# Investing in a Negative Npv Project Today Is a Feasible Choice If - PDF

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```					FN2 - ADVANCED CORPORATE FINANCE

MODULE 2

HANDOUT I
FN2 Ron Muller 2010-11

MODULE 2: CAPITAL BUDGETING UNDER UNCERTAINTY

TEST YOUR KNOWLEDGE QUESTION

Q. Sunrise Energy Incorporated is an Alberta-based integrated energy company,
and has decided to acquire a large dump truck for its oil sands operation. Based
on the following information, calculate in the initial investment outlay of the new
truck.

Cost of the truck                                    \$5,500,000
Investment tax credit to purchase the truck          10%
CCA rate                                             30%
Useful life                                          20 years
Salvage value                                        \$500,000

A. Initial investment outlay = Purchase price – Investment tax credit

= \$5,500,000 – (0.10 x \$5,500,000)
= \$4,950,000

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FN2 Ron Muller 2010-11

MODULE 2: CAPITAL BUDGETING UNDER UNCERTAINTY

REVIEW QUESTIONS

QUESTION 1

Timber Inc. is considering a new project. The company is currently financed with 40%
debt and 60% equity. The company’s borrowing rate is 5% and its corporate tax rate is
20%. Timber’s weighted average cost of capital is 14%. The T-bill rate is 4% and the
risk premium is 8%.

Timber Inc. is considering investing in a forestry company. The initial investment will be
2 million and annual after tax cash flows will be \$550,000 over the next 5 years. To
finance the project Timber Inc. will use the same proportion of debt and equity that it
currently uses. A publicly traded forestry company has a debt ratio of 30%, a tax rate of
20% and a beta of 1.50. This company is similar to the one that Timber is considering

Answer each of the following.

a) Calculate the unlevered beta of the publicly traded forestry company.

b) Should Timber buy the forestry company?

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FN2 Ron Muller 2010-11

QUESTION 2

A company is evaluating a set of investment proposals as part of its annual capital
budgeting process. Of the 5 available projects, all are independent except for A and
B, which are mutually exclusive of each other but independent of all other projects.

As a financial analyst for the firm, you have estimated project cash flows and
calculated several measures of project success, as shown in the exhibit below:

EXHIBIT
Comparing Investment Proposals
Project    Initial Investment       NPV           Discounted Payback           IRR
A                \$500,000              \$ 120,000              4.3 years              13%
B                 400,000                90,000               3.5 years           13%
C                 600,000               125,000                6 years            12%
D                 200,000                40,000                5 years            14%
E                 300,000                50,000                2 years           13.5%

Required
Write a report explaining your assessment of the set of investment projects
and recommend which should be undertaken if there is no capital constraint.
Explain the effect of your decision upon the firm’s value.

Also consider which projects to undertake if only \$1,000,000 is available to
invest and what the effect of your decision will be on the firm’s value.

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FN2 Ron Muller 2010-11

QUESTION 3

Hardware Co. purchased land 5 years ago at a cost of \$100,000. Market value today is
\$500,000 and in 15 years it will be worth \$1,000,000. Hardware is contemplating adding
a new facility. The new facility would increase pretax earnings to \$800,000 per year for
15 years. Pretax earnings of current operations are \$400,000. If the new facility is not
built, certain materials could be sold to an “outsider” for \$225,000 per year but, Hardware
would incur \$25,000 annual selling costs. Hardware Co.’s tax rate is 40% and its cost of
capital is 12%.

The proposed new facility would result in the following costs:

Survey                               \$ 20,000
Building (CCA rate: 20%)              750,000
Equipment (CCA rate: 30%)             500,000
Working capital                         5,000
One time training cost                  2,000

At the end of the 15 years, the salvage on the building will be \$100,000 and the salvage
on the equipment will be \$50,000. Determine the NPV of the project.

