Question

Singh Development Co. is deciding whether to proceed with Project X. The cost would be $10 million in Year 0. There is a 50% chance that X would be hugely successful and would generate annual after-tax cash flows of $6 million per year during Years 1, 2, and 3. However, there is a 50% chance that X would be less successful and would generate only $1 million per year for the 3 years. If Project X is hugely successful, it would open the door to another investment, Project Y, which would require an outlay of $9 million at the end of Year 2. Project Y would then be sold to another company at a price of $18 million at the end of Year 3. Singh’s WACC is 14%.

If the company does not consider real options, what is Project X’s expected NPV? Enter your answers in millions.

What is X’s expected NPV with the growth option? Enter your answers in millions.

What is the value of the growth option?

Answer 1

If the project is hugely successful (without considering real options)

NPV = -10 + 6/1.14+6/1.14^2+6/1.14^3 = $3.929792 million = $3,929,792

If the project is less successful

NPV = -10 + 1/1.14+1/1.14^2+1/1.14^3 = - $7.678368 million = - $7,678,368

So,

Project X's Expected NPV (without considering real options)

= 0.5*3929792+0.5*(-7678368) = - $1,874,288 = -$1.874288 million

If the project is hugely successful (considering real options)

NPV = -10 + 6/1.14+6/1.14^2 - 9/1.14^2 +6/1.14^3 + 18/1.14^3 = $9.154072 million = $9,154,072

So,

Project X's Expected NPV (with real options) = 0.5*9154072+0.5*(-7678368) = $737852 = $0.737852 million

Expected value of growth option = Expected NPV (with real options) - Expected NPV (without real options)

=0.737852 - (-1.874288)

= $2.61214 million