Question

We are evaluating a project that costs $1,140,000, has a life of 10 years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 36,000 units per year. Price per unit is $50, variable cost per unit is $20, and fixed costs are $720,000 per year. The tax rate is 23 percent and we require a return of 12 percent on this project. a. Calculate the accounting break-even point. b-1. Calculate the base-case cash flow and NPV. b-2. What is the sensitivity of NPV to changes in the sales figure? c. What is the sensitivity of OCF to changes in the variable cost figure?

Answer 1

Part a:

So if the company produces 24000 units, it will reach the accounting break even

Part b-1: Following steps need to be taken:

1. Calculate depreciation
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2. Calculate annual CF for years 1-10

   • Particulars	Remark	CF years 1-10
     Units sales	Given	36000
     SP	Given	50
     Sales	SP x Unit sales	50 x 36000 = 1800000
     VC per unit	Given	20
     Total Variable cost	VC per unit x Unit sales	20 x 36000 = 720000
     Fixed cost	Given	720000
     EBITDA	Sales-Total Variable cost-Fixed Cost	1800000-720000-720000 = 360000
     Depreciation	Calculated above	$ 114,000.00
     EBT	EBITDA-Depreciation	$ 2,46,000.00
     Tax	23% x EBT	$56,580.00
     EAT	EBT-Tax	$ 1,89,420.00
     Depreciation	Added back as non cash	114000
     OCF	EAT+Depreciation	$ 3,03,420.00

3. Calculate NPV

   • Year	CF	Discount Factor		Discounted CF
     0	$   -11,40,000.00	1/(1+0.12)^0=	1	1*-1140000=	$   -11,40,000.00
     1	$       3,03,420.00	1/(1+0.12)^1=	0.892857	0.892857142857143*303420=	$       2,70,910.71
     2	$       3,03,420.00	1/(1+0.12)^2=	0.797194	0.79719387755102*303420=	$       2,41,884.57
     3	$       3,03,420.00	1/(1+0.12)^3=	0.71178	0.711780247813411*303420=	$       2,15,968.36
     4	$       3,03,420.00	1/(1+0.12)^4=	0.635518	0.635518078404831*303420=	$       1,92,828.90
     5	$       3,03,420.00	1/(1+0.12)^5=	0.567427	0.567426855718599*303420=	$       1,72,168.66
     6	$       3,03,420.00	1/(1+0.12)^6=	0.506631	0.506631121177321*303420=	$       1,53,722.01
     7	$       3,03,420.00	1/(1+0.12)^7=	0.452349	0.452349215336893*303420=	$       1,37,251.80
     8	$       3,03,420.00	1/(1+0.12)^8=	0.403883	0.403883227979369*303420=	$       1,22,546.25
     9	$       3,03,420.00	1/(1+0.12)^9=	0.36061	0.36061002498158*303420=	$       1,09,416.29
     10	$       3,03,420.00	1/(1+0.12)^10=	0.321973	0.321973236590696*303420=	$           97,693.12
     				NPV = Sum of all Discounted CF	$       5,74,390.67

   • So NPV =  $574,390.67
   • Positive NPV suggests we should invest in the project

Part b-2: Lets increase and decrease the sales by 1% and see the impact of the same on NPV

Following is the table showing the change in OCF:

Particulars	Base Case	1%	-1%
Units sales	36000	36000	36000
SP	50	50.5	49.5
Sales	1800000	1818000	1782000
VC per unit	20	20	20
Total Variable cost	720000	720000	720000
Fixed cost	720000	720000	720000
EBITDA	360000	378000	342000
Depreciation	$ 1,14,000.00	114000	114000
EBT	$ 2,46,000.00	$    2,64,000.00	$ 2,28,000.00
Tax	$     56,580.00	$       60,720.00	$     52,440.00
EAT	$ 1,89,420.00	$    2,03,280.00	$ 1,75,560.00
Depreciation	114000	114000	114000
OCF	$ 3,03,420.00	$    3,17,280.00	$ 2,89,560.00

NPV Calculation is as follows:

