Chapter 11, Problem 11.1STP

Book value, taxes, and initial investment Irvin Enterprises is considering the purchase of a new piece of equipment to replace the current equipment. The new version costs $75,000 and requires $5,000 in installation costs. It will be depreciated under MACRS, using a 5-year recovery period. The old piece of equipment was purchased 4 years ago for an installed cost of $50,000; it was being depreciated under MACRS, using a 5-year recovery period. The old equipment can be sold today for $55,000 net of any removal or cleanup costs. As a result of the proposed replacement, the firm’s investment in net working capital is expected to increase by $15,000. The firm pays taxes at a rate of 40%. (Table 4.2 contains the applicable MACRS depreciation percentages.)

1. a. Calculate the book value of the old piece of equipment.
2. b. Determine the taxes. if any, attributable to the sale of the old equipment.
3. c. Find the initial investment associated with the proposed equipment replacement.

Summary Introduction

To determine:

Book value of the old asset.

Introduction:

The capital budgeting is the process of making huge investments by the firms to make their capital assets grow faster such as the building of new buildings, purchase of advanced costly machineries etc.

The incremental cash flow is the additional cash flow for the firm that is generated out of the new capital investment that the firm has undertaken.

Explanation of Solution

Here, the new total installed cost of the new asset is given to be $80,000 including the $5,000 installation cost and $75,000 price of the new asset. The asset is depreciable under the MARCS 5 year period. The MACRS provides the depreciation percentages by recovery year of various years. The table below depicts the depreciation percentages of the assets by recovery period on the basis of the first four property classes as follows:

Recovery year	Percentage by recovery year
	3 Years	5 Years	7 Years	10 Years
1	33%	20%	14%	10%
2	45	32	25	18
3	15	19	18	14
4	7	12	12	12
5		12	9	9
6		5	9	8
7			9	7
8			4	6
9				6
10				6
11				4
Totals	100%	100%	100%	100%

On the basis of the above depreciation percentages given by the MACRS method, the asset's depreciating value for each year can be calculated by multiplying the depreciable value with the percentage per year as follows:

Year	Percentage	Depreciation of new machine
1	20%	$80,000\times 0.20=16,000$
2	32	$80,000\times 0.32=25,600$
3	19	$80,000\times 0.19=15,200$
4	12	$80,000\times 0.12=9,600$
5	12	$80,000\times 0.12=9,600$
6	5	$80,000\times 0.05=4,000$

The proceeds from the sale of old asset is $55,000 and the installed cost of the old machine was $50,000 before 4 years. This means that the old machine have completed 4 years of life out of its 5 year usable life. At the period of 4 years, the machine will depreciate by 0.83 percent which means the depreciation value can be calculated by multiplying the installed value with the depreciation percent as follows:

$\begin{array}{c}{\text{Depreciation value}}_{3\text{ years}}=\text{Installed value}\times \text{Depreciation percent}\\ =50,000\times 0.83\\ =41,500\end{array}$

The depreciation value is $41,500. Thus, the book value of the asset at the fourth year can be calculated by subtracting the accumulated depreciation from the installed cost as follows:

$\begin{array}{c}{\text{Book value}}_{\text{4 years}}=\text{Installed cost}-{\text{Depreciation}}_{\text{4 years}}\\ =50,000-41,500\\ =8,500\end{array}$

Thus, the book value of the old piece of equipment is $8,500.

Summary Introduction

To determine:

Taxes if any attributable to the sale of old asset.

Explanation of Solution

Tax on the proceeds from sale of the asset can be calculated by subtracting the book value from the before tax proceeds from the sale and multiplying it with the tax percentage. Here, the book value is calculated to be $8,500 whereas the before tax proceeds from the sale of old piece of equipment is to be $55,000. When the value is negative, there will be tax savings otherwise tax burden.

$\begin{array}{c}\text{Tax on the sale of proposed asset}=\left(\begin{array}{l}\text{Before tax proceeds from sale}\\ -\text{Book value}\end{array}\right)\times \text{Tax percent}\\ =\left(55,000-8,500\right)\times 0.40\\ =46,500\times 0.40\\ =18,600\end{array}$

Thus, the tax on sale proceeds is $18,600 which means that the firm gets a tax liability of $18,600 for its gain on sale.

Summary Introduction

To determine:

The initial investment for the equipment replacement.

Explanation of Solution

The installed cost of the new machine is given to be $80,000 which includes the equipment price of $75,000 and the installation cost of $5,000. The total after tax proceeds from the sale of the proposed old asset at 4 year can be calculated by subtracting the tax on the gain from sale of the old asset. The tax on the gain from sale of old equipment is calculated to be $18,600. So, the after tax proceeds from the sale of the old equipment can be calculated by subtracting the tax value from the sale price of the old equipment as follows:

$\begin{array}{c}\text{After tax proceeds from sale of old asset}=\text{Sale price}-\text{tax}\\ =55,000-18,600\\ =36,400\end{array}$

Thus, the after tax proceeds from the sale of the old equipment is calculated to be $36,400. The change in the net working capital of the firm is expected to increase by $15,000 and thus, this value have to be added to calculate the initial investment for the new asset. it can be calculated by subtracting the after tax total proceeds from the sale of the old asset from the total installed cost of the new asset and adding the increase in the net working capital. It can be calculated as follows:

$\begin{array}{c}\text{Initial investment}=\left({\text{Installed cost}}_{\text{New asset}}-{\text{After tax proceeds}}_{\text{Old asset}}\right)+\text{Working capital}\\ =\left(80,000-36,400\right)+15,000\\ =43,600+15,000\\ =58,600\end{array}$

Thus, the initial investment for the new asset is $58,600.