Question

Freedom Ltd is considering whether to lease or buy an advanced machine for its new product. The following information is available for this decision: Buy: The purchase price of the machine is $4.85 million. The machine will be depreciated using straight-line method over 4 years with a zero salvage value. Lease: The annual lease payments will be $1.1 million, payable at the beginning of each of the four years of the lease. The annual interest rate of secured debt is 11.67%. The corporate tax rate is 40%.

(b) Calculate the maximum amount of lease payment that Freedom Ltd is willing to pay. (Show your calculations).

Answer 1

Case 1 : On purchase of Machinary

Calculation of present value of future savings due to depreciation

Year	Savings ( In millions)	Tax Rate	Tax savings	Disc @ 11.67%	Discounted cash inflow due to Tax savings ( In millions)
1	$1.2125	0.4	$0.49	0.895495657	$0.43
2	$1.2125	0.4	$0.49	0.801912471	$0.39
3	$1.2125	0.4	$0.49	0.718109135	$0.35
4	$1.2125	0.4	$0.49	0.643063612	$0.31
					$1.48

Calcuation of Actual cost of Machinary

S.No	Particulars	Amount ( million)
A	Actual cost of Machinary	$4.85
	Less: Savings in taxation ( Since depreciation is claimed is expenditure due to that tax portion is reducred)	$1.48
	Net Cost of machinary	$3.37

So Actual cost of machinary after considering the taxation benefit is $ 3.37 millions

Case 2 :   When the Machinary is taken on hire basis

Year ( Beginning)	Cash outflow ( million )	Disc @ 11.67%	Discounted cash outlow ( million)
1	$1.10	1	$1.10
2	$1.10	0.895495657	$0.99
3	$1.10	0.801912471	$0.88
4	$1.10	0.718109135	$0.79
		3.415517264	$3.76

Since due to lease payments we are getting tax benefit in the form of reduction of tax

Computation of Tax inflow ( Reduction in tax ) due to lease payments

Year	Cash outflow ( million)	Tax rate	Tax inflow	Disc @ 11.67%	Discounted tax inflow ( million)
1	$1.10	0.4	$0.44	0.895495657	$0.39
2	$1.10	0.4	$0.44	0.801912471	$0.35
3	$1.10	0.4	$0.44	0.718109135	$0.32
4	$1.10	0.4	$0.44	0.643063612	$0.28
					$1.35

Computation of cost incurred due to lease paymet

Particulars	Amount ( Millions)
Annual lease payments ( Discounted)	$3.76
Less: Tax inflow	$1.35
Net cost of lease payments	$2.41

Decision: It is better to hire a machinary because the cost of machinary is higher than the lease payments

Net savings due to the above decision =  $ 3.37-$ 2.41

= $ 0.96

Maximum the company can bear total lease payment cost ( expressed in present value ) is $ 3.76

Let the Annual lease payment be X

Year ( Beginning )	Cash outflow	Disc @ 11.67%	Discounted cash outlow ( million $ )
1	X	1	X
2	X	0.8955	0.8955X
3	X	0.8019	0.8019X
4	X	0.7181	0.7181X
	Total	3.4155	3.4155X

Computation of tax benefit on lease payment

Year	Cash outflow ( million $ )	Tax rate	Tax inflow	Disc @ 11.67%	Discounted tax inflow ( million $ )
1	X	0.4	0.4X	0.8955	0.3582X
2	X	0.4	0.4X	0.8019	0.32076X
3	X	0.4	0.4X	0.7181	0.28724X
4	X	0.4	0.4X	0.6431	0.25724X
				3.0586	1.22344x

Computation of cost incurred due to lease paymet

Particulars	Amount ( million)
Annual lease payments ( Discounted)	$ 3.4155X
Less: Tax inflow	$ 1.22344X
Net cost of lease payments	$3.76

By writing the above content in the form of equation we get

$ 3.4155X - $ 1.22344X = $ 3.76

2.19206X = $ 3.76

X = $ 1.7152 millios

Maximum company can tolerate the lease payment is $ 1.7152 million p.a