Year	CF	Discount Factor		Discounted CF
0	$   -11,40,000.00	1/(1+0.12)^0=	1	1*-1140000=	$   -11,40,000.00
1	$       3,17,280.00	1/(1+0.12)^1=	0.892857	0.892857142857143*317280=	$       2,83,285.71
2	$       3,17,280.00	1/(1+0.12)^2=	0.797194	0.79719387755102*317280=	$       2,52,933.67
3	$       3,17,280.00	1/(1+0.12)^3=	0.71178	0.711780247813411*317280=	$       2,25,833.64
4	$       3,17,280.00	1/(1+0.12)^4=	0.635518	0.635518078404831*317280=	$       2,01,637.18
5	$       3,17,280.00	1/(1+0.12)^5=	0.567427	0.567426855718599*317280=	$       1,80,033.19
6	$       3,17,280.00	1/(1+0.12)^6=	0.506631	0.506631121177321*317280=	$       1,60,743.92
7	$       3,17,280.00	1/(1+0.12)^7=	0.452349	0.452349215336893*317280=	$       1,43,521.36
8	$       3,17,280.00	1/(1+0.12)^8=	0.403883	0.403883227979369*317280=	$       1,28,144.07
9	$       3,17,280.00	1/(1+0.12)^9=	0.36061	0.36061002498158*317280=	$       1,14,414.35
10	$       3,17,280.00	1/(1+0.12)^10=	0.321973	0.321973236590696*317280=	$       1,02,155.67
				NPV = Sum of all Discounted CF	$       6,52,702.76

Year	CF	Discount Factor		Discounted CF
0	$   -11,40,000.00	1/(1+0.12)^0=	1	1*-1140000=	$   -11,40,000.00
1	$       2,89,560.00	1/(1+0.12)^1=	0.892857	0.892857142857143*289560=	$       2,58,535.71
2	$       2,89,560.00	1/(1+0.12)^2=	0.797194	0.79719387755102*289560=	$       2,30,835.46
3	$       2,89,560.00	1/(1+0.12)^3=	0.71178	0.711780247813411*289560=	$       2,06,103.09
4	$       2,89,560.00	1/(1+0.12)^4=	0.635518	0.635518078404831*289560=	$       1,84,020.61
5	$       2,89,560.00	1/(1+0.12)^5=	0.567427	0.567426855718599*289560=	$       1,64,304.12
6	$       2,89,560.00	1/(1+0.12)^6=	0.506631	0.506631121177321*289560=	$       1,46,700.11
7	$       2,89,560.00	1/(1+0.12)^7=	0.452349	0.452349215336893*289560=	$       1,30,982.24
8	$       2,89,560.00	1/(1+0.12)^8=	0.403883	0.403883227979369*289560=	$       1,16,948.43
9	$       2,89,560.00	1/(1+0.12)^9=	0.36061	0.36061002498158*289560=	$       1,04,418.24
10	$       2,89,560.00	1/(1+0.12)^10=	0.321973	0.321973236590696*289560=	$           93,230.57
				NPV = Sum of all Discounted CF	$       4,96,078.58

Sensitivity of NPV is shown in the below table:

Particulars	Base Case	1%	-1%
Sales	$           18,00,000.00	$           18,18,000.00	$           17,82,000.00
NPV	$             5,74,390.67	$             6,52,702.76	$             4,96,078.58
Percentage change		652701.76/574390.67 -1 =14%	496078.58/574390.67 -1 = -14%

So with a change of 1% in the sales, the NPV changes by 14% in the same direction as sales.

Part C:

Particulars	Base Case	1%	-1%
Units sales	36000	36000	36000
SP	50	50	50
Sales	$ 18,00,000.00	$ 18,00,000.00	$ 18,00,000.00
VC per unit	20	20.2	19.8
Total Variable cost	720000	727200	712800
Fixed cost	720000	720000	720000
EBITDA	360000	352800	367200
Depreciation	$    1,14,000.00	114000	114000
EBT	$    2,46,000.00	$    2,38,800.00	$    2,53,200.00
Tax	$       56,580.00	$       54,924.00	$       58,236.00
EAT	$    1,89,420.00	$    1,83,876.00	$    1,94,964.00
Depreciation	114000	114000	114000
OCF	$    3,03,420.00	$    2,97,876.00	$    3,08,964.00
Percentage change		2,97,876.00/3,03,420.00 -1 = -1.83%	3,08,964.00/3,03,420.00-1 = 1.83%

So with a change of 1% in the Variable coast per unit, the OCF changes by 1.83% in the opposite direction.