Question

One year​ ago, your company purchased a machine used in manufacturing for

$ 105 comma 000$105,000.

You have learned that a new machine is available that offers many advantages and you can purchase it for

$ 145 comma 000$145,000

today. It will be depreciated on a​ straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin​ (revenues minus operating expenses other than​ depreciation) of

$ 60 comma 000$60,000

per year for the next 10 years. The current machine is expected to produce a gross margin of

$ 24 comma 000$24,000

per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, and has no salvage​ value, so depreciation expense for the current machine is

$ 9 comma 545$9,545

per year. The market value today of the current machine is

$ 65 comma 000$65,000.

Your​ company's tax rate is

40 %40%​,

and the opportunity cost of capital for this type of equipment is

11 %11%.

Should your company replace its​ year-old machine?

Answer 1

Calculation of Book Value of Current Machine :

Annual Depreciation of current machine = $9545
Book Value of current machine today = Cost of machine – (Annual Depreciation * No of years depreciated)
                                                         = 105000 – (9545 * 1)
                                                         = 105000 - 9545
                                                         = 95455

Calculation of Post Tax Salvage Value of Current Machine :
Post Tax Salvage Value of current machine        = Sale Value + [(Book Value - Sale Value) * Tax Rate]
                                                                            = 65000 + [(95455 – 65000) * 0.40]
                                                                            = 65000 + [30455 * 0.40]
                                                                            = 65000 + 12182
                                                                            = 77182
                                                                           
Cost of New Machine = $145000

Net Incremental Cost = Cost of New Machine – Post tax Salvage Value of old machine
                                          = $145000 – 77182
                                          = $67818

Calculation of Annual Incremental Depreciation :
Annual Depreciation on current machine = 9545 million
Annual Depreciation on new machine = (145000 – 0) / 10 = 14500 million

Annual Incremental Depreciation = Annual Depreciation on new machine - Annual Depreciation on current machine
                                                                   = 14500 – 9545
                                                                   = 4955

Calculation of incremental gross margin :
Incremental Gross Margin = Gross Margin from new machine – Gross margin from current machine
                                                     = 60000 – 24000
                                                     = $36000

Calculation of Pound free cash flows :

PARTICULARS	Year	0	1 to 10
INCREMENTAL GROSS MARGIN		0.00	36000.00
INCREMENTAL DEPRECIATION		0.00	4955.00
INCREMENTAL SAVINGS BEFORE TAX		0.00	31045.00
INCOME TAX @40%		0.00	12418.00
INCREMENTAL SAVINGS AFTER TAX		0.00	18627.00
ADD : DEPRECIATION		0.00	4955.00
LESS : NET INITIAL OUTFLOW		-67818.00	0.00
POUND FREE CASH FLOW		-67818.00	23582.00

Calculation of Present Value of annual tax savings :
NPV = (PVAF(11%,10) * 23582) -67818
         = (5.88923201 * 23582) -67818
         = 138879.86 – 67818
         = 71061.86

Since the NPV incremental of incremental savings is more than 0, the company should replace its year old machine.

Note : PVAF (11%,10) is calculated by adding the Present Value Factor for 11% for 10 years.
Present Value Factor have been calculated as = (1/1+r)n
Where
r= Cost of Capital (Discount rate)
n= No of Year