91Ó°ÊÓ

Hercules Exercise Equipment Co. purchased a computerized measuring device two years ago for \(58,000. The equipment falls into the five-year category for MACRS depreciation and can currently be sold for \)24,800.

A new piece of equipment will cost \(148,000. It also falls into the five-year category for MACRS depreciation. Assume the new equipment would provide the following stream of added cost savings for the next six years:

Year Cost Savings

1 .................... \)62,000

2 .................... 54,000

3 .................... 52,000

4 .................... 50,000

5 .................... 47,000

6 .................... 36,000

The firm’s tax rate is 35 percent and the cost of capital is 12 percent.

a. What is the book value of the old equipment?

b. What is the tax loss on the sale of the old equipment?

c. What is the tax benefit from the sale?

d. What is the cash inflow from the sale of the old equipment?

e. What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.)

f. Determine the depreciation schedule for the new equipment.

g. Determine the depreciation schedule for the remaining years of the old equipment.

h. Determine the incremental depreciation between the old and new equipment and the related tax shield benefits.

i. Compute the aftertax benefits of the cost savings.

j. Add the depreciation tax shield benefits and the aftertax cost savings, and determine the present value. (See Table 12-20 as an example.)

k. Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e). Should the replacement be undertaken?

Step by step solution

01

Computation of book value Part a

Hercules Exercise Equipment Co.
Year	Depreciation Base ($)	Percentage Depreciation	Annual Depreciation ($)
		(Table 12-9)
1	58,000	0.200	11,600
2	58,000	0.320	18,560
Total depreciation to date			30,160

$\begin{array}{rcl}\mathbf{Bookvalue}& \mathbf{=}& \mathbf{PurchasePrice}\mathbf{-}\mathbf{Totaldepreciationtodate}\\ & \mathbf{=}& \mathbf{58}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{30}\mathbf{,}\mathbf{160}\\ & \mathbf{=}& \mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{840}\\ & & \end{array}$

02

Computation of tax loss on sale Part B

$\begin{array}{rcl}\mathbf{Taxlossonthesales}& \mathbf{=}& \mathbf{BookValue}\mathbf{-}\mathbf{SalesPrice}\\ & \mathbf{=}& \mathbf{27}\mathbf{,}\mathbf{840}\mathbf{-}\mathbf{24}\mathbf{,}\mathbf{800}\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{040}\\ & & \end{array}$

03

Computation of tax benefit Part C

$\begin{array}{rcl}\mathbf{TaxBenefit}& \mathbf{=}& \mathbf{Taxlossonthesales}\mathbf{×}\mathbf{Taxrate}\\ & \mathbf{=}& \mathbf{3}\mathbf{,}\mathbf{040}\mathbf{×}\mathbf{35}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{064}\\ & & \end{array}$

04

Computation of tax benefit Part D

$\begin{array}{rcl}\mathbf{CashinflowfromthesaleoftheoldEquipment}& \mathbf{=}& \mathbf{Salespriceofoldequipment}\mathbf{+}\mathbf{taxbenefitfromthesales}\\ & \mathbf{=}& \mathbf{24}\mathbf{,}\mathbf{800}\mathbf{+}\mathbf{1}\mathbf{,}\mathbf{064}\\ & \mathbf{=}& \mathbf{\$}\mathbf{25}\mathbf{,}\mathbf{864}\\ & & \end{array}$

05

Computation of Net cost of the new equipment Part E

$\begin{array}{rcl}\mathbf{Netcostofthenewequipment}& \mathbf{=}& \mathbf{Priceofthenewequipment}\mathbf{-}\mathbf{Cashinflowfromthesaleoftheoldequipment}\\ & \mathbf{=}& \mathbf{148}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{25}\mathbf{,}\mathbf{864}\\ & \mathbf{=}& \mathbf{\$}\mathbf{122}\mathbf{,}\mathbf{136}\\ & & \end{array}$

06

Preparation of depreciation schedule of new equipment Part F

Year	Depreciation Base	Percentage depreciation (Table 12-9)	Annual Depreciation
	($)		($)
1	148,000	0.200	29,600
2	148,000	0.320	47,360
3	148,000	0.192	28,416
4	148,000	0.115	17,020
5	148,000	0.115	17,020
6	148,000	0.058	8,548
			148,000

07

Preparation of depreciation schedule of new equipment Part G

Year	Depreciation Base	Percentage depreciation (Table 12-9)	Annual Depreciation
	($)		($)
1	58,000	0.192	11,136
2	58,000	0.115	6,670
3	58,000	0.115	6,670
4	58,000	0.058	3,364

08

Incremental Depreciation and tax shield benefits Part H 

1	2	3	4	5	6
Year	Depreciation on new equipment ($)	Depreciation of old equipment ($)	Incremental Depreciation ($)	Tax rate	Tax shield benefits ($)
1	29,600	11,136	18,464	0.35	6,462
2	47,360	6,670	40,690	0.35	14,242
3	28,416	6,670	21,746	0.35	7,611
4	17,020	3,364	13,656	0.35	4,780
5	17,020		17,020	0.35	5,957
6	8,584		8,584	0.35	3,004

09

Computation of after-tax benefits of the cost savings Part i

Year	Savings ($)	(1-Tax rate)	After-tax savings ($)
1	62,000	0.65	40,300
2	54,000	0.65	35,100
3	52,000	0.65	33,800
4	50,000	0.65	32,500
5	47,000	0.65	30,550
6	36,000	0.65	23,400

10

Computation of present values of the total incremental benefits Part j

1	2	3	4	5	6
Year	Tax shield Benefits from depreciation ($)	After-tax cost savings ($)	Total annual benefits ($)	Present value factor 12%	Present value ($)
1	6,462	40,300	46,762	0.893	41,758
2	14,242	35,100	49,342	0.797	39,326
3	7,611	33,800	41,411	0.712	29,485
4	4,780	32,500	37,280	0.636	23,710
5	5,957	30,550	36,507	0.567	20,699
6	3,004	23,400	26,404	0.507	13,387

11

Computation of net present valuesPart k

$\begin{array}{rcl}\mathbf{NetPresentValue}& \mathbf{=}& \mathbf{PresentValueofIncrementalBenefits}\mathbf{-}\mathbf{NetCostofNewEquipment}\\ & \mathbf{=}& \mathbf{168}\mathbf{,}\mathbf{365}\mathbf{-}\mathbf{122}\mathbf{,}\mathbf{136}\\ & \mathbf{=}& \mathbf{\$}\mathbf{46}\mathbf{,}\mathbf{229}\\ & & \end{array}$

As per the analysis of the present value, the company should replace the equipment.

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