Question

You are considering a proposal to produce and market a new sluffing machine. The most likely outcomes for the project are as follows:

Expected sales: 30,000 units per year

Unit price: $50

Variable cost: $30

Fixed cost: $300,000

The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 30%, and the required rate of return is 12%.

However, you recognize that some of these estimates are subject to error. Sales could fall 30% below expectations for the life of the project and, if that happens, the unit price would probably be only $40. The good news is that fixed costs could be as low as $200,000, and variable costs would decline in proportion to sales.

a. What is project NPV if all variables are as expected? (Do not round intermediate calculations. Enter your answer in thousands not in millions and round your answer to the nearest whole dollar amount.)

b. What is NPV in the worst-case scenario? (Do not round intermediate calculations. Enter your answer in thousands not in millions and round your answer to the nearest whole dollar amount. Negative amount should be indicated with a minus sign.)

Answer 1

Part A:

NPV :
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.
Dep per anum = [ COst - Salvage Value ] / Life

= [ $ 1000000 - 0 ] / 10

= $ 100000

Cash flow = PAT + Dep

PAT = profit after tax

Assumption: Dep is in addition to Fixed Cost

Particulars	Amount	Formula	Calculation
Sales	$ 15,00,000.00	Qty * price	30000*50
Variable cost	$   9,00,000.00	Qty * VC	30000*30
Fixed Cost	$   3,00,000.00	Given
Dep	$   1,00,000.00	Calculated
PBT	$   2,00,000.00	Sales- Total Cost	1.5M - 1.3M
Tax @30%	$      60,000.00	PBT * tax Rate	200000*30%
PAT	$   1,40,000.00	PBT - Tax	200000 - 60000
Cash Flow	$   2,40,000.00	PAT + Dep	140000 + 100000

NPV:

Year	Cash Flow	PVF @12 %	Disc CF
0	$         -10,00,000.00	1.0000	$        -10,00,000.00
1 - 10	$             2,40,000.00	5.6502	$         13,56,053.53
NPV			$           3,56,053.53

Best case NPV is $ 356053.53

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Part B:

Particulars	Amount	Formula	Calculation
Sales	$   8,40,000.00	Qty * price	21000*40
Variable cost	$ 6,30,000.00	Qty * VC	21000*30
Fixed Cost	$   2,00,000.00	Given
Dep	$   1,00,000.00	Calculated
PBT	$   -90,000.00	Sales- Total Cost	840000 - 930000
Tax @30%	$   -27,000.00	PBT * tax Rate	-90000*30%
PAT	$   -63,000.00	PBT - Tax	-90000-(-27000)
Cash Flow	$    37,000.00	PAT + Dep	-63000+100000

NPV:

Year	Cash Flow	PVF @12 %	Disc CF
0	$         -10,00,000.00	1.0000	$        -10,00,000.00
1 - 10	$                37,000.00	5.6502	$           2,09,058.25
NPV			$         -7,90,941.75

Worst case NPV is $ - 790941.75