Question

2) Bart and Millhouse own a small factory that manufactures rubber snakes used to scare away birds from houses, gardens and playgrounds. A recent and unexplained increase in the bird population in Springfield has significantly increased the demand for
rubber snakes. To take advantage of this opportunity, Bart and Millhouse plan to add a new molding machine that will double the output of their existing facility. The cost of the new machine is $20,000. With this purchase, current assets must increase by $5,000 and current liabilities will increase by $3,000. The economic life of the machine is 4 years, and it falls under the MACRS three year depreciation schedule. The machine is expected to be obsolete at the end of the fourth year and have no salvage value.

Bart and Millhouse anticipate recouping 100% of the additional investment in net working capital at the end of year 4. Sales are expected to increase by $20,000 each year in year 1 and 2 and by $10,000 each year in year 3 and 4. The increase in operating expenses is estimated to be 20% of the annual change in sales. Assume that the marginal tax rate is 40%.

Assume that the company’s discount rate is 14%. Calculate the NPV of this project. Would you recommend that Bart and Millhouse add this machine to their factory?

Answer 1

Depreciation Schedule is as follows:

Year	Depreciation rate	Depreciation	BV at the end of the year
1.00	33.33%	$          6,666.00	$           13,334.00
2.00	44.45%	$          8,890.00	$              4,444.00
3.00	14.81%	$          2,962.00	$              1,482.00
4.00	7.41%	$          1,482.00	$                           -

NPV is calculated below:

Particulars	Remark	0	1	2	3	4
Sales Increase	Given		$       20,000.00	$       20,000.00	$       10,000.00	$       10,000.00
Opex	20% of sales increase		$          4,000.00	$          4,000.00	$          2,000.00	$          2,000.00
EBITDA	Sales increase - Opex		$       16,000.00	$       16,000.00	$          8,000.00	$          8,000.00
Depreciation	Given		$          6,666.00	$          8,890.00	$          2,962.00	$          1,482.00
EBT	EBITDA-Depreciation		$          9,334.00	$          7,110.00	$          5,038.00	$          6,518.00
Tax	0.40% x EBT		$          3,733.60	$          2,844.00	$          2,015.20	$          2,607.20
EAT	EBT-Tax		$          5,600.40	$          4,266.00	$          3,022.80	$          3,910.80
Depreciation	Added back as non cash		$          6,666.00	$          8,890.00	$          2,962.00	$          1,482.00
OCF	EAT+Depreciation		$       12,266.40	$       13,156.00	$          5,984.80	$          5,392.80
FCINV	Given	$       -20,000.00
WCINV	5000-3000	$          -2,000.00				$          2,000.00
FCF	OCF+FCINV+WCINV	$       -22,000.00	$       12,266.40	$       13,156.00	$          5,984.80	$          7,392.80
Discount factor Formula	at 14 %	1/(1+14)^0	1/(1+14)^1	1/(1+14)^2	1/(1+14)^3	1/(1+14)^4
Discount factor	Calculated using above formula	1	0.877192982	0.769467528	0.674971516	0.592080277
DCF	FCF x Discount Factor	$       -22,000.00	$       10,760.00	$       10,123.11	$          4,039.57	$          4,377.13
NPV = sum of all DCF	$                                 7,299.82

As NPV is positive,the project should be invested in