FNCE
370v8 Assignment 3
1.
Define mutually exclusive investment decisions, and give an example of this
type of decision. (3 marks)
2.
Consider the following cash flow[-100,+230,-132].We want to decide under what
range of discount rate this is an advantageous investment. But noting the
change in sign, we conclude IRR is not a suitable instrument.(10 marks)
a.
Write the expression for NPV using the unknown r as discount rate.
b.
Write this expression as a function of[1/(1+r)].
c.
Show that the expression in (b) as a quadratic equation. Look this up if
necessary.
d.
Solve the quadratic equation for its two roots.
e.
Prepare a table of NPV vs .r for r=0,
10, 20, 40, 100%.
f. Draw the graph of NVP vs .r.
g.
Under what range of r values is this an acceptable investment?
h.
Noting that NPV increases then declines as r grows from 0to 40%, determine at
what level of r NPV is a maximum (recall that d(NPV)/d s=0, where NPV is a
maximum). If you have sufficient back ground, solve this using calculus. If
not, graphically find the top of the NPV hill (where slope =0).
What
is the maximum value of NPV? (There is one bonus point for the correct answer
using calculus).
3.Considerthe
following information for projects A and B, which are mutually exclusive.(7 marks)
|
Year
|
Project A
|
Project B
|
Note
|
|
0
|
-100,000
|
-120,000
|
A –B = -100,000 –(-120,000)= +20,000
|
|
1
|
31,250
|
0
|
|
|
2
|
31,250
|
0
|
|
|
3
|
31,250
|
0
|
|
|
4
|
31,250
|
0
|
|
|
5
|
31,250
|
200,000
|
|
a.
At what discount rate will the two projects have the same net present value?
b.
At the discount rate of 10%, which is the better project?
(Hint
1: If the two projects have the same NPV, then NPVA – NPVB = 0. You can
subtract line by line.)
(Hint
2: If the difference in initial investment comes out positive and your
financial calculator is programmed to accept negative PV, adjust the FV accordingly.)
4.
Canadian Classics manufactures parts for classic automobiles. The CFO is
considering the purchase of a two-ton press, which will allow the firm to stamp
auto fenders. The equipment costs $250,000. The project is expected to produce
after-tax cash flows of $80,000 per year. Liquidating the equipment will net
the firm $10,000 in cash at the end of five years. The firm requires a 15% rate
of return on all investments. The firm’s tax rate is 38%. Ignore the effects of
CCA. (10 marks)
a.
What is the payback period for the proposed investment?
b.
What would happen to the payback period if the sale of the equipment at the end
of five years nets the firm $200,000, rather than $10,000?
c.
What is the project’s discounted payback period?
d.
What is the project’s net present value?
e.
What is the project’s profitability index?
f.
What is the project’s internal rate of return?
5.
(4 marks)
a.
Why is it important to consider additions to net working capital in developing
cash flows?
b.
What is the effect of an increase in net working capital on a project’s
operating cash flow?
c.
What normally happens to the additions to net working capital as the project
winds down?
6.
Given the following cash flows for two mutually exclusive projects (A and B),
which project should be chosen?
Assume
that the required rate of return of both projects is 11%.
(Hint:
Use EAC.) (10 marks)
|
Year\Project
|
A
|
B
|
|
0
|
-$1,000,000
|
-$850,000
|
|
1
|
300,000
|
187,500
|
|
2
|
300,000
|
187,500
|
|
3
|
300,000
|
187,500
|
|
4
|
300,000
|
187,500
|
|
5
|
300,000
|
187,500
|
|
6
|
|
187,500
|
|
7
|
|
187,500
|
|
8
|
|
187,500
|
7.
A firm is considering bidding on a project to produce eight widgets per year
for the next four years. In order to complete the project, the firm must lease
facilities for $30,000 per year, purchase equipment that costs $100,000, as
well as pay labour and material costs of $19,000 per unit produced. The
equipment can be depreciated at the Class 8 CCA rate of 20%. At the end of the
fourth year, it can be sold for $10,000, and the asset class will remain open
after the disposal of the equipment. In addition, net working capital will
increase by $50,000 if the project is undertaken, but these can be recovered at
the end of the project. The company’s tax rate is 40%.
What
is the minimum bid per widget if the firm requires 18% return on its
investment? (10 marks)
8.
