Question

1. You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 160 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%.     (17 marks total)

a. Based on your experience, the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ± 10%. What are the upper and lower bounds for these projections for unit sales, variable cost, and fixed cost?       

b. What is the base-case NPV?                                                         (1 mark)

c. What are the NPVs in the best-case and worst-case scenarios?          

d. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.                                                                                                  (2.5 marks)

e. What is this project’s cash break-even level of output (ignoring taxes)? (1 mark)

f.   What is the accounting break-even level of output for this project, and what is the degree of operating leverage (DOL) at the accounting break-even point? How do you interpret this DOL number?                                          (2.5 marks)

g. What is the financial break-even level of output for this project, and what is the degree of operating leverage (DOL) at the financial break-even point? How do you interpret this DOL number?                                                 

Answer 1

Part a:

Scenarios	Base Case	Worst Case	Best Case
Unit sales	160	144	176
VC per unit	14000	15400	12600
VC	2240000	2217600	2217600
Fixed Cost	150000	165000	135000

• Base case figures are given. VC = VC per unit x Unit Sales
• Worst Case:
  • Unit sales = Base case sales x 0.9 =160 x 0.9 =144
  • VC per unit = Base case VC per unit x 1.10 = 14000 x 1.10 = 15400
  • Fixed Cost = Base case Fixed Cost x 1.10 = 150000 x 1.10 = 165000
• Best Case:
  • Unit sales = Base case sales x 1.10 =160 x 1.10 =176
  • VC per unit = Base case VC per unit x 0.90 = 14000 x 0.90 = 12600
  • Fixed Cost = Base case Fixed Cost x 1.10 = 150000 x 0.90 = 135000

Part B: Base case NPV is calculated below

Base case
Year	Remark	0	1	2	3	4
Unit sales	Given		160	160	160	160
SP	Given		19000	19000	19000	19000
VC per unit	Given		14000	14000	14000	14000
Sales	SP x Unit Sales		3040000	3040000	3040000	3040000
VC	VC per unit x Unit Sales		2240000	2240000	2240000	2240000
Fixed Cost	Given		150000	150000	150000	150000
EBITDA	Sales - CV -Fixed Cost		650000	650000	650000	650000
Depreciation	Calculated		170000	170000	170000	170000
EBT	EBITDA-Depreciation		480000	480000	480000	480000
Taxes	0.35 x EBT		168000	168000	168000	168000
EAT	EBT-Taxes		312000	312000	312000	312000
Depreciation	Added back as Non Cash		170000	170000	170000	170000
OCF	EAT+Depreciation		482000	482000	482000	482000
FCINV	Given	-680000
FCF	OCF+FCINV	-680000	482000	482000	482000	482000
Discount factor formula		1/1.15^0	1/1.15^1	1/1.15^2	1/1.15^3	1/1.15^4
Discount factor		1	0.869565217	0.756143667	0.657516232	0.571753246
DCF	Discount factor x xFCF	-680000	419130.4348	364461.2476	316922.824	275585.0644
NPV	Sum of all DCF	696099.5708

Part C: NPVs in the best-case and worst-case scenarios are calculated below:

Worst case
Year	Remark	0	1	2	3	4
Unit sales	Given		144	144	144	144
SP	Given		19000	19000	19000	19000
VC per unit	Given		15400	15400	15400	15400
Sales	SP x Unit Sales		2736000	2736000	2736000	2736000
VC	VC per unit x Unit Sales		2217600	2217600	2217600	2217600
Fixed Cost	Given		165000	165000	165000	165000
EBITDA	Sales - CV -Fixed Cost		353400	353400	353400	353400
Depreciation	Calculated		170000	170000	170000	170000
EBT	EBITDA-Depreciation		183400	183400	183400	183400
Taxes	0.35 x EBT		64190	64190	64190	64190
EAT	EBT-Taxes		119210	119210	119210	119210
Depreciation	Added back as Non Cash		170000	170000	170000	170000
OCF	EAT+Depreciation		289210	289210	289210	289210
FCINV	Given	-680000
FCF	OCF+FCINV	-680000	289210	289210	289210	289210
Discount factor formula		1/1.15^0	1/1.15^1	1/1.15^2	1/1.15^3	1/1.15^4
Discount factor		1	0.869565217	0.756143667	0.657516232	0.571753246
DCF	Discount factor x xFCF	-680000	251486.9565	218684.31	190160.2696	165356.7562
NPV	Sum of all DCf	145688.2923

