Question

One year ago, your company purchased a machine used in manufacturing for $120,000. You have learned that a new machine is available that offers many advantages; you can purchase it for $200,000 today. It will be depreciated on a straight-line basis over 5 years, after which it has no salvage value. You expect that the new machine will produce EBITDA (earnings before interest, taxes, depreciation, and amortization) of $100,000 per year for the next 5 years. The current machine is expected to produce EBITDA of $45,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 6 years, after which it will have no salvage value, so depreciation expense for the current machine is $20,000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $80,000. Your company's tax rate is 45%, and the opportunity cost of capital for this type of equipment is 12%. Is it profitable to replace the year- old machine?

Answer 1

Ans:

GIven data

	Current Machine	Proposed machine
EBITDA	45000	100000
Cost	120000	200000
Useful life	6 years	5 Years
Tax rate	45%

As per the requirement of the question, we have to evaluate whether to replace the current machine with the proposed new one.

Basic computations for evaluating the above proposal are as follow:

	Current Machine	Proposed Machine
Depreciation	=Cost of machine ÷ Use full life
	=120000/6 = 20000	= 200000/5 = 40000
Earning before tax (EBT)	=EBITDA - Interest - Depreciation
	=45000-0-20000 =25000	=100000-0-40000 =60000
Earning after tax (EAT)	=EBT × (1-taxrate)
	=25000 × (1-0.45) =13750	=60000 × (1-0.45) =33000
Cashflow per year	=EAT+Depreciation
	=13750+20000 =33750	=33000+40000 =73000
Present value of yearly cash Flow	=sum of { cashflows ÷ (1 + r)^n } Where r = cost of capital = 12% i.e 0.12 (assumed post tax) n= period i.e 1,2,3,4 & 5
	={ 33750 ÷ (1 + 0.12)^1 } + { 33750 ÷ (1 + 0.12)^2 } + { 33750 ÷ (1 + 0.12)^3 } + { 33750 ÷ (1 + 0.12)^4 } + { 33750 ÷ (1 + 0.12)^5 } = 30133.93 + 26905.29 + 24022.58 + 21448.74 + 19150.66 =121661 (r.off)	={ 73000 ÷ (1 + 0.12)^1 } + { 73000 ÷ (1 + 0.12)^2 } + { 73000 ÷ (1 + 0.12)^3 } + { 73000 ÷ (1 + 0.12)^4 } + { 73000 ÷ (1 + 0.12)^5 } = 65178.57 + 58195.15 + 51959.96 + 46392.82 + 41422.16 = 263149 (r.off)

Written down value (WDV) of the current machinery	= Cost of machinery - depreciation till date Where Depreciation till date = 20000 since it has been used for only 1 year Hence WDV = 120000 - 20000 =100000
Loss on sale of current machinery	=WDV of the machinery - Market value of the machinery = 100000 - 80000 = 20000

let's evaluate the above proposal:

New Machinery

The net present value of cash flows from new machinery if it replaces the current machine is as follows

	The present value of yearly cash inflow flow	263149
Add:	Tax saving on sale of current machinery = Loss on sale × tax rate	= 20000 × 0.45 = 9000
Add:	Sale proceeds of current machinery	80000
Less:	The purchase cost of new machine	200000
Net present value		$152149

Existing current Machinery

The net present value of cash flow from old machinery if it is not replaced by the new one would be the present value of yearly cashflow i.e $121661

Conclusion:

Hence based on the above evaluation it is more profitable to replace the old machine with the new one since replacing the existing machine with the new machine generate higher net present value than continuing with the existing machine.