Tutorial 1: Capital Budgeting and Real Option
1. Home Builder Supply, a retailer in the home improvement industry, currently operates
seven retail outlets in Georgia and South Carolina. Management is contemplating
building an eighth retail store across town from its most successful retail outlet. The
company already owns the land for this store, which currently has an abandoned
warehouse located on it. Last month, the marketing department spent $12,000 on
market research to determine the extent of customer demand for the new store. Now
Home Builder Supply must decide whether to build and open the new store.
Which of the following should be included as part of the incremental earnings for the
proposed new retail store?
a. The cost of the land where the store will be located.
b. The cost of demolishing the abandoned warehouse and clearing the lot.
c. The loss of sales in the existing retail outlet, if customers who previously drove
across town to shop at the existing outlet become customers of the new store instead.
d. The $12,000 in market research spent to evaluate customer demand.
e. Construction costs for the new store.
f. The value of the land if sold.
g. Interest expense on the debt borrowed to pay the construction costs.
Answer
a. No, this is a sunk cost and will not be included directly. (But see (f) below.)
b. Yes, this is a cost of opening the new store.
c. Yes, this loss of sales at the existing store should be deducted from the sales at the
new store to determine the incremental increase in sales that opening the new store
will generate for HBS.
d. No, this is a sunk cost.
e. This is a capital expenditure associated with opening the new store. These costs
will, therefore, increase HBS’s depreciation expenses.
f. Yes, this is an opportunity cost of opening the new store. (By opening the new store,
HBS forgoes the after-tax proceeds it could have earned by selling the property.
This loss is equal to the sale price less the taxes owed on the capital gain from the
sale, which is the difference between the sale price and the book value of the
property. The book value equals the initial cost of the property less accumulated
depreciation.)
g. While these financing costs will affect HBS’s actual earnings, for capital budgeting
purposes we calculate the incremental earnings without including financing costs
to determine the project’s unlevered net income.
2. Your firm is considering a project that would require purchasing $7.2 million worth of
new equipment. Determine the present value of the depreciation tax shield associated
with this equipment if the firm’s tax rate is 31%, the appropriate cost of capital is 9%,
and the equipment can be depreciated
a. Straight-line over a 10-year period, with the first deduction starting in one year.
b. Straight-line over a five-year period, with the first deduction starting in one year.
c. Using MACRS depreciation with a five-year recovery period and starting
immediately.
d. Fully as an immediate deduction.
Answer
Equipment cost = 7.2
Tax rate = 31%
Cost of capital = 9%
PV(DTS)
[MACRS]
0
1
2
3
4
5
20%
32%
19%
12%
12%
6%
Option a
$1.43
0.22
0.22
0.22
0.22
0.22
Option b
$1.74
0.45
0.45
0.45
0.45
0.45
Option c
$1.93
0.45
0.71
0.43
0.26
0.26
0.13
Option d
$2.23
2.23
6
7
8
9
10
0.22
0.22
0.22
0.22
0.22
3. Consider two investment projects, both of which require an upfront investment of $12
million and pay a constant positive amount each year for the next 10 years. Under what
conditions can you rank these projects by comparing their IRRs?
Answer
They have the same scale, and the same timing (10-year annuities). Thus, as long as
they have the same risk (and therefore, cost of capital), we can compare them based on
their IRRs.
4. Machines A and B are mutually exclusive and are expected to produce the following
real cash flows:
Cash Flows ($ thousands)
Machines
C0
C1
C2
A
-100
+110
+121
B
-120
+110
+121
The real opportunity cost of capital is 10%.
a. Calculate the NPV of each machine.
C3
+133
Answer
NPVA = -100 +
NPVB = -120 +
𝟏𝟏𝟎
𝟏𝟐𝟏
+ 𝟏.𝟏𝟎𝟐 = $100
𝟏.𝟏𝟎
𝟏𝟏𝟎
𝟏.𝟏𝟎
𝟏𝟐𝟏
𝟏𝟑𝟑
+ 𝟏.𝟏𝟎𝟐 + 𝟏.𝟏𝟎𝟑 = $179.92
b. Calculate the equivalent annual cash flow from each machine
Answer
PV annuity factor =
1−(1+𝑟)−𝑡
𝑟
PV annuity factor for A =
𝐍𝐏𝐕𝐀
𝟏−(𝟏+𝟎.𝟏𝟎)−𝟐
𝟎.𝟏𝟎
= 1.7355
𝟏𝟎𝟎
EACA = 𝐏𝐕 𝐚𝐧𝐧𝐮𝐢𝐭𝐲 𝐟𝐚𝐜𝐭𝐨𝐫 𝐟𝐨𝐫 𝐀 = 𝟏.𝟕𝟑𝟓𝟓 = $57.62
PV annuity factor for B =
𝐍𝐏𝐕𝐁
𝟏−(𝟏+𝟎.𝟏𝟎)−𝟑
𝟎.𝟏𝟎
= 2.4869
𝟏𝟕𝟗.𝟗𝟐
EACB = 𝐏𝐕 𝐚𝐧𝐧𝐮𝐢𝐭𝐲 𝐟𝐚𝐜𝐭𝐨𝐫 𝐟𝐨𝐫 𝐁 = 𝟐.𝟒𝟖𝟔𝟗 = $72.35
c. Which machine should you buy?
