# Valuing real options. Cant seem to wrap my head around this question

Hi all,

I am studying for a CFA exam and am currently going through some mock-up exams. For some reason, I cannot make sense of the multiple-choice answers to a set of questions regarding real options, so I hope some of you could help me out.

"A project costs \$104 when t=0. The payout from the project will be \$180 with 40% probability and \$60 with 60% probability in t=1. The risk-free rate is 5%"

From this, I can calculate the NPV to \$-1.14. Great. The following questions are:

"1) Assume you have a timing-option which allows you to delay the investment until t=1, but the investment will cost 109.20 (104(1+0.05)). What is the value of the project at t=0?"*

a. 26.97
b. 28.95
c. -77.03
d. 28.32

My issue: To me, all of the cash-flows are just moved one period using the 5% risk-free rate. Hence, the discounted value of the cash-flows will still equal -1.14?

"2) Now suppose you have an expansion option instead of timing-option. The expansion option contains the option to double the value of the project at t=1, if you invest an additional \$80"

a. 44.00
b. 140.95
c. 36.95
d. 67.43

Again, none of my calculations are close to the options given above. Also, I feel like the question can be interpreted in numerous ways. I.e. will the doubling of cash flow come immediately as the \$80 is invested - or in the subsequent period? Or will the \$80 be invested immediately at t=0?

There are similar questions with contraction and staging options.

I hope some of you can help me with understanding how to approach these different options/demonstrate the calculations used to arrive at the correct answer. Also, sorry if there are any grammatical errors. English is not my first language.

Thank you so much!