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# Real option for Bradford Services

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Bradford Services Inc. (BSI) is considering a project that has a
cost of \$10 million and an expected life of 3 years. There is a 30% probability of
good conditions, in which case the project will provide a cash flow of \$9 million
at the end of each year for 3 years. There is a 40% probability of medium conditions,
in which case the annual cash flows will be \$4 million, and there is a 30%
probability of bad conditions and a cash flow of \$1 million per year. BSI uses a
12% cost of capital to evaluate projects like this.

a. Find the projectâ??s expected present value, NPV, and the coefficient of variation
of the present value.

b. Now suppose that BSI can abandon the project at the end of the first year by
selling it for \$6 million. BSI will still receive the Year 1 cash flows, but will
receive no cash flows in subsequent years.

c. Now assume that the project cannot be shut down. However, expertise gained
by taking it on would lead to an opportunity at the end of Year 3 to undertake
a venture that would have the same cost as the original project, and the new
projectâ??s cash flows would follow whichever branch resulted for the original
project. In other words, there would be a second \$10 million cost at the end of
Year 3, and then cash flows of either \$9 million, \$4 million, or â?"\$1 million for the following 3 years. Use decision tree analysis to estimate the value of the
project, including the opportunity to implement the new project at Year 3.
Assume the \$10 million cost at Year 3 is known with certainty and should be
discounted at the risk-free rate of 6%.

d. Now suppose the original (no abandonment and no additional growth) project
could be delayed a year. All the cash flows would remain unchanged, but
information obtained during that year would tell the company exactly which
set of demand conditions existed. Use decision tree analysis to estimate the
value of the project if it is delayed by 1 year. (Hint: Discount the \$10 million
cost at the risk-free rate of 6% since it is known with certainty.)

Bradford Services Inc. (BSI) is considering a project that has a cost of \$10 million and an expected life of 3 years. There is a 30 percent probability of good conditions, in which case the project will provide a cash flow of \$9 million at the end of each year for 3 years. There is a 40 percent probability of medium conditions, in which case the annual cash flows will be \$4 million, and there is a 30 percent probability of bad conditions and a cash flow of -\$1 million per year. BSI uses a 12 percent cost of capital to evaluate projects like this.

a. Find the project's expected cash flows and NPV.

WACC= 10%

Condition Probability CF CF x Prob.
Good 30% \$45 \$13.50
Medium 40% \$30 \$12.00
Expected CF= \$30.00

Time line of Expected CF
0 1 2 3
-\$70 \$30.00 \$30.00 \$30.00

NPV= \$74.61

Without any real options, reject the project. It has a negative NPV and is quite risky.

b. Now suppose the BSI can abandon the project at the end of the first year by selling it for \$6 million. BSI will still receive the Year 1 cash flows, but will receive no cash flows in subsequent years. Assume the salvage value is risky and should be discounted at the WACC.

WACC= 10% Salvage Value = \$6
Risk-free rate = 6%

Decision Tree Analysis

Cost Future Cash Flows NPV this Probability
0 Probability 1 2 3 Scenario x NPV

30%
-\$10 40%
30%

Expected NPV of Future CFs =

When abandonment is factored in, the very large negative NPV under bad conditions is reduced, and the expected NPV becomes positive. Note that even though the NPV of medium is still negative, it is higher than it would be if the project was abandoned at year 1 if conditions are medium.

c. Now assume that the project cannot be shut down. However, expertise gained by taking it on will lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project's cash flows would follow whichever branch resulted for the original project. In other words, there would be a second \$10 million cost at the end of Year 3, and then cash flows of either \$9 million, \$4 million, or -\$1million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project in Year 3. Assume the \$10 million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of 6 percent. Hint: do one decision tree for the operating cash flows and one for the cost of the project, then sum their NPVs.

WACC= 10%
Risk-free rate = 6%

Decision Tree Analysis
Cost Future Operating Cash Flows (Discount at WACC) NPV this
0 Probability 1 2 3 4 5 6 Scenario

30%
-\$10 40%
30%

Expected NPV of Future Operating CFs =

Future Cost of Implementing Additional Project (Discount at Risk-free rate) NPV this
0 Probability 1 2 3 4 5 6 Scenario

30%
40%
30%

Expected NPV of Future Operating CFs =

Total NPV (NPV of Future Operating CF plus NPV of Future Year 3 cost of implenting additional project) =

Here the project has a positive expected NPV, so by this criterion it can be accepted.

d. Now suppose the original (no abandonment and no additional growth) project could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed. Use decision tree analysis to estimate the value of the project if it is delayed by 1 year. Hint: Discount the \$10 million cost at the risk-free rate since it is known with certainty. Show two time lines, one for operating cash flows and one for the cost, then sum their NPVs.

WACC= 12%
Risk-free rate = 6%

Decision Tree Analysis: Optg. CFs "Future Operating Cash Flows
(Discount at WACC)"
NPV this Probability
0 Probability 1 2 3 4 Scenario x NPV

30%
40%
30%

Expected PV of Future CFs =

Decision Tree Analysis: Costs "Future Cost of Implementation
(Discount at Risk-Free Rate)"
Cost NPV this Probability
0 Probability 1 2 3 4 Scenario x NPV

30%
40%
30%

Expected PV of Future CFs =

"Total NPV (NPV of Future Operating CF plus
NPV of Future Year 1 cost of implenting additional project) ="

Since the NPV from waiting is positive and the NPV from immediate implementation is negative, it makes sense to delay the decision for a year.

e. Go back to part c. Instead of using decision tree analysis, use the Black-Scholes model to estimate the value of the growth option. The risk-free rate is 6 percent, and the variance of the project's rate of return is 22 percent.

Risk-free rate= 6%
Variance of project's rate of return= 22%

Financial Option Real Option
rRF = Risk-free interest rate = Risk-free interest rate
t = Time until the option expires = Time until the option expires
X = Strike price = Cost to implement the project
P = Current price of the underlying stock = Current value of the additional project
s2 = Variance of the stock's rate of return = Variance of the project's rate of return

Find current value of the additional project's cash flows. This includes all cash flows except cost of implementation.

Cost Future Operating Cash Flows of Additional Project (Discount at WACC) NPV this
0 Probability 1 2 3 4 5 6 Scenario

30%
40%
30%

Expected NPV of Future Operating CFs =

rRF =
t =
X =
P =
s2 =

d1 = { ln (P/X) + [rRF + s2 /2) ] t } / (s t1/2 ) =
d2 = d1 - s (t 1 / 2) =
N(d1)=
N(d2)=

V = P[ N (d1) ] - Xe-rRF t [ N (d2) ] =

Value of original project=
Value of growth option=
Total Value=

Even though the original project has a negative NPV, the value of the growth option is large enough so that the combination of the original project and the growth option is greater than zero. Therefore, the project should be accepted.