Machine B
5. Cellular Access, Inc. is a cellular telephone service provider that reported net income
of $241 million for the most recent fiscal year. The firm had depreciation expenses of
$128 million, capital expenditures of $159 million, and no interest expenses. Working
capital increased by $10 million. Calculate the free cash flow for Cellular Access for
the most recent fiscal year.
Answer
FCF = Unlevered Net Income + Depreciation – CapEx – Increase in NWC= 241 + 128 – 159 – 10 = $200
million.
6. United Pigpen is considering a proposal to manufacture high-protein hog feed. The
project would make use of an existing warehouse, which is currently rented out to a
neighboring firm. The next year’s rental charge on the warehouse is $100,000 and
thereafter the rent is expected to grow in line with inflation at 4% a year. In addition to
using the warehouse, the proposal envisages an investment in plant and equipment of
$1.2 million. This could be depreciated for the purposes straight-line over 10 years.
However, Pigpen expects to terminate the project at the end of eight years and to resell
the plant and equipment in year 8 for $400,000. Finally, the project requires an initial
investment in working capital of $350,000. Thereafter, working capital is forecasted to
be 10% of sales in each of years 1 through 7.
Answer
Year 1 sales of hog feed are expected to be $4.2 million, and thereafter sales are
forecasted to grow by 5% a year, slightly faster than inflation rate. Manufacturing costs
are expected to be 90% of sales, and profits are subject to tax at 35%. The cost of capital
is 12%. What is the NPV of Pigpen’s project?
Answer (SEE EXCEL WORKSHEET)
All numbers are in thousands:
t=0
t=1
t=2
t=3
t=4
Sales
4,200.0 4,410.0 4,630.5 4,862.0
Manufact
3,780.0 3,969.0 4,167.5 4,375.8
uring
Costs
Depreciati
120.0 120.0 120.0 120.0
on
Rent
100.0 104.0 108.2 112.5
Earnings
before 200.0 217.0 234.8 253.7
Taxes
Taxes
70.0
76.0
82.2
88.8
Cash
Flow— 250.0 261.1 272.6 284.9
Operations
t=5
t=6
t=7
t=8
5,105.1 5,360.4 5,628.4 5,909.8
4,594.6 4,824.4 5,065.6 5,318.8
120.0
120.0
120.0
120.0
117.0
273.5
121.7
294.3
126.5
316.3
131.6
339.4
95.7
297.8
103.0
311.3
110.7
325.6
118.8
340.6
Working
350.0 420.0
Capital
Increase
350.0
70.0
in W.C.
Initial
1,200.0
Investmen
t
Sale
of
Plant
Tax
on
Sale
441.0
463.1
486.2
510.5
536.0
562.8
0.0
21.0
22.1
23.1
24.3
25.5
26.8
-562.8
Net
Cash 180.0
Flow-1,550.0
NPV (at $85.8
12%) =
240.1
400.0
56.0
250.5
261.8
273.5
285.8
298.8
7. Describe the benefits and costs of delaying an investment opportunity.
Answer
1,247.4
By delaying, you delay the benefits of taking on the project and your competitors might
take advantage of this delay. However, by delaying, uncertainty can be resolved, so you
can become better informed and make better decisions.
8. What implicit assumption is made when managers use the equivalent annual benefit
method to decide between two projects with different lives that use the same resource?
Answer
The equivalent annual cost method implicitly assumes that, at the end of the life of the
shorter length project, you can replace the shorter length project on the original terms.
9. Your engineers are developing a new product to launch next year that will require both
software and hardware innovations. The software team requests a budget of $6 million
and forecasts an 80% chance of success. The hardware team requests a $11 million
budget and forecasts a 53% chance of success. Both teams will need 6 months to work
on the product, and the risk-free interest rate is 3% APR with semiannual compounding.
a. Which team should work on the project first?
b. Suppose that before anyone has worked on the project, the hardware team comes
back and revises their proposal, changing the estimated chance of success to 78%
based on new information. Will this affect your decision in (a)?
Answer
a. We use the Failure cost index:
Failure cost index 
1  PV(success)
PV(investment)
Software: FCI = (1 – 0.8/1.015) / 6 = 0.035
Hardware: FCI = (1 – 0.53/1.015) / 11 = 0.043
Thus, Hardware should go first
b. Hardware: FCI = (1 – 0.78/1.015) / 11 = 0.021
Yes, software should go first now.
10. Define and briefly explain each of the following terms:
a. Sensitivity analysis:
Answer
Analysis of how project profitability and NPV would change if different assumptions
were made about sales, cost, and other key variables. Typically, each key variable might
have a low value, an expected value, and a high value.
b. Scenario analysis:
Answer
This changes several inputs at once, so that the analyst can predict the NPV under
certain ‘scenarios’.
c. Break-even analysis:
Answer
Determines the level of future sales at which project profitability or NPV equals zero.
Sales or costs turned out to be worse than we forecasted. How bad sales can get before
the project begins to lose money.
d. Monte Carlo simulation:
Answer
e. Monte Carlo Simulation is a statistical method applied in financial modelling. The
simulation relies on the repetition of random samples to achieve numerical results. It
can be used to understand the effect of uncertainty and randomness in forecasting
models.
f. Decision tree
Answer:
A graphical technique for displaying possible future events and decisions taken in
response to those events.
g. Real option:
Answer
Option to modify a project at a future date. The flexibility to modify, postpone, expand
or abandon a project. It is the right — but not the obligation — to undertake certain
business initiatives, such as deferring, abandoning, expanding, staging, or contracting
a capital investment project.