Question

Use the following information to answers questions 13 to 15. (Short Answer – Chapter 7) The Quorum Company has a prospective 6-year project that requires initial fixed assets costing $963,000, annual fixed costs of $403,400, variable costs per unit of $123.60, a sales price per unit of $249, a discount rate of 14 percent, and a tax rate of 21 percent. The asset will be depreciated straight-line to zero over the life of the project.

1.Compute the accounting break even sales quantity

2. At what sales quantity per year will the investment break even on a financial basis?

3. Explain in words why is there a difference between the two answers?

Answer 1

1. Accounting BP is where there is no profit
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   • As units cant be fractional, the next highest integer = 3127 units
2. Following is the NPV schedule. We need to use the excel's goal seek to find the financial BEP i.e. the point where NPV = 0

   • Particulars	Remark	0	1	2	3	4	5	6
     Units Sold	Calculated using excel's goal seek function		5376.452752	5376.452752	5376.452752	5376.452752	5376.452752	5376.452752
     SP	Given		249	249	249	249	249	249
     Sales	SP x Units		$ 13,38,736.74	$ 13,38,736.74	$ 13,38,736.74	$ 13,38,736.74	$ 13,38,736.74	$ 13,38,736.74
     VC per unit	Given		$             123.60	$             123.60	$             123.60	$             123.60	$             123.60	$             123.60
     Total VC	VC per unit x Units		$    6,64,529.56	$    6,64,529.56	$    6,64,529.56	$    6,64,529.56	$    6,64,529.56	$    6,64,529.56
     Fixed cost	Given		$    4,03,400.00	$    4,03,400.00	$    4,03,400.00	$    4,03,400.00	$    4,03,400.00	$    4,03,400.00
     EBITDA	Sales-Total VC-Fixed Cost		$    2,70,807.18	$    2,70,807.18	$    2,70,807.18	$    2,70,807.18	$    2,70,807.18	$    2,70,807.18
     Depreciation	963000/6		$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00
     EBT	EBITDA-Depreciation		$    1,10,307.18	$    1,10,307.18	$    1,10,307.18	$    1,10,307.18	$    1,10,307.18	$    1,10,307.18
     Tax	21% x EBT		$       23,164.51	$       23,164.51	$       23,164.51	$       23,164.51	$       23,164.51	$       23,164.51
     EAT	EBT-Tax		$       87,142.67	$       87,142.67	$       87,142.67	$       87,142.67	$       87,142.67	$       87,142.67
     Depreciation	Added back as non cash		$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00	$    1,60,500.00
     OCF	EAT+Depreciation		$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67
     FCINV	Given	$ -9,63,000.00
     FCF	OCF+FCINV	$ -9,63,000.00	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67	$    2,47,642.67
     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	1/1.14^5	1/1.14^6
     Discount factor	Calculated using above formula	1	0.877192982	0.769467528	0.674971516	0.592080277	0.519368664	0.455586548
     DCF	FCF x Discount Factor	-963000	217230.4108	190552.9919	167151.7473	146624.3397	128617.8419	112822.6683
     NPV = sum of all DCF	0

   • As the quantity cant be fractional we can say that financial BEP is at 5377 units.
3. As accounting BEP only considers annual costs and revenues it shows a lower BEP units while the Financial BEP considers the initial investment and time value of money to calculate the BEP units, both the methods lead to different answer. Former looks at only annual BEP while the latter looks at the recovery of initial investment also..