You are evaluating a project for Ultimate Inc. The project produces
chew-resistant doghouses. You estimate the sales price of these doghouses to be
$500 and sales volume to be 2,500 units per year over the project’s three-year
life. Variable costs amount to $300 per unit and fixed costs (not including
depreciation) are $150,000 per year. The project requires an initial investment
of $250,000 and this will be depreciated on a straight-line basis to zero over
the three-year project life. There will be an initial net working capital
investment of $90,000 (t0) and two further investments of $90,000 at the
beginning of each year thereafter. The full amount of working capital will be
recovered at the end of the project’s life (i.e., $270,000 at t3). The tax rate
is 35% and the required return on the project is 15%. (10 marks)
a.
What is the EBIT for the project in the first year?
b.
What is the operating cash flow for the project in year 2?
c.
Suppose the actual market value of the initial investment at the end of year 3
is $50,000. What is the effect of the $50,000 salvage value on year 2 cash
flows?
d.
What is the NPV of this project?
9.
Describe how the inclusion of a strategic option can affect setting a bid
price. (4 marks)
10.
A project requires an initial investment of $10,000, straight-line depreciable
to zero over four years. The discount rate is 10%. The firm’s tax bracket is
34%, and they receive a tax credit for negative earnings in the year in which
the loss occurs. Additional information for variables with forecast error is
shown below: (10 marks)
|
Item
|
Base Case
|
Lower Bound
|
Upper Bound
|
|
Unit Sales
|
3,000
|
2,750
|
3,250
|
|
Price/Unit
|
$14
|
$13
|
$16
|
|
Variable cost/unit
|
$9
|
$10
|
$8
|
|
Fixed costs
|
$9,000
|
$10,000
|
$8,500
|
a.
What is the base case NPV for the project?
b.
What is the worst case NPV for the project?
c.
What is the best case NPV for the project?
d.
Suppose you want to conduct a sensitivity analysis for the possible changes
from the base case in unit sales. What is the IRR when the sales level equals
3,250 units?
e.
Suppose you are interested in the project’s sensitivity to unit price. What is
the NPV for the base case at a price of $13 per unit?
f.
What is the base case accounting break-even point?
g.
What is the base case cash break-even point?
h. What is the base case financial break-even point? Ignore
taxes.
11. A firm is considering the purchase of equipment which
will cost $3 million. This equipment will last for 10 years, at the end of
which it can be sold for $800,000. The CCA rate for this asset class is 30%,
and the firm expects to have other assets in this asset class at the end of
year 10. This equipment is expected to increase before-tax operating cash flows
by $750,000 per year. However, in order to put the equipment to use, an
additional $150,000 will need to be invested in net working capital initially
(i.e., at t=0). The required rate of return is 16% and the firm’s marginal tax
rate is 35%. (12 marks)
a. Should the firm purchase this equipment?
b. Suppose that to arrive at the before-tax operating cash
flows in part (a), we have used the following estimates:
Fixed costs = $120,000
Variable costs = 60% of sales
What is the Net Present Value of the new equipment if, in
the best-case scenario, we estimate that fixed costs could be lower by 20% and
sales revenues could be higher by 25%?
c. Given the information in (a), and assuming that fixed
costs are $120,000 and variables costs are 60% of sales, what is the sales
level at which Net Present Value equals zero? (In other words, what is the
financial break-even sales level?)
12. A project has the following estimated data: price = $65
per unit; variable costs = $33 per unit; fixed costs = $4,000; required return
= 16%; initial investment = $9,000; life = three years. Ignore the effect of taxes
and assume straight-line depreciation to zero. (10 marks)
a. What is the accounting break-even quantity?
b. What is the cash break-even quantity?
c. What is the financial break-even quantity?
d. What is the degree of operating leverage at the
financial break-even level of output?
TUTORIAL PREVIEW
12.
A project has the following estimated data: price = $65 per unit; variable
costs = $33 per unit; fixed costs = $4,000; required return = 16%; initial
investment = $9,000; life = three years. Ignore the effect of taxes and assume
straight-line depreciation to zero. (10 marks)
a.
What is the accounting break-even quantity?
The accounting breakeven for the project is:
And the accounting breakeven equation is:
QA = (FC + D)/(P – v)
QA = [$4,000 + ($9,000/3)]/($65 – 33)
QA = 218.75
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