Question

Consider the following project for Hand Clapper, Inc. The company is considering a 4-year project to manufacture clap-command garage door openers. This project requires an initial investment of $16.2 million that will be depreciated straight-line to zero over the project’s life. An initial investment in net working capital of $1,020,000 is required to support spare parts inventory; this cost is fully recoverable whenever the project ends. The company believes it can generate $13.3 million in revenues with $5.3 million in operating costs. The tax rate is 22 percent and the discount rate is 14 percent. The market value of the equipment over the life of the project is as follows:

  

Year	Market Value ($ millions)
1		$	14.20
2			11.20
3			8.70
4			2.05

  

a.	Assuming Hand Clapper operates this project for four years, what is the NPV?

b-1	Compute the project NPV assuming the project is abandoned after only one year.

b-2	Compute the project NPV assuming the project is abandoned after only two years.

b-3	Compute the project NPV assuming the project is abandoned after only three years.

Answer 1

1. NPV

the NPV= sum of all the present value of cash inflow- initial cost

so we need to find the present value of the free cash flow

	Initial	1	2	3	4
Initial investment- Cost of machinery	$                      -16,200,000
Additional working capital	$                        -1,020,000
Total capital required	$                      -17,220,000
Sales		$       13,300,000	$         13,300,000	$       13,300,000	$     13,300,000
-operating cost		$        -5,300,000	$          -5,300,000	$        -5,300,000	$      -5,300,000
-depreciation	16200000/4	$        -4,050,000	$          -4,050,000	$        -4,050,000	$      -4,050,000
EBIT		$          3,950,000	$           3,950,000	$          3,950,000	$       3,950,000
- Income tax	EBIT* 22%	$            -869,000	$             -869,000	$            -869,000	$         -869,000
PAT		$          3,081,000	$           3,081,000	$          3,081,000	$       3,081,000
+dep.		$          4,050,000	$           4,050,000	$          4,050,000	$       4,050,000
+Working capital recovered					$       1,020,000
+ sales of asset					$       2,050,000
Operating cash flow		$          7,131,000	$           7,131,000	$          7,131,000	$     10,201,000
Discount factor (1/(1+r%)^n	for r= 14% 1/(1+14%)^0	1/(1+14%)^1	1/(1+14%)^2	1/(1+14%)^3	1/(1+14%)^4
DF	1.000	0.877	0.769	0.675	0.592
Discounted cash flow (DF*cash flow)	$                      -17,220,000	$    6,255,263.16	$     5,487,072.95	$    4,813,221.88	$ 6,039,810.91

The working capital is recovered after 4 years and the machinery can be sold at $2.05 mil at the end of 4 yrs

So the NPV=

So the NPV= sum of all the present value of cash inflow- initial cost

6255263.16+5487072.95+4813072.95+4813221.88+4826046.34+6039810.91-17220000

$5,375,368.89

b.1. If the cost ends after 1 year

The asset will be sold at the prevailing market price and the working capital will be recoverd

	Initial	1
Initial investment- Cost of machinery	$                      -16,200,000
Additional working capital	$                        -1,020,000
Total capital required	$                      -17,220,000
Sales		$       13,300,000
-operating cost		$       -5,300,000
-depreciation	16200000/4	$        -4,050,000
EBIT		$          3,950,000
- Income tax	EBIT* 22%	$            -869,000
PAT		$          3,081,000
+dep.		$          4,050,000
+Working capital recovered		$          1,020,000
+ sales of asset		$       14,200,000
Operating cash flow		$       22,351,000
Discount factor (1/(1+r%)^n	for r= 14% 1/(1+14%)^0	1/(1+14%)^1
DF	1.000	0.877
Discounted cash flow (DF*cash flow)	$                      -17,220,000	$ 19,606,140.35

So the NPV= 19606140.35-1722000= $2,386,140.35

b.2. if the project ends after 2 years

the assets will be sold at the end of 2nd year and the cash flow will be discounted for 2 years

	Initial	1	2
Initial investment- Cost of machinery	$                      -16,200,000
Additional working capital	$                        -1,020,000
Total capital required	$                      -17,220,000
Sales		$       13,300,000	$         13,300,000
-operating cost		$        -5,300,000	$          -5,300,000
-depreciation	16200000/4	$        -4,050,000	$          -4,050,000
EBIT		$          3,950,000	$           3,950,000
- Income tax	EBIT* 22%	$            -869,000	$             -869,000
PAT		$          3,081,000	$           3,081,000
+dep.		$          4,050,000	$           4,050,000
+Working capital recovered			$           1,020,000
+ sales of asset			$         11,200,000
Operating cash flow		$          7,131,000	$         19,351,000
Discount factor (1/(1+r%)^n	for r= 14% 1/(1+14%)^0	1/(1+14%)^1	1/(1+14%)^2
DF	1.000	0.877	0.769
Discounted cash flow (DF*cash flow)	$                      -17,220,000	$    6,255,263.16	$   14,889,966.14

So the NPV = 14.88+6.255-17.22= $3.925 or $3925229.30

b. 3 .

if the project ends after 3 years

the assets will be sold at the end of 3^rd year and the cash flow will be discounted for 3 years

	Initial	1	2	3
Initial investment- Cost of machinery	$ -16,200,000
Additional working capital	$     -1,020,000
Total capital required	$ -17,220,000
Sales		$       13,300,000	$         13,300,000	$       13,300,000
-operating cost		$        -5,300,000	$          -5,300,000	$        -5,300,000
-depreciation	16200000/4	$        -4,050,000	$          -4,050,000	$        -4,050,000
EBIT		$          3,950,000	$           3,950,000	$          3,950,000
- Income tax	EBIT* 22%	$            -869,000	$             -869,000	$            -869,000
PAT		$          3,081,000	$           3,081,000	$          3,081,000
+dep.		$          4,050,000	$           4,050,000	$          4,050,000
+Working capital recovered				$          1,020,000
+ sales of asset				$          8,700,000
Operating cash flow		$          7,131,000	$           7,131,000	$       16,851,000
Discount factor (1/(1+r%)^n	for r= 14% 1/(1+14%)^0	1/(1+14%)^1	1/(1+14%)^2	1/(1+14%)^3
DF	1.000	0.877	0.769	0.675
Discounted cash flow (DF*cash flow)	$                      -17,220,000	$    6,255,263.16	$     5,487,072.95	$ 11,373,945.02

So the NPV= $5896281.12