Question

Part I: Market Rate: 10% Company A will get a machine that costs $4,000 today. Machine has a lifetime of 4 years and will depreciate straight-line to zero at the end of its life. Tax rate is 20%.

The cash flow that the machine will create has the following details:

Revenue Per Year = Price*Quantity

Cost Per Year = Variable Cost*Quantity + Fixed Cost

where Price=m=3, Variable Cost is n=1, and Quantity is 1,600 units, and fixed cost is $500.

Company thinks the current NWC does not need to be increased in the face of the increased activity.

What is the NPV? (Clearly calculate the cash flow corresponding to years 0,1,2,3,and 4. Show your work.)

Part II: What is the annual accounting and financial break-even quantities?

Answer 1

Part I) NPV is calculated in the below schedule:

Particulars	Remark	0	1	2	3	4
Units Sold	Given		1600.00	$     1,600.00	$     1,600.00	$     1,600.00
SP	Given		$             3.00	$             3.00	$             3.00	$             3.00
Sales	SP x Units		$     4,800.00	$     4,800.00	$     4,800.00	$     4,800.00
VC per unit	Given		$             1.00	$             1.00	$             1.00	$             1.00
Total VC	Units x vc per unit		$     1,600.00	$     1,600.00	$     1,600.00	$     1,600.00
Fixed cost	Given		$         500.00	$         500.00	$         500.00	$         500.00
EBITDA	Sales-Total VC-Fixed Cost		$     2,700.00	$     2,700.00	$     2,700.00	$     2,700.00
Depreciation	4000/4 = 1000		$     1,000.00	$     1,000.00	$     1,000.00	$     1,000.00
EBT	EBITDA-Depreciation		$     1,700.00	$     1,700.00	$     1,700.00	$     1,700.00
Tax	40% x EBT		$         680.00	$         680.00	$         680.00	$         680.00
EAT	EBT-Tax		$     1,020.00	$     1,020.00	$     1,020.00	$     1,020.00
Depreciation	Added back as non cash		$     1,000.00	$     1,000.00	$     1,000.00	$     1,000.00
OCF	EAT+Depreciation		$     2,020.00	$     2,020.00	$     2,020.00	$     2,020.00
FCINV	Given	$ -4,000.00
FCF	OCF+FCINV	$ -4,000.00	$     2,020.00	$     2,020.00	$     2,020.00	$     2,020.00
Discount factor Formula	at 10 %	1/(1+0.1)^0	1/(1+0.1)^1	1/(1+0.1)^2	1/(1+0.1)^3	1/(1+0.1)^4
Discount factor	Calculated using above formula	1	0.909090909	0.826446281	0.751314801	0.683013455
DCF	FCF x Discount Factor	$ -4,000.00	$     1,836.36	$     1,669.42	$     1,517.66	$     1,379.69
NPV = sum of all DCF	$                                 2,403.13

So the NPV = 2403.13

Part II) Accounting BEP is calcualted through the following formula:

(SP - VC) x (Accounting BEP) = Fixed cost + depreciation (3 – 1) ~ (Accounting BEP) = 500 + 1000 1500 AccountingBEP = 2 AccountingbEp = 750 units

To find the financial BEP, the NPV should equal to 0 so the sum of Discounted OCF should add up to 4000

We are given the following information:

r	10.00%
n	4
PV	$              4,000.00

We need to solve the following equation to arrive at the required PCF

PV = OCF x 1-(1+r)-n 4000 = OCE 1-(1 +0.1)-4 0.1 OCF = 1261.88

OCF = ((SP - VC) (BEP) – Fixed cost – Depreciation) x (1 – tar rate) + Depreciation

OCF={{{SP-VC)x(BEP)- Fixed cost-depreciation) x(1-tax rate))+ Depreciation 1261.88 = (((3 – 1) x (BEP) - 500 – 1000) x (1 – 0.40))+1000 BEP = 968.24 tunits

As units cant be fractional we can say they are 969 units

Below is the NPV schedule to confirm the BEP

Particulars Remark Units Sold Given SP Given Sales SP x Units VC per unit Given Total vc Units x vc per unit Fixed cost Given EBITDA Sales-Total VC-Fixed Cost Depreciation 4000/4 = 1000 EBT EBITDA-Depreciation Тах 35% x EBT EAT ЕВТ-Тах Depreciation Added back as non cash OCF EAT+Depreciation FCINV Given FCF OCF+FCINV Discount factor Formula at 12% Discount factor Calculated using above formula DCF FCF x Discount Factor NPV = sum of all DCF $ 0.00 21 968.24 $ 968.24 $ 968.24 $ 968.24 $ 3.00 $ 3.00$ 3.00 $ 3.00 $ 2,904.71 $ 2,904.71 $ 2,904.71 $ 2,904.71 $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 968.24 $ 968.24 $ 968.24 $ 968.24 $ 500.00 $ 500.00 $ 500.00 $ 500.00 $ 1,436.47 $ 1,436.47 $ 1,436.47 $ 1,436.47 $ 1,000.00 $ 1,000.00 $ 1,000.00 $ 1,000.00 $ 436.47 $ 436.47 $ 436.47 $ 436.47 $ 174.59 $ 174.59 $ 174.59 $ 174.59 $ 261.88 $ 261.88 $ 261.88 $ 261.88 $ 1,000.00 $ 1,000.00 $ 1,000.00 $ 1,000.00 $ 1,261.88 $ 1,261.88 $ 1,261.88 $ 1,261.88 $-4,000.00 $-4,000.00 $ 1,261.88 $ 1,261.88 $ 1,261.88 $ 1,261.88 1/(1+0.1)^0 1/(1+0.1)^1 1/(1+0.1)^2 1/(1+0.1)^3 1/(1+0.1)^4 1 0.909090909 0.826446281 0.751314801 0.683013455 $-4,000.00 $ 1,147.17 $ 1,042.88 $ 948.07 $ 861.88