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FN2 Ron Muller 2010-11

QUESTION 4

Shilo Company Example – NPV, IRR, Payback and PI

Shilo Co. has decided to consider two proposals A and B for its expansion. Project A
requires an initial investment of \$9,000 and Project B’s initial investment is \$7,000.
Subsequent after tax net cash inflows are given as follows:

Year                  Project A              Project B
1                     \$ 3,250                \$ 2,500
2                     3,500                  2,500
3                     3,500                  3,000
4                     3,500                  3,000

Required:

a) Assuming a weighted average cost of capital of 14 percent, rank the two projects in
terms of:

i) Payback period - assuming a target of 3 years
ii) NPV
iii) PI
iv) IRR

b) How do you account for the differences in ranking? Which project do you prefer?
Why? How might capital rationing change your answer?

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FN2 Ron Muller 2010-11

QUESTION 5

An investment project requires an immediate cash outflow of \$100,000, and then
provides cash inflows of \$45,000 at the end of each year for 5 years. The firm uses a
discount rate of 17% for projects of this type due to the extremely high risk involved.

What is the discounted payback period for this project?

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FN2 Ron Muller 2010-11

QUESTION 6 (Multiple Choice)

Q1. According to the Profitability Index Rule, when should a project be accepted?
1) When its profitability index is less than zero.
2) When its profitability index is greater than zero.
3) When its profitability index is less than one.
4) When its profitability index is greater than one.

Q2. What is the best measure of the relative profitability of an investment project?
1) Internal rate of return
2) Coefficient of variation
3) Profitability Index
4) Net present value

Q3. When investment projects are analyzed under inflationary conditions, the real
method of dealing with inflation involves which of the following?
1) Estimating nominal cash flows for each year of the project life.
2) Adding a premium to the discount rate to reflect the higher required return of
investors.
3) Estimating cash flows based on current day dollars for each year of the project life.
4) Assuming revenues and costs are affected differently by inflation and adjusting each
cash flow component for inflation separately.

Q4. Which factor(s) would favour using the real method of capital budgeting rather
than the nominal method under inflationary circumstances?
1) Costs and prices are affected differently by inflation.
2) Historical costs are used for CCA calculations.
3) Inflation rates are expected to vary from year to year over the life of the project.
4) Inflation rates are expected to be constant over the life of the project.

Q5. Which statement is the best description of a “sunk cost”?
1) Any costs that are irrelevant because they exist regardless of the investment decision
2) All costs that do not directly result in a revenue increase
3) All committed costs by way of contract or otherwise
4) All costs that are capital in nature.

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FN2 Ron Muller 2010-11

QUESTION 1 SOLUTION

(a)

βL = βU + (1 – T) (D/E)βU

1.5 = βU + (1 - .2)(30/70) βU

1.5 = 1.342857143βU

βU = 1.117 = 1.12

(b) We need to determine the NPV; however we must first determine an appropriate
discount rate to evaluate the project.

(i) Calculate beta:

Formula: βL = βU + (1 – T) (D/E)βU
βL = 1.12 + (1 – .2) (40/60)1.12
= 1.7173
= 1.72

(ii) Calculate the cost of equity:

Formula: Ke = rf + β(rm - rf)
= .04 + β(.08)
= .04 + 1.72(.08)
= .1776

(iii) Calculate WACC

Formula: WACC = Kdebt [D/(D + E)] + Kequity [E/(D + E)]
= .05(1 - .2)(40%) + Kequity(60%)
= .016 + .1776 (60%)
= .1226 = 12.26%

(iv) Calculate NPV

NPV = - 2,000,000 + 550,000a512.26%
= - 2,000,000 + 1,969,923
= - 30,007

Therefore, don’t buy it.

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FN2 Ron Muller 2010-11

QUESTION 2 SOLUTION

In this problem, a set of investment proposals is to be assessed using a variety of capital
budgeting criteria. Two of the investment proposals are mutually exclusive while the rest
are independent. Choices must be made first without a capital constraint and then under
capital rationing. The answer should be presented as a report that includes the following
information:

Without a capital constraint
All projects have positive NPVs, ranging from \$40,000 for D to \$125,000 for C, so the
independent projects, C, D, and E, should all be undertaken. Also, the better of the
two mutually exclusive projects, A and B, should be undertaken. Project A has a
higher NPV, \$120,000 compared to B’s \$90,000, so A will be selected.

