \left(1-40\%\right)\\ =\$5,000\times 60\%\\ =\$3,000\end{array}$

Thus, the value of equipment removal net of tax effects is $3,000.

To determine

Compute the depreciation tax shield.

Explanation of Solution

Depreciation:

Depreciation is the method of calculating the value of the assets for the current accounting period. The value of any capital asset cannot be accounted for the total cost it has incurred in the period that it has been bought in. The value of the asset is distributed over different accounting periods according to the utility of the asset.

Compute the depreciation tax shield:

Year	Depreciation	Tax shield	PV factor	Present value
1	$40,000	$16,000	0.862	$13,792
2	$70,000	$28,000	0.743	$20,804
3	$30,000	$12,000	0.641	$7,692
4	$30,000	$12,000	0.552	$6,624
5	$30,000	$12,000	0.476	$5,712
Total	$200,000	$80,000		$54,624

Table: (1)

Thus, the PV of the depreciation schedule is $54,624.

To determine

Compute the foregone tax benefits of the old equipment.

Explanation of Solution

Tax shield:

Tax shield refers to a reduction in taxable income. The reduction in taxable income is achieved by claiming the allowable deductions.

Compute the foregone tax benefits of the old equipment:

$\begin{array}{c}\text{Forgone tax benefits = }\frac{\text{Existing tax value of equipment }}{\text{Number of years}}\times \text{Tax rate}\\ \text{= }\frac{\$100,000}{10}\times 40\%\\ =\$40,000\times 0.40\\ =\text{\$}4,000\end{array}$

Thus, the value of foregone tax benefits is $4,000.

To determine

Compute the cash inflow, net of taxes, from the sale of the new equipment in year 10.

Explanation of Solution

Gain:

Gain is the resultant value of the difference between revenue earned on sale and the cost of the same.

Compute gain from salvage of new equipment:

$\begin{array}{c}\text{Gain from salvage of new equipment= Salvage value }\times \left(1-\text{Tax rate}\right)\\ =\$60,000\times \left(1-40\%\right)\\ =\$60,000\times 60\%\\ =\$36,000\end{array}$

Thus, the value of gain from salvage of new equipment is $36,000.

To determine

Compute the tax benefit arising from the loss on the old equipment.

Explanation of Solution

Tax shield:

Tax shield refers to a reduction in taxable income. The reduction in taxable income is achieved by claiming the allowable deductions.

Compute the tax benefit arising from a loss on old equipment:

$\begin{array}{c}\text{Tax benefit = }\left(\text{Book value of equipment }-\text{ Salvage value of equipment}\right)\times \text{Tax rate }\\ \text{=}\left(\$100,000-\$40,000\right)\times 40\%\\ =\$60,000\times 40\%\\ =\$24,000\end{array}$

Thus, the value of the tax benefit is $24,000.

To determine

Compute the annual differential cash flows arising from the investment in years 1 through 10.

Explanation of Solution

Differential cash flow:

Differential cash flow is the difference between several options of businesses’ cash flows.

Compute the differential cash flows:

$\begin{array}{c}\text{Differential cash flows = }\left(\begin{array}{l}\left(\begin{array}{c}\left(\text{Labor cost + other cost}\right)\text{ of present equipment}\\ -\left(\text{Labor cost + other cost}\right)\text{ of new equipment}\end{array}\right)\\ \times \left(\text{1}-\text{Tax rate}\right)\end{array}\right)\\ =\left(\left(\$30,000+\$48,000\right)-\left(\$25,000+\$20,000\right)\right)\times \left(1-40\%\right)\\ =\left(\$78,000-\$45,000\right)\times 60\%\\ =\$19,800\end{array}$

Thus, the value of differential cash flows is $19,800.

To determine

Compute the net present value of the project.

Explanation of Solution

Net present value (NPV):

Net present value (NPV) is a type of intrinsic valuation analysis. NPV is the sum total of all the future cash flows (inflows/outflows) that will occur over the lifetime of a project discounted to the present.

	Year
Particulars	0	1	2	3	4	5	6	7	8	9	10
Investment flows:
Equipment cost	($200,000)
Removal	($3,000)
Salvage of old equipment	$40,000
Tax benefit-sale of old equipment	$24,000
Periodic operating flows		$19,800	$19,800	$19,800	$19,800	$19,800	$19,800	$19,800	$19,800	$19,800	$19,800
Tax shield from depreciation:
Year 1		$16,000
Year 2			$28,000
Year 3-5				$12,000	$12,000	$12,000
Old equipment (forgone)		($4,000)	($4,000)	($4,000)	($4,000)	($4,000)	($4,000)	($4,000)	($4,000)	($4,000)	($4,000)
Disinvestment:
Proceeds of disposal											$60,000
Tax on gain											($24,000)
Total cash flows	($139,000)	$31,800	$43,800	$27,800	$27,800	$27,800	$15,800	$15,800	$15,800	$15,800	$51,800
PV factor	$1.000	$0.862	$0.743	$0.641	$0.552	$0.476	$0.410	$0.354	$0.305	$0.263	$0.227
Present value $\left(\begin{array}{l}\text{Total cahs flow}\\ \times \text{PV factor}\end{array}\right)$	($139,000)	$27,412	$32,543	$17,820	$15,346	$13,233	$6,478	$5,593	$4,819	$4,155	$11,759
Net present value	$157

Table: (1)

Thus, the NPV of the project is $157.