Question

Man-U-Facturing Inc. will buy a machine that has a cost of $850,000 and is expected to be useful for 10 years. At the end of the 10th year, the firm intends to sell the machine for an estimated price of $52,036. In addition, the yearly benefits are expected to be $201,952 while the annual maintenance costs are predicted to be $51,300. The company uses a 9% interest rate for this project and it is currently being taxed at a flat tax rate of 21%. Assume Man-U-Facturing Inc. uses SOYD depreciation. What the is the after-tax net present value (NPV)?

Answer 1

We first need to calculate the annual depreciation schedule using the SOYD method:

Year	Calculation	Fraction of depreciation	Opening balance	Depreciation	Closing balance
1	10/55 =	0.181818182	$        7,97,964.00	$ 1,45,084.36	$      6,52,879.64
2	9/55 =	0.163636364	$        6,52,879.64	$ 1,30,575.93	$      5,22,303.71
3	8/55 =	0.145454545	$        5,22,303.71	$ 1,16,067.49	$      4,06,236.22
4	7/55 =	0.127272727	$        4,06,236.22	$ 1,01,559.05	$      3,04,677.16
5	6/55 =	0.109090909	$        3,04,677.16	$     87,050.62	$      2,17,626.55
6	5/55 =	0.090909091	$        2,17,626.55	$     72,542.18	$      1,45,084.36
7	4/55 =	0.072727273	$        1,45,084.36	$     58,033.75	$         87,050.62
8	3/55 =	0.054545455	$            87,050.62	$     43,525.31	$         43,525.31
9	2/55 =	0.036363636	$            43,525.31	$     29,016.87	$         14,508.44
10	1/55 =	0.018181818	$            14,508.44	$     14,508.44	$                    0.00
55

• Opening balance of year 1= Cost -salvage value
• Opening balance = previous year's closing balance for all years after year 1
• Sum of 1 to 10 = 55
• In year 1 there are 10 years left so the fraction of depreciation is 10/55 and similarly fraction of depreciation of all other years is calculated.
• Depreciation =fraction of depreciation rate x (850000-52036)
• Closing balance = Opening balance - depreciation

NPV is calculated as follows:

Particulars	Remark	0	1	2	3	4	5	6	7	8	9	10
Sales increase	Given		2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00	2,01,952.00
Cost increase	Given		51,300.00	51,300.00	51,300.00	51,300.00	51,300.00	51,300.00	51,300.00	51,300.00	51,300.00	51,300.00
EBITDA	Sales increase-Cost increase		1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00	1,50,652.00
Depreciation	As per above schedule		1,45,084.36	1,30,575.93	1,16,067.49	1,01,559.05	$    87,050.62	72542.18182	$ 58,033.75	$ 43,525.31	$ 29,016.87	$     14,508.44
EBT	EBITDA-Depreciation		5,567.64	20,076.07	34,584.51	49,092.95	63,601.38	78,109.82	92,618.25	1,07,126.69	1,21,635.13	1,36,143.56
Tax	21% x EBT		1,169.20	4,215.98	7,262.75	10,309.52	13,356.29	16,403.06	19,449.83	22,496.61	25,543.38	28,590.15
EAT	EBT-Tax		4,398.43	15,860.10	27,321.76	38,783.43	50,245.09	61,706.76	73,168.42	84,630.09	96,091.75	1,07,553.42
Depreciation	Added back as non cash		1,45,084.36	1,30,575.93	1,16,067.49	1,01,559.05	87,050.62	72,542.18	58,033.75	43,525.31	29,016.87	14,508.44
OCF	EAT+Depreciation		1,49,482.80	1,46,436.02	1,43,389.25	1,40,342.48	1,37,295.71	1,34,248.94	1,31,202.17	1,28,155.39	1,25,108.62	1,22,061.85
FCINV	Given	-8,50,000.00
FCF	OCF+FCINV	-8,50,000.00	1,49,482.80	1,46,436.02	1,43,389.25	1,40,342.48	1,37,295.71	1,34,248.94	1,31,202.17	1,28,155.39	1,25,108.62	1,22,061.85
Discount factor Formula	at 9 %	1/(1+0.09)^0	1/(1+0.09)^1	1/(1+0.09)^2	1/(1+0.09)^3	1/(1+0.09)^4	1/(1+0.09)^5	1/(1+0.09)^6	1/(1+0.09)^7	1/(1+0.09)^8	1/(1+0.09)^9	1/(1+0.09)^10
Discount factor	Calculated using above formula	1.00	0.92	0.84	0.77	0.71	0.65	0.60	0.55	0.50	0.46	0.42
DCF	FCF x Discount Factor	-8,50,000.00	1,37,140.18	1,23,252.27	1,10,722.81	99,422.15	89,232.79	80,048.26	71,772.08	64,316.87	57,603.49	51,560.25
NPV = sum of all DCF	35,071.14