Four projects will be undertaken: A, C, D, and E. The total NPV of the four projects is
\$335,000, and this is the amount by which the firm’s value will increase to shareholders’
wealth.

With a \$1,000,000 capital constraint
The four projects, A, C, D, and E would cost a total of \$1.6 million, so they cannot all be
undertaken with a \$1 million spending limit.

To answer this question, it is helpful to look at the total NPV of feasible combinations
of projects, as shown in the Exhibit below:

EXHIBIT
NPV of Feasible Combinations of Projects
Combination                    Total Investment                      Total NPV

A,D,E                          \$1,000,000                            \$210,000
B,C                            \$1,000,000                            \$215,000
B,D,E                          \$ 900,000                             \$180,000

In conclusion, the best combination of projects is B and C, with a total increase in the
firm’s value of \$215,000, and thus maximizes shareholders’ wealth.

Note that payback period and IRR were not needed in the analysis since the NPV rule
is consistent with firm value maximization, which was the objective.

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FN2 Ron Muller 2010-11

QUESTION 3 SOLUTION

NPV = Land (opportunity cost) = - 500,000                  ( 420,000)
Less: Capital gains tax: (500,000 - 100,000) x
40% x 1/2 = 80,000
Building                                                   ( 750,000)
Equipment                                                  ( 500,000)
Working capital                                            ( 5,000)
One time training cost (BE CAREFUL) 2,000 (1               ( 1,200)
- .4)
INITIAL INVESTMENT                                         ( 1,676,200)

+ PV after tax cash flows
New: 800,000
Current (400,000)
Opportunity cost: 225,000 - 25,000 (200,000)
200,000 (1 - .4) 12%                                       + 817,304
+ PV CCA tax shield - PV lost tax shield on
salvage (on depreciable assets)
BUILDING:
750,000 x .2 x .4(2.12) - 1 x 100,000 x .2 x .4            + 172,888
15
2 (.2 + .12) (1.12)       (1.12) x (.2 + .12)
177,455 - 4,567
EQUIPMENT:
500,000 x .3 x .4(2.12) - 1 x 50,000 x .3 x .4             + 132,594
15
2 (.3 + .12) (1.12)      (1.12)        x (.3 + .12)
135,204 - 2,610
15
+ PV salvage on building: 100,000/(1.12)                   + 18,270
15
+ PV salvage on equipment: 50,000/(1.12)                   + 9,135
15
+ PV salvage on working capital: 5,000/(1.12)              + 913
+ PV salvage on land                                       + 149,811
15
1/(1.12) [ 1,000,000 - (1/2) ( 40%) (1,000,000
- 100,000) ]
NPV                                                        (375,285)
CONCLUSION: NPV is negative, reject the
project.

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FN2 Ron Muller 2010-11

QUESTION 4 SOLUTION

i) Payback
Machine A: - 9,000 + 3,250 + 3,500 + 2,250/3,500 = 2.64 years
Machine B: - 7,000 + 2,500 + 2,500 + 2,000/3,000 = 2.67 years

Conclusion: BOTH projects would be accepted according to this technique, but Project A
is slightly better.

ii) NPV
Project A: NPV = -9,000 + 3,250 + 3,500 + 3,500 + 3,500
2        3          4
(1.14) (1.14) (1.14) (1.14)
= -9,000 + 9,978.69

= 978.69

Project B: NPV = -7,000 + 2,500 + 2,500 + 3,000 + 3,000
2        3          4
(1.14) (1.14)       (1.14) (1.14)
= -7,000 + 7,917.81

= 917.81

Conclusion: Based on NPV rule, Project A should be selected because it has a higher NPV.

iii) Profitability Index
Project A: PV cash flows = 9,978.69 = 1.109
initial investment         9,000

Project B: PV cash flows = 7,917.81 = 1.131
initial investment         7,000

Conclusion: Based on PI rule, Project B should be selected because it has a higher PI.

iv) IRR
Project A: IRR = 19.14% (exact, computer calculation)

Project B: IRR = 20.01% (exact, computer calculation)

Conclusion: According to the IRR technique Project B is better.

