Question

N0PV Corporation is considering buying a cost saving machine. The new machine costs $1 million and will last for 10 years. The new machine will be linearly depreciated over 10 years. Assume that they expect the machine to be worthless after 10 years. If they decide to buy the new machine, they will sell the old machine for $200,000. The current book value of the old machine is $250,000. The old machine has a remaining life of 2 years in which the remaining book value is linearly depreciated. The new machine will result in a cost saving of $130,000 every year before tax. Assume a tax rate of 30%. N0PV uses the company WACC to evaluate the project as it has the same risk as N0PV in general and will be financed with the same mix of equity and debt. The equity beta of N0PV is 1.5. The risk-free rate is 2% and the expected return on the market is 7%. The cost of debt before tax is 4%. The market value of debt to equity is 1. If they decide not to do the project they can use the old machine for another 10 years. If they decide to keep the old machine (and not buy the new one) the old machine will be worthless after 10 years.

Question: What is the present value (after tax) of the annual cost savings?

Answer 1

Calculation of Net Initial Outflow :
Cost of New Machine = $1 million
Post Tax Salvage Value of old machine = Sale Value + [(Book Value – Sale Value) * Tax Rate]
                                                                            = 200,000 + [(250,000-200,000) * 0.30]
                                                                            = 200,000 + (50,000 * 0.30)
                                                                            = 200,000 + 15,000
                                                                            = 215,000

Net Incremental Cost = Cost of New Machine – Post tax Salvage Value of old machine
                                          = $1,000,000 – 215,000
                                          = $785,000

Calculation of Annual Incremental Depreciation :
Annual Depreciation = (Cost of Machinery – Salvage Cost) / No. of years remaining
Annual Depreciation on new machine for year 1 to 10 = ($1,000,000 – 0)/10
                                                                      = $100,000

Depreciation on Old Machinery in Year 1 & 2 = (Book Value – Salvage Value)/No of Years
                                                                        = (250,000 – 0) / 2
                                                                        = $125,000

	Year 1 – 2	Year 3 - 10
Depreciation on new machinery	$100,000	$100,000
Depreciation on old machinery	$125,000	0
Annual Incremental Depreciation	-$25,000	$100,000

a) Calculation of WACC :
Calculation of Cost of Equity

Risk free Rate of return (Rf) = 2%
Return on the market portfolio (Rm) = 7%
Equity Beta = 1.5

As per the Capital Asset Pricing Model
Re = Rf + (Rm – Rf) Beta

Where Re = Cost of Equity
              Rm – Rf = Market Risk Premium

Re = 2 + (7 - 2) 1.5
     = 2 + (5 )1.5
= 5 +7.5
= 9.50%

Pre tax Cost of Debt = 4%
Post Tax Cost of Debt = 4 * (1-0.30)
                                           = 2.8%

D/E Ratio = 1
This means Weight of Equity and Weight of debt are both 0.50

WACC = (Cost of Equity * Weight of Equity) + (Cost of Debt * Weight of Post Tax Debt)
            = (9.50 * 0.50) + (2.8 * 0.50)
            = 4.75 + 1.4
            = 6.15%

Calculation of Present Value of annual tax savings :

PARTICULARS	Year	0	1	2	3	4	5	6	7	8	9	10
INCREMENTAL COST SAVINGS		0.000	130000.000	130000.000	130000.000	130000.000	130000.000	130000.000	130000.000	130000.000	130000.000	130000.000
INCREMENTAL DEPRECIATION		0.000	-25000.000	-25000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000
INCREMENTAL SAVINGS BEFORE TAX		0.000	155000.000	155000.000	30000.000	30000.000	30000.000	30000.000	30000.000	30000.000	30000.000	30000.000
INCOME TAX @30%		0.000	46500.000	46500.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000
INCREMENTAL SAVINGS AFTER TAX		0.000	108500.000	108500.000	21000.000	21000.000	21000.000	21000.000	21000.000	21000.000	21000.000	21000.000
ADD : DEPRECIATION		0.000	-25000.000	-25000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000	100000.000
LESS : NET INITIAL OUTFLOW		785000.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
ADD :SALVAGE VALUE OF EQUIPMENT		0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
POUND FREE CASH FLOW		-785000.000	83500.000	83500.000	121000.000	121000.000	121000.000	121000.000	121000.000	121000.000	121000.000	121000.000
PRESENT VALUE FACTOR @6.15%		1	0.94206312	0.88748292	0.83606493	0.78762593	0.74199334	0.69900456	0.65850642	0.62035461	0.5844132	0.55055412
PRESENT VALUE @6.15%		-785000.00	78662.27	74104.82	101163.86	95302.74	89781.19	84579.55	79679.28	75062.91	70714.00	66617.05
NPV = SUM OF PRESENT VALUE AT EACH YEAR											30667.67

NPV = $30667.67