Question

Assume that laban Company is considering the purchase of a newer, more efficient yogurt-making
machine. If purchased, it would require the new machine on January 2, year 1. laban expects to sell
600,000 gallons of yogurt in each of the next five years at a $2 per gallon selling price.
laban has two options:

(1) continue to operate the old machine purchased four years ago or
(2) sell it and purchase the new machine.

The following information has been prepared to help decide which option is more desirable.

	old machine	new machine
Original cost of machine at acquisition	$1,600,000	$2,000,000
Useful life from date of acquisition	7 years	5 years
Expected annual cash operating expenses:
variable cost per gallon	$1.20	$1.00
total fixed cash costs	$400,000	$160,000

depreciation is as follows:

age of equipment (years)	tax depreciation rate
1	15%
2	25%
3	20%
4	20%
5	20%

Estimated cash value of machines follows:	old machine	new machine
January 2, year 1	$ 400,000	$ 2,000,000
31 December, year 3	$ 200,000	$ 1,000,000

laban is subject to a 40% income tax rate on all income. Assume that tax depreciation is calculated
without regard to salvage value. Use an after-tax discount rate of 10%.

Answer 1

Solution.

Step 1: Calculate after tax Income in both the option. In this case we will calculate 3 year operation income and loss as old machine can be used for 3 more years.

Option 1 Sell it and purchase new machine

Option 2 continue with old machine and sale after 3 years

Step 2: Calculate Net Cash Inflow / (Outflow) as per following

After Tax Income / (Loss) + Depreciation + sale value of machine - New machine cost

Step 3: Calculate incremental Cash Flow

Step 4: Discount incremental cash flow with discount rate 10%

		0	1	2	3
Net Operating Income of new machine			1,200,000	1,200,000	1,200,000
Less: Operating Expenses			(600,000)	(600,000)	(600,000)
Less: Fixed Cost			(160,000)	(160,000)	(160,000)
Less: Depreciation			(300,000)	(500,000)	(400,000)
Add: Profit on sale of Machine		80,000			200,000
Taxable Income	A	80,000	140,000	(60,000)	240,000
Taxation	B	32,000	56,000	(24,000)	96,000
Profit After Tax	C = A-B	48,000	84,000	(36,000)	144,000
Purchase of Machine	D	(2,000,000)
Sale of Machine	E	400,000			1,000,000
Depreciation	F	-	300,000	500,000	400,000
Cash Inflow / (Outflow)	G = (C+D+E+F)	(1,552,000)	384,000	464,000	1,544,000
Net Operating Income of old machine			1,200,000	1,200,000	1,200,000
Less: Operating Expenses			(720,000)	(720,000)	(720,000)
Less: Fixed Cost			(400,000)	(400,000)	(400,000)
Less: Depreciation			(320,000)	-	-
Add: Profit on sale of Machine					200,000
Taxable Income	H	-	(240,000)	80,000	280,000
Taxation	I	-	(96,000)	32,000	112,000
Profit After Tax	J = H-I	-	(144,000)	48,000	168,000
Sale of Machine	K				200,000
Depreciation	L	-	320,000	-	-
Cash Inflow / (Outflow)	M = J+K+L	-	176,000	48,000	368,000
Incremental FCF	N=G - M	(1,552,000)	208,000	416,000	1,176,000
PV factor @ 10%		1.00	0.91	0.83	0.75
NPV		(1,552,000)	189,091	343,802	883,546
Net NPV (Sum of all years)		(135,561)

Purchase of new machine is not viable option as it gives negative cash flow of $ 135,561

So continue with old machine Net Present value is higher of $ 135,561

Note: Tax on sale is calulated @ 40% of Net value which is Cost - Total depreciation claimed