Question

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $120. The materials cost for a standard diamond is $40. The fixed costs Incurred each year for factory upkeep and administrative expenses are $212,000. The machinery costs $2.2 million and is depreciated straight-line over 10 years to a salvage value of zero. a. What is the accounting break-even level of sales in terms of number of diamonds sold? Break-even sales b. What is the NPV break-even level of sales assuming a tax rate of 40%, a 10 year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Break-even sales

Answer 1

Accounting BEp can be calculated by solving the following formula:

(SP – VC) x BEP Accounting = Fixed cost

(120 – 40) x BEPAccounting = 212000

BEPAccounting = 2650

So at 2650 units, the firm will just cover the Fixed costs and not get any profits.

NPV BEP is calculated using the financial calculator or Excel's goal seek function:

Particulars	Remark	0	1	2	3	4	5	6	7	8	9	10
Units Sold	Given		8928.440857	8928.440857	8928.440857	8928.440857	8928.440857	8928.440857	8928.440857	8928.440857	8928.440857	8928.440857
SP	Given		120	120	120	120	120	120	120	120	120	120
Sales	SP x Units		$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90	$ 10,71,412.90
VC per unit	Given		$                40.00	$                40.00	$                40.00	$                40.00	$                40.00	$                40.00	$                40.00	$                40.00	$                40.00	$                40.00
Total VC	VC per unit x Units		$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63	$    3,57,137.63
Fixed cost	Given		$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00	$    2,12,000.00
EBITDA	Sales-Total VC-Fixed Cost		$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27	$    5,02,275.27
Depreciation	2.2million/10		$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00
EBT	EBITDA-Depreciation		$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27	$    2,82,275.27
Tax	0.40% x EBT		$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11	$    1,12,910.11
EAT	EBT-Tax		$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16	$    1,69,365.16
Depreciation	Added back as non cash		$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00	$    2,20,000.00
OCF	EAT+Depreciation		$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16
FCINV	Given	$ -22,00,000.00
FCF	OCF+FCINV	$ -22,00,000.00	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16	$    3,89,365.16
Discount factor Formula	at 12 %	1/(1+12)^0	1/(1+12)^1	1/(1+12)^2	1/(1+12)^3	1/(1+12)^4	1/(1+12)^5
Discount factor	Calculated using above formula	1	0.892857143	0.797193878	0.711780248	0.635518078	0.567426856	0.506631121	0.452349215	0.403883228	0.360610025	0.321973237
DCF	FCF x Discount Factor	$ -22,00,000.00	$    3,47,647.47	$    3,10,399.52	$    2,77,142.43	$    2,47,448.60	$    2,20,936.25	$    1,97,264.51	$    1,76,129.03	$    1,57,258.06	$    1,40,408.98	$    1,25,365.16
NPV = sum of all DCF	$                                       -0.00

NPV BEP sales =  $10,71,412.90 and the units are 8928.44. As units can't be fractional, we can say they are 8929 units.