Question

Your firm needs a $725,000 machine. If purchased, the machine will be depreciated straight-line over seven years and is expected to have a residual value of $25,000 at the end of the seventh year. Your (pre-tax) cost of borrowing is 6.5% and tax rate is 21%. If this is a non-tax lease, with beginning of year payments, what is the maximum lease payment for which you would prefer the lease to the alternative of borrowing money to buy the machine?

Answer 1

Answer :

Maximum lease payment for which you would prefer the lease to the alternative of borrowing money to buy the machine :

Steps to calculate :

1. Cost to be Capitalized if buy the machine = Cost of Machine - Residual Value = $ 725000 - $ 25000 = $ 700000/-

2. Discounting factor for six years as it is given that the payment of lease is started from beginning of the year. Therefore the period for discounting be taken as (t-1 ) i.e 6years ( 7 years -1 )

The Post tax cost of borrowing rate is 6.5% annually

3. Calculation of Cash flow :

Here we are calculating the amount of depreciation and the benefit of tax on depreciation to arrive lease rent

It is given that firm follows  straight-line depreciation on machin over seven years. Therefore

Depreciation per year = (Cost of Machine - Residual Value ) / Number of Years = ( $ 725000-$25000)/ 7years = $ 100,000 /- per year

Year	Depreciation per year	Tax benefit on Depreciation at tax rate 21% = Depreciation for the year x Tax Rate	Salvage Value	Total Cash Outflow
1	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
2	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
3	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
4	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
5	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
6	$100,000	= $ 100,000 x 21% = $ 21,000	0	= $ 100000 - $ 21000 = $ 79000
7	$100,000	= $ 100,000 x 21% = $ 21,000	$ 25000	= $ 100000 - $ 21000 -$ 25000 = $ 54000
	Total			$ 528,000

We further discounted it at ( Pre tax) rate 6.5% annually for 6 years as the first payment to be made at beginning of the year and tax rate is 21% therefore Post Tax rate be 5.1350% ( 6.5% x ( 1-21% )

Year	Cash Flow ( 1 )	Discounting Factor @ 5.1350% (2)	Discounted Cash Flow (3) = (1) x (2)
1	$ 79,000	1	= $ 79,000 x 1 = $ 79,000
2	$ 79,000	0.9512	= $ 79,000 x 0.9512 = $ 75,144.80
3	$ 79,000	0.9047	= $ 79,000 x 0.9047 = $ 71,471.30
4	$ 79,000	0.8606	= $ 79,000 x 0.8606 = $ 67,987.40
5	$ 79,000	0.8186	= $ 79,000 x 0.8186 = $ 64,669.40
6	$ 79,000	0.7787	= $ 79,000 x 0.7787 = $ 61,517.30
7	$ 54000	0.7407	= $ 54,000 x 0.7407 = $ 39,997.80
	Total		$ 459,788.00

Minimum Required Recovery Through Lease Rental = Cost of Machine - Discounted cash flow through Depreciation and other benefits = $ 725,000 - $ 459,788 = $ 265,212 /-

Post - Tax Lease Rental = Minimum Required Recovery Through Lease Rental / Annuity Discount Factor

= $ 265,212 / ( 1+0.9512+0.9047+0.8606+0.8186+0.7787+0.7407) = $ 265,212 / 6.0545 = $ 43804.11 /- Annually

Pre Tax Lease Rental = $ 43804.11 x 100 / ( 1 - 21% ) = $ 55448.24 /- Annually

Lease Rental per thousand per year = $ 55448.24 x 1000/ 725000 = $ 76.4803 /-