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FN2 Ron Muller 2010-11

b) Generally, differences in ranking are caused primarily by differences in the time
patterns of cash flows and by unequal initial investments.

Payback does not take into account the time value of money or the cash flows after the
payback period. So, it is quite possible that it could give a different result than NPV.

IRR technique assumes a reinvestment rate equal to the IRR while the net present value
assumes a reinvestment rate equal to the discount rate. For this reason the IRR ranking
differs from the NPV.

If a firm were faced with a capital rationing situation AND IF it could invest the \$2,000
that is saved by not investing in Project A and earn a NPV greater than \$61, Project B
would be more attractive. In capital rationing situations, management should attempt to
maximize the NPV of the entire investment package.

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FN2 Ron Muller 2010-11

QUESTION 5 SOLUTION

-100,000 + 45,000 + 45,000 + 45,000
(1.17)   (1.17)2 (1.17)3

-100,000 + 38,461.54 + 32,873.11 + 28,096.68 + X = 0

X = 568.68 more cash inflow needed

The portion of the year = 568.68/PV of 45,000 in Year 4
= 568.68/24,014.25
= .024 years

The result is a discounted payback period of 3.024 years.

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FN2 Ron Muller 2010-11

QUESTION 6 SOLUTIONS

1 (4)

2 (3)

3 (3)

4 (4)

5 (1)

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FN2 Ron Muller 2010-11

MODULE 2: CAPITAL BUDGETING UNDER UNCERTAINTY

SAMPLE FINAL EXAM QUESTION

Source: December 2009, Question 3

Jane & Jane Corporation (JJ), a pharmaceutical company, engages in the formulation,
clinical testing, registration, manufacture, and distribution of pharmaceutical products in
Canada and the United States. After spending \$50 million and 10 years in research,
development, and testing, JJ has just received the license for its new drug from the
government regulator. It is planning to manufacture and distribute the new drug.

To manufacture the drug, equipment will be purchased and installed in an existing
building for \$100 million. The CCA rate for the equipment will be 30%. The building is 20
years old and has a CCA rate of 5%. Though not in use right now, the building may be
rented out as a warehouse at an annual rate of \$500,000 (pre-tax) if JJ decides not to
manufacture the new drug or to manufacture the new drug elsewhere. The new drug is
expected to be the only one of its kind on the market for the next 15 years. After that,
competitors will manufacture and sell its alternatives at much cheaper prices. Thus, the
new drug has an economic life of 15 years and will contribute \$50 million in sales and
cost \$20 million to produce and distribute each year. However, JJ is expected to lose
\$10 million per year in operating profit (pre-tax) due to lost sales of some existing drugs.

New working capital in the amount of \$10 million will be needed but this amount will not
require external financing. At the end of year 15, the investment in working capital will be
recovered and the equipment will have a salvage value of \$5 million.

JJ plans to finance the equipment with 50% debt and 50% new equity. Its company-wide
debt ratio is 40%. The pre-tax effective annual interest rate on JJ’s bond issue is 10%.
However, the provincial government has offered a low-interest (interest only) loan for the
debt amount required at an effective annual rate of 5%.

The investment bank hired by JJ estimates that the flotation costs associated with the
new bond and equity will be 3% of the funds raised for the investment. JJ has cash
available to pay this cost. JJ has a levered beta of 1.75 and its tax rate is 40%. The
stock market is expected to return 12% per year in the coming years and T-bills are
yielding an annual rate of 4%. JJ has decided to apply for the maximum amount of the
provincial government low-interest loan. You have been asked to help evaluate this
project.

