Question

ABC Ltd. is contemplating have an access to a machine for a period of 5 years. The company can have use of the machine for the stipulated period through leasing arrangement or the requisite amount can be borrowed to buy the machine. In case of leasing, the company received a proposal to pay annual end of year rent of $240,000 for a period of 5 years

In case of purchase (which cost $1000,000) the company would have a 12%, 5 years loan to be paid in equated installments, each installment becoming due to the beginning of each years. It is estimated that the machine can be sold for $200,000 at the end of 5th year. The company used straight line method of depreciation. Corporate tax rate is 30%. Post tax cost of capital of ABC is 10%

You are required to advise:

Whether the machine should be bought or taken on lease

Answer 1

Step 1: Calculate the Amount of Loan Installment

The amount of loan installment can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV,1) where Rate = Interest Rate, Nper = Period, PV = Present Value, FV =Future Value (if any) and 1 indicates Annuity Due (as payments are made at the beginning of each year).

Here, Rate = 12%, Nper = 5, PV = $1,000,000 and FV = 0

Using these values in the above function/formula for PMT, we get,

Amount of Loan Installment = PMT(12%,5,1000000,0,1) = $247,687

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Step 2: Calculate Amount of Annual Interest Payment on Loan

The amount of annual interest payment on loan is determined as below:

Year	Annual Loan Installment (A)	Annual Interest (B)	Principal Repayment (A-B)	Balance
				1,000,000
0	247,687	0	247,687	752,313
1	247,687	90,278 (12%*752,313)	157,410	594,903
2	247,687	71,388 (12%*594,903)	176,299	418,604
3	247,687	50,232 (12%*418,604)	197,455	221,149
4	247,687	26,538 (221,149*12%)	221,149	0
5	0	0

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Step 3: Calculate Annual Cash Outflows Associated with Loan Alternative

The annual cash outflows associated with the loan alternative are calculated as follows:

	End of Year
	0	1	2	3	4	5
Loan Installment	247,687	247,687	247,687	247,687	247,687	0
Interest		90,278	71,388	50,232	26,538	0
Annual Depreciation [(1,000,000 - 200,000)/5]		160,000	160,000	160,000	160,000	160,000
Tax Shield [Interest+Depreciation)*Tax Rate]		75,083	69,417	63,070	55,961	48,000
Net Cash Outflow [Loan Installment - Tax Shield]	$247,687	$172,604	$178,271	$184,618	$191,726	-$48,000

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Step 4: Calculate Present Value of Annual Cash Outflows Associated with Loan Alternative

The present value of annual cash outflows associated with loan alternative is determined as below:

Present Value of Annual Cash Outflows Associated with Loan Alternative = Cash Flow Year 0/(1+Cost of Capital)^0 + Cash Flow Year 1/(1+Cost of Capital)^1 + Cash Flow Year 2/(1+Cost of Capital)^2 + Cash Flow Year 3/(1+Cost of Capital)^3 + Cash Flow Year 4/(1+Cost of Capital)^4 + Cash Flow Year 5/(1+Cost of Capital)^5 - Salvage Value/(1+Cost of Capital)^5

Present Value of Annual Cash Outflows Associated with Loan Alternative = 247,687/(1+10%)^0 + 172,604/(1+10%)^1 + 178,271/(1+10%)^2 + 184,618/(1+10%)^3 + 191,726/(1+10%)^4 - 48,000/(1+10%)^5 - 200,000/(1+10%)^5 = $667,600

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Step 6: Calculate Present Value of Annual Cash Outflows Associated with Leasing Alternative

The present value of annual cash outflows associated with leasing alternative is arrived as follows:

Present Value of Annual Cash Outflows Associated with Leasing Alternative = Annual Lease Payment*(1-Tax Rate)*PVIFA(Interest Rate,Years) = 240,000*(1-30%)*PVIFA(10%,5) = 168000*3.7908 = $636,852

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Step 7: Take Decision

The final decision would be to take the machine on lease as it results in a lower present value of net cash outlows.