Best case
Year	Remark	0	1	2	3	4
Unit sales	Given		176	176	176	176
SP	Given		19000	19000	19000	19000
VC per unit	Given		12600	12600	12600	12600
Sales	SP x Unit Sales		3344000	3344000	3344000	3344000
VC	VC per unit x Unit Sales		2217600	2217600	2217600	2217600
Fixed Cost	Given		135000	135000	135000	135000
EBITDA	Sales - CV -Fixed Cost		991400	991400	991400	991400
Depreciation	Calculated		170000	170000	170000	170000
EBT	EBITDA-Depreciation		821400	821400	821400	821400
Taxes	0.35 x EBT		287490	287490	287490	287490
EAT	EBT-Taxes		533910	533910	533910	533910
Depreciation	Added back as Non Cash		170000	170000	170000	170000
OCF	EAT+Depreciation		703910	703910	703910	703910
FCINV	Given	-680000
FCF	OCF+FCINV	-680000	703910	703910	703910	703910
Discount factor formula		1/1.15^0	1/1.15^1	1/1.15^2	1/1.15^3	1/1.15^4
Discount factor		1	0.869565217	0.756143667	0.657516232	0.571753246
DCF	Discount factor x xFCF	-680000	612095.6522	532257.0888	462832.2512	402462.8271
NPV	Sum of all DCf	1329647.819

Part d: To evaluate the sensitivity of base case NPV to fixed cost, we increase the fixed cost by 1% and decrease it by 1%, then we calculate the NPV under each case keeping all other values constant. We get the following table

Fixed Cost	150000	150000 x 0.99 = 148500	150000 x 1.01= 151500
NPV	696099.57	698883.175	693315.97
Sensitivity		698883.175/696099.57 - 1 = 0.40%	693315.97/696099.57 - 1 = -0.40%

So with every 1% change in the fixed cost, the NPV changes by 0.40% in the inverse direction

Part e:

Part f:

DOL implies how much of the company's operating income will change if sales changes, so if sales changes by $1.88 the operating income will change by $1

Part g: Financial BEP is when the NPV = 0

As number of units cant be fractional, the financial BEP units = 85

Best case
Year	Remark	0	1	2	3	4
Unit sales	Given		84.97859664	84.97859664	84.97859664	84.97859664
SP	Given		19000	19000	19000	19000
VC per unit	Given		14000	14000	14000	14000
Sales	SP x Unit Sales		1614593.336	1614593.336	1614593.336	1614593.336
VC	VC per unit x Unit Sales		1189700.353	1189700.353	1189700.353	1189700.353
Fixed Cost	Given		150000	150000	150000	150000
EBITDA	Sales - CV -Fixed Cost		274892.9832	274892.9832	274892.9832	274892.9832
Depreciation	Calculated		170000	170000	170000	170000
EBT	EBITDA-Depreciation		104892.9832	104892.9832	104892.9832	104892.9832
Taxes	0.35 x EBT		36712.54412	36712.54412	36712.54412	36712.54412
EAT	EBT-Taxes		68180.43908	68180.43908	68180.43908	68180.43908
Depreciation	Added back as Non Cash		170000	170000	170000	170000
OCF	EAT+Depreciation		238180.4391	238180.4391	238180.4391	238180.4391
FCINV	Given	-680000
FCF	OCF+FCINV	-680000	238180.4391	238180.4391	238180.4391	238180.4391
Discount factor formula		1/1.15^0	1/1.15^1	1/1.15^2	1/1.15^3	1/1.15^4
Discount factor		1	0.869565217	0.756143667	0.657516232	0.571753246
DCF	Discount factor x xFCF	-680000	207113.4253	180098.6307	156607.5049	136180.4391
NPV	Sum of all DCf	0

DOL implies how much of the company's operating income will change if sales changes, so if sales changes by $1.54 the operating income will change by $1