Question

3.   Louie's Leisure Products is considering replacing a project which will require the purchase of $1.4 million in new equipment. The equipment will be depreciated straight-line to a zero book value over the 7-year life of the project. Louie's expects to sell the equipment at the end of the project for 20% of its original cost. The existing equipment of this project was purchased 3 years back for $700,000 and has been depreciated using 5 year MACRS schedule. This machine has salvage value of $500,000 today. The machine has another 7 years useful life left, after which it can be sold for $50,000. Annual incremental cost saving from this project are estimated at $1.2 million. Net working capital equal to 20% of sales will be required to support the project. All of the net working capital will be recouped at the end of the project. The firm desires a minimal 14% rate of return on this project. The tax rate Is 34%. Required: Should Louie's accept the project by replacing the existing equipment with the new one? Use NPV and IRR decision rule in making your decision.   (15)

Answer 1

The purchase of $1.4 million in new equipment.

The equipment will be depreciated straight-line to a zero book value over the 7-year life of the project.

Louie's expects to sell the equipment at the end of the project for 20% of its original cost.

The existing equipment of this project was purchased 3 years back for $700,000 and has been depreciated using 5 year MACRS schedule.

This machine has salvage value of $500,000 today.

The machine has another 7 years useful life left, after which it can be sold for $50,000.

Annual incremental cost saving from this project are estimated at $1.2 million. Net working capital equal to 20% of sales will be required to support the project. All of the net working capital will be recouped at the end of the project.

The firm desires a minimal 14% rate of return on this project.

The tax rate Is 34%.

.

Required: Should Louie's accept the project by replacing the existing equipment with the new one? Use NPV and IRR decision rule in making your decision.

.

Initial investment =

Purchase cost of new equip = 1400000 (outflow)

Proceeds from old equip =

Market value = 500000

Cost = 700000

Accumulated depreciation = sum of 3 year MACRS rate * cost = 700000 * 71.2% = 498400

Book value = 700000 - 498400 = 201600

Taxable gain = 500000 - 201600 = 298400

Tax exp on gain = 298400*34% = 101456

Net proceeds from sale = 500000 - 101456 = 398544 (inflow)

Net initial investment = 1400000 - 398544 = 1001456

net working capital = 20% * 1200000 = 240000

.

Years	0	1	2	3	4	5	6	7
Cost save		1200000	1200000	1200000	1200000	1200000	1200000	1200000
-tax exp@34%		408000	408000	408000	408000	408000	408000	408000
=A3After tax savings		792000	792000	792000	792000	792000	792000	792000
Add deprecition tax shield		40582.4	40582.4	54291.2	68000	68000	68000	68000
=Operating cash flow		832582.4	832582.4	846291.2	860000	860000	860000	860000
Initial investment	-1001456
Net working capital	-240000
Release of NWC								240000
Net terminal cash flow								151800
Net cash flow	-1241456	832582.4	832582.4	846291.2	860000	860000	860000	1251800
PV factor of $1 @14%	1	0.8772	0.7695	0.675	0.5921	0.5193	0.4556	0.3996
PV of cash flow	-1241456	730341.2813	640672.1568	571246.56	509206	446598	391816	500219.28
NPV	2548663

.NPV = PV of cash flow - net initial investment

.

deprecition tax shield
years	1	2	3	4	5	6	7
New equip(straigt line) = 1400000 / 7 = 200000	200000	200000	200000	200000	200000	200000	200000
Old equipment (MACRS 5 years) past 3 year are depreciated	11.52%	11.52%	5.76%	0	0	0	0
cost = 700000	80640	80640	40320	0	0	0	0
Incremental depreciation	119360	119360	159680	200000	200000	200000	200000
Depreciation tax shield = Incremental dep. * tax rate	40582.4	40582.4	54291.2	68000	68000	68000	68000

.

Salvage value at end

Market value of new equip = 20% of its original cost. = 1400000 *20% = 280000

Book value at end = 0

Taxable gain = 280000

Tax exp. On gain = 280000 * 34% = 95200

Net proceeds from sales = 280000 - 95200 = 184800

Less opportunity cost of lost sales of old equipment* = 33000

Net terminal cash flow = 184800 - 33000 = 151800

*Market value if exist = 50000

Book value = 0

Taxable gain = 50000

Tax = 50000 * 34% = 17000

Proceeds from old equip if exist(opportunity cost ) = 50000 - 17000 = 33000

.

IRR

For calculating IRR find a rate that will get NPV is negative

If NPV is negative the the used discount rate is should higher than IRR.

There is need a discount rate and with positive NPV( for this purpose we can use actual NPV that calculated already above) the 14% must less than calculated IRR

The formula is

IRR = Discount rate @NPV positive + ( NPV @ Lower discount rate / (Difference between two NPV’s ) * (Higher discount rate - Lower discount rate)

Where,

Discount rate @NPV positive = 14% (this is lower discount rate )

NPV @ Lower discount rate = 2548663

Next find Higher discount rate and its NPV

How ever the NPV should negative, using Trail and error method

Here we use

Higher discount rate =70%

Years	0	1	2	3	4	5	6	7
Net cash flow	-1241456	832582.4	832582.4	846291.2	860000	860000	860000	1251800
PV factor of $1 @70%	1	0.5882	0.3460	0.2035	0.1197	0.0704	0.04142	0.02437
PV of cash flow	-1241456	489724.9677	288073.5104	172220.2592	102942	60544	35621.2	30506.366
NPV	-61682

.

Difference between two NPV’s = 2548663 - -61682 = 2610345

.

IRR = 14% + ( 2548663 / 2610345 ) * ( 70% - 14% )

IRR = 14% + 0.9763 * 56%

IRR = 14% + 54.68% = 68.68%

..

**Base on NPV and IRR, the project should accept, because the NPV of the project is positive and IRR is hgher than cost of capital