Build a model : Capital Structure and Real options

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Build a Model

Solution 7/16/15
Chapter: 26
Problem: 9
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= 12%
Condition Probability CF CF x Prob.
Good 30% $9
Medium 40% $4
Bad 30% -$1
Expected CF=
Time line of Expected CF
0 1 2 3
-$10
NPV=
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= 12% 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= 12%
Risk-free rate = 6%
Decision Tree Analysis
Cost Future Operating Cash Flows (Discount at WACC) NPV this
Michael C. Ehrhardt: Discount at WACC since these are risky cash flows. Include original cost, but not the cost of implementing additional project at Year 3.		 Prob.
0 Probability 1 2 3 4 5 6 Scenario x NPV
30%
-$10 40%
30%
Expected NPV of Future Operating CFs =
Future Cost of Implementing Additional Project (Discount at Risk-free rate) NPV this
Michael C. Ehrhardt: Discount at risk-free rate since cost is known with certainty. Don't include orginal cost, since it is already included in the decision tree above. 		Prob.
0 Probability 1 2 3 4 5 6 Scenario x PV
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
Michael C. Ehrhardt: Discount at risk-free rate since the cost is known with certainty.		 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
Michael C. Ehrhardt: Discount at WACC since these are risky cash flows. This should include all cash flows, just like the price of a stock includes all cash flows, even those that occur if you don't exercise a stock option. Also, since a stock's price isn't affected by an option's exercise price, the current value of the project is not affected by the "exercise" cost of the real option.
Michael C. Ehrhardt: Sum of -$1 operating CF and salvage value of $6.		 Prob.
0 Probability 1 2 3 4 5 6 Scenario x NPV
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=

DII Labs: NPV from part a.
Michael C. Ehrhardt: Discount at risk-free rate since cost is known with certainty. Don't include orginal cost, since it is already included in the decision tree above.
Michael C. Ehrhardt: Discount at risk-free rate since the cost is known with certainty.
Michael C. Ehrhardt: Use the NORMSDIST function.
Michael C. Ehrhardt: Use the NORMSDIST function.		 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.