Required:

a. Briefly explain which of the three methods [adjusted present value (APV), weighted
average cost of capital (WACC), or equity residual method (ERM)] you should use to
evaluate this project. (2 marks)

b. Calculate the net initial outlay for this investment. Indicate whether you would include
the \$50 million JJ spent in research, development, and testing in your calculation and
briefly explain why. (2 marks)

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FN2 Ron Muller 2010-11

c. Calculate the annual after-tax operating income. Briefly explain how to deal with the
potential rental revenue and the lost operating profit from the existing drugs in the
operating income calculation. (3 marks)

d. Calculate the discount rates to be used in your evaluation. (4 marks)

e. Calculate the base-case net present value (NPV) and determine whether this project
is financially feasible if only shareholders’ equity (retained earnings) is used to finance
the project. (6 marks)

f. Calculate the adjusted present value (APV) of the project and determine whether this
project is financially feasible without the provincial government’s low-interest loan. (4
marks)

g. Determine the extent to which the low-interest loan from the provincial government

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FN2 Ron Muller 2010-11

Solution:

a. The APV should be used because this project involves financial side effects as a
result of government subsidized loans.

b. Net initial outlay = Cost of equipment + Net working capital increase = \$100 million +
\$10 million = \$110 million

The \$50 million JJ spent in research, development, and testing is not included in the
calculation because it is a sunk cost.

c. Annual after-tax operating income = (\$50M – \$20M – \$0.5M – \$10M) (1 – 40%) =
\$19.5M (60%) = \$11.7M
The potential rental revenue and lost operating profit are opportunity costs brought about
by the new drug project. These amounts are deducted in the operating income
calculation.

d. The discount rates are: 1) unlevered cost of equity used to calculate the base-case
NPV; 2) after-tax cost of debt used to calculate the present value of financing-related
cash flows.

To compute the first discount rate, we need the unlevered beta. Given the levered beta,
βL = 1.75, we need to de-lever it.

Unlevered beta:

Unlevered cost of equity: kU = 4% + 1.25 × (12% – 4%) = 14%

After-tax cost of debt: kB = 10% (1 – 40%) = 6%

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FN2 Ron Muller 2010-11

e. Present value of annual after-tax operating income discounted at the unlevered cost
of equity:
\$11.7M × PVIFA (14%, 15) = \$71.8634M

Present value of CCA tax shield on the equipment:

= \$25.5981M-\$0.1910M=\$25.4071M

Present value of salvage value for the equipment:
\$5M / (1+14%)15 = \$0.7005M

Present value of recovered net working capital:
\$10M / (1 + 14%)15 = \$1.4010M

The base-case NPV: NPVB = \$71.8634M + \$25.4071M + \$0.7005M + \$1.4010M –
\$100M – \$10M = –\$10.6280M < 0

This negative number indicates that the project is not financially feasible if only
shareholders’ equity (retained earnings) is used.

f. Flotation costs = \$100M × 3% = \$3M

Net flotation costs for new equity and bond issue = \$3M – \$3M/5 × 40% × PVIFA (6%, 5)
= \$1.9890M

Interest tax shield on bond = \$100M × 50% × 10% × 40% × PVIFA (6%, 15) =
\$19.4245M

Adjusted NPV including financing side effects:
–\$10.6280M – \$1.9890M + \$19.4245M = \$6.8075M > 0

The project is financially feasible if JJ finances half of it with a bond issue since the APV
> 0.

g. If JJ takes the maximum low-interest loan (\$50M) from the provincial government:
Interest tax shield on the debt financing:
\$50M × 5% × 40% × PVIFA (6%, 15) = \$9.7122M

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FN2 Ron Muller 2010-11

Value of low-interest loan:
\$50M – \$50M × 5% × (1 – 40%) × PVIFA (6%, 15) – \$50M × PVIF (6%, 15)
= \$50M – \$14.5684M – \$20.8633M = \$14.5683M

Adjusted NPV with government subsidy = –\$10.6280M – \$1.9890M / 2 + \$9.7122M +
\$14.5683M = \$12.6580M > 0

With the low-interest loan from the provincial government, JJ should take the project.

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