Ch. 15-10 Build a Model Solution								3/11/2001
Chapter 15. Solution to Ch 15-10 Build a Model
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	$2.70
Medium	40%	$4	$1.60
Bad	30%	-$1	-$0.30
		Expected CF=	$4.00
Time line of Expected CF
	0	1	2	3
	-$10	$4.00	$4.00	$4.00
NPV=	-$0.39
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
		$9	$9	$9		$11.62	$3.48
-$10	40%	$4	$4	$4		-$0.39	-$0.16
	30%
		Sum of -$1 operating CF and salvage value of $6. $5	$0	$0		-$5.54	-$1.66
						Expected NPV of Future CFs =	$1.67
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%
Decision Tree Analysis
Cost		Future Operating Cash Flows (Discount at WACC)						Discount at WACC since these are risky cash flows. Include original cost, but not the cost of implementing additional project at Year 3. NPV this	Prob.
0	Probability	1	2	3	4	5	6	Scenario	x NPV
		$9	$9	$9	$9	$9	$9	$27.00	$8.10
-$10	40%	$4	$4	$4	$0	$0	$0	-$0.39	-$0.16
	30%
		-$1	-$1	-$1	$0	$0	$0	-$12.40	-$3.72
								Expected NPV of Future Operating CFs =	$4.22
		Future Cost of Implementing Additional Project (Discount at Risk-free rate)						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. NPV this	Prob.
0	Probability	1	2	3	4	5	6	Scenario	x PV
		$0	$0	-$10	$0	$0	$0	-$7.12	-$2.14
	40%	$0	$0	$0	$0	$0	$0	$0.00	$0.00
	30%
		$0	$0	$0	$0	$0	$0	$0.00	$0.00
								Expected NPV of Future Operating CFs =	-$2.14
								Total NPV (NPV of Future Operating CF plus NPV of Future Year 3 cost of implenting additional project) =	$2.09
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			Future Operating Cash Flows (Discount at WACC)
		Cost				NPV this	Probability
0	Probability	1	2	3	4	Scenario	x NPV
			$9	$9	$9	$21.62	$6.48
	40%		$0	$0	$0	$0.00	$0.00
	30%
			$0	$0	$0	$0.00	$0.00
						Expected PV of Future CFs =	$6.48
Decision Tree Analysis			Future Cost of Implementation (Discount at Risk-Free Rate)
		Cost				Discount at risk-free rate since the cost is known with certainty. NPV this	Probability
0	Probability	1	2	3	4	Scenario	x NPV
		-$10	$0	$0	$0	-$9.43	-$2.83
	40%		$0	$0	$0	$0.00	$0.00
	30%
			$0	$0	$0	$0.00	$0.00
						Expected PV of Future CFs =	-$2.83
Total NPV (NPV of Future Operating CF plus NPV of Future Year 1 cost of implenting additional project) =
							$3.65
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
kRF =	Risk-free interest rate			=	Risk-free interest rate
t =	Time until the option expires			=	Time until the option expires
X =	Exercise 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)						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. NPV this	Prob.
0	Probability	1	2	3	4	5	6	Scenario	x NPV
		$0	$0	$0	$9	$9	$9	$15.39	$4.62
	40%	$0	$0	$0	$4	$4	$4	$6.84	$2.74
	30%
		$0	$0	$0	-$1	-$1	-$1	-$1.71	-$0.51
								Expected NPV of Future Operating CFs =	$6.84
	kRF =	6%
	t =	3
	X =	$10.00
	P =	$6.84
	s2 =	22.0%
	d1 =	{ ln (P/X) + [kRF + s2 /2) ] t } / (s t1/2 )			=	0.160
	d2 =	d1 - s (t 1 / 2)			=	-0.65
	N(d1)=	Use the NORMSDIST function. 0.56
	N(d2)=	Use the NORMSDIST function. 0.26
	V =	P[ N (d1) ] - Xe-kRF t [ N (d2) ]			=	$1.71
		Value of original project=	NPV from part a. -$0.39
		Value of growth option=	$1.71
		Total Value=	$1.31
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.