Use the following Information to Answer Problems 1 and 2

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.

Problem 1: Find the projects expected cashflow and NPV

Condition	Probability	Cash Flow	Prob.*Cash Flow
Good	0.3	$9
Medium	0.4	$4
Bad	0.3	-$1
		Expected CF

Expected CF =

	T=0	T=1	T=2	T=3
CF

NPV of Project =

What can you conclude regarding this project?

Problem 2: find the projects standard deviation and coefficient variation?

Condition	Probability	NPV
Good	0.3
Medium	0.4
Bad	0.3
	Expected NPV

NPV of Project in Good Condition =

NPV of Project in Average Condition =

NPV of Project in Bad Condition =

Variance =

Coefficient Variation =

Now suppose the original 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. The cash flow and the cost of project will be shifted one year and the project will be implement only if we are in good condition. Estimate the value of the project if it is delayed by 1 year. The risk-free rate is 6% and the cost of capital is 12%

Problem 3: Using Decision Tree to estimate the value of real option (Option to wait one year and implement only if the demand is good)

	Probability	T=1	T=2	T=3	T=4	NPV@t=0
$0	Good 0.3=
	Medium= 0.4
	Bad= 0.3

A) What is the expected NPV of project if wait one year and implement only if the demand is good?

B) What is the standard deviation of projects NPV?

C) What is the Coefficient Variation of the project?

	Implement Today	Wait One Year (Decision Tree)
Expected NPV
Standard Deviation
Coefficient Variation

Problem 4: Using the information above and Black Scholes to estimate the value of real option (Option to wait one year)

P = PV of all projects future expected cash flows

P does not include the project cost

Step 1: Find the PV of future CFs at the options exercise year.

T=0	State	Prob.	T =1	T =2	T =3	T =4	PV@ T=1
	Good	0.3
	Medium	0.4
	Bad	0.3

PV of CF at the option exercise year for Good Condition

PV of CF at the option exercise year for Medium Condition

PV of CF at the option exercise year for Bad Condition

Step 2: Find the expected PV at the current date year 0

T=0	Prob.	PV@ year T =1
	0.3
	0.4
	0.3
	Expected PV

Expected PV @ T =1

Expect PV @ T = 0

Estimate Variance using the Direct Approach

T=0	Prob.	PV@ year T =1	Return
	0.3
	0.4
	0.3
		Expected Return
		Variance of Return

Return for High State =

Return for Average State =

Return for Low State

Expected Return =

Variance of return =

Determine the value of real option using Black Scholes by using the variance based on the direct Estimate

X
P
Rf
T
Variance

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

d₁ = [ln(P/X)+[(Rf+s²/2)](t)]/st

d2 = d₁-st

D1 =

D2 =

N(d1) =

N(d2) =

V =