Question

The executives of Garner-Wagner Inc. are considering a project that will cost $85 million. The cost of capital for this type of project is 10 percent and the risk-free rate is 5 percent. There is a 50 percent chance of high demand, with future cash flows of $50 million per year for 3 years. There is a 40 percent chance of average demand, with cash flows of $30 million per year for 3 years. If demand is low (a 10 percent chance), cash flows will be only $20 per year for 3 years

a. What is the expected NPV?

b. If Garner-Wagner Inc makes the investment today, then it will have the option to replicate the project at the end of project life if the demand is high. The cash flow will be repeated (i.e., the demand will continue to be high).

Use decision-tree analysis to calculate the expected NPV of this project, including the option to replicate.

c. If Garner-Wagner Inc wants to use Black-Sholes formula to estimate the value of this real option, What would be the value of P in the Blacksholes formula?

d. Estimate the variance in the Black-Sholes formula.

Answer 1

No of Years	Nature of Demand	Probability	Quantity of Cash Flow	PV factor for 10% of expected return
1	50% of High	0.50	$50 Millions	0.909
2	50% of High	0.50	$50 Millions	0.826
3	50% of High	0.50	$50 Millions	0.751
4	40% of High	0.40	$30 Millions	0.683
5	40% of high	0.40	$30 Millions	0.621
6	40% of high	0.40	$30 Millions	0.564
7	10%of High	0.10	$ 20 Millions	0.513
8	10% of high	0.10	$20 Millions	0.467
9	10% of high	0.10	$20 Millions	0.424

Cost of Capital(Ke) = 10% and Risk free return (Rf) = 5%

1) Total Years cash flow= 0.50(50)+0.50(50)+ 0.50(50)+0.40(30)+0.40(30)+0.40(30)+0.10(20)+0.10(20)+0.10(20)

Present value of cash flows =25(0.909)+25(0.826)+25(0.751)+12(0.683)+12(0.621)+12(0.564)+2(0.513)+2(0.467)+2(0.424)

= 22.725+20.65+18.775+8.196+7.452+6.768+1.026+0.934+0.848

=$87.374

Expected NPV= Expected Cash flow - Initial Outlay= $87.374-$85= $2.347

2) Risk free rate of return is