Question

Stulz Co. is considering to start a new project. If Stulz Co. commits and invests $450 mil today, the present value project is $500 mil (i.e. NPV = $50 mil). If the project gets off to a good start and demand is high in year 1, the cash flow at year 1 will be $62.5 mil and the value of project rises to $625 mil. But, if things don't work out, the cash flow at year 1 is only $40 mil and the value of project falls to $400 mil. Although the project lasts indefinitely, we assume that investment can’t be postponed beyond the end of the first year, and therefore we observe only the cash flows for the first year and the possible value of project at the end of the first year. If Stulz Co. undertakes project right away, it captures the first year’s cash flows ($62.5 mil or $40 mil). If Stulz Co. delays, it misses out this cash flow, but it will have more information on how the project is likely to work out. Risk free interest rate is 2%. Calculate the value of timing (delay) option.

A. $22.90 mil B. $105.88 mil C. $48.52 mil D. $37.19 mil E. $57.17 mil F. $78.59 mil G. $98.03 mil H. $72.73 mil

Answer 1

Option (c) $48.52 million

Using Binomial method to value this Real Option:

1. Calculate risk-neutral probabilities of high and low demand

If demand is high in the first year, the project has a cash flow of $62.5 million and a year-end value of $625 million. The total return is (62.5+625)/500 - 1 = 0.5278 = 37.50%

If the demand is low in the first year, the project has a cash flow of $40 million and a year-end value of $400 million. The total return is (40+400)/500 - 1 = -0.1200 = -12%

In a risk-neutral world, the expected return would be equal to the interest rate, which is 2%

Expected return = probability of high demand*37.50% + (1-probability of high demand)*(-12%) = 2%

Therefore, the risk-neutral probability of high demand is 28.3% and of low demand is 71.7%.

We want to value a call option on the project with an exercise price of $450 million. We begin backward, i.e. value the option at the end of year 1.

If the project value is $400 million, the option to invest is worthless. At the other extreme, if the project value is $625 million, option value is $625-$450 = $175 million.

To calculate the value of the option today, we work out the expected payoffs in a risk-neutral world and discount at the interest rate of 2%. Thus, the value of option to invest in the project is

(28.3%*175 + 71.7%*0)/1.02 = $48.52 million