Question

You are examining the viability of a capital investment

in which your firm is interested. The project will require

an initial investment of $500,000 and the projected revenues

are $400,000 a year for five years. The projected

cost-of-goods-sold is 40% of revenues, and the tax rate

is 40%. The initial investment is primarily in plant and

equipment and can be depreciated straight line over five

years (the salvage value is zero). The project makes use

of other resources that your firm already owns:

• Two employees of the firm, each with a salary of

$40,000 a year, who are currently employed by another

division, will be transferred to this project. The

other division has no alternative use for them, but

they are covered by a union contract that will prevent

them from being fired for three years (during which

they would be paid their current salary).

• The project will use excess capacity in the current

packaging plant. Although this excess capacity has

no alternative use now, it is estimated that the firm

will have to invest $250,000 in a new packaging plant

in Year 4 as a consequence of this project using

up excess capacity (instead of Year 8 as originally

planned).

• The project will use a van currently owned by the

firm. Although the van is not currently being used,

it can be rented out for $3,000 a year for five years.

The book value of the van is $10,000, and it is being

depreciated straight line (with five years remaining

for depreciation).

• The discount rate to be used for this project is 10%.

a. What (if any) is the opportunity cost associated

with using the two employees from another

division?

b. What (if any) is the opportunity cost associated

with the use of excess capacity of the packaging

plant?

c. What (if any) is the opportunity cost associated with

the use of the van?

d. What is the after-tax operating cash flow each year

on this project?

e. What is the NPV of this project?

Answer 1

a) The opportunity cost associated with using the two employees from another division is NIL since they are covered by a union contract that will prevent them from being fired for three years (the salary will be paid whether they work or not) and the other division has no alternative use for them implying there is no loss of revenue in moving them to another project. Although for the 4th and 5th Year employing the 2 employees would increase the cost of this project by $80,000 p.a. ($40,000 per employee per year)

b) The opportunity cost associated with the use of excess capacity of the packaging plant is $100,000 ($250,000*10%*4Years), Since we had to invest in the new packaging plant 4 years earlier than anticipated, therefore we have charged the Interest Income lost on $250,000 per year. This cost of $100,000 will be charged in year 4 and 5 @ $50,000 p.a.

c) The opportunity cost associated with the use of the van $1,000 p.a. {3,000 - (10,000/5)} since we could have rent it out and earned an additional income that is why it has been taken as the oppoirtunity cost net of depreciation of use of van for the project.

d) & e) after-tax operating cash flow each year and NPV of this project

Particulars\Year	0	1	2	3	4	5
Initial Investmet	$       (500,000)	$                   -	$                   -	$                   -	$                 -	$                 -
Revenues	$                     -	$        400,000	$        400,000	$        400,000	$     400,000	$     400,000
less:- cost-of-goods-sold @ 40%	$                     -	$     (160,000)	$     (160,000)	$     (160,000)	$   (160,000)	$   (160,000)
less :- Depreciation on Project ($500,000/5 Years)	$                     -	$     (100,000)	$     (100,000)	$     (100,000)	$   (100,000)	$   (100,000)
less :- Salary to Employees transferred from another division	$                     -	$                   -	$                   -	$                   -	$     (80,000)	$     (80,000)
less :- opportunity cost for use of excess capacity of the packaging plant	$                     -	$                   -	$                   -	$                   -	$     (50,000)	$     (50,000)
less :- opportunity cost for use of van	$                     -	$          (1,000)	$          (1,000)	$          (1,000)	$        (1,000)	$        (1,000)
Total	$       (500,000)	$        139,000	$        139,000	$        139,000	$          9,000	$          9,000
less:- Tax @ 40%	$                     -	$        (55,600)	$        (55,600)	$        (55,600)	$        (3,600)	$        (3,600)
Add :- Depreciation	$                     -	$        100,000	$        100,000	$        100,000	$     100,000	$     100,000
Net Operating Cash Flows after Tax	$       (500,000)	$        183,400	$        183,400	$        183,400	$     105,400	$     105,400
PVF @ 10%	1.00	0.91	0.83	0.75	0.68	0.62
PV of Cash Flows	$ (500,000.00)	$ 166,710.60	$ 151,488.40	$ 137,733.40	$ 71,988.20	$ 65,453.40
NPV	$      93,374.00