Question

A proposed project costs $500 today in order to explore its feasibility. If the decision is made to continue the project it will cost an additional $1,500 a year from today.   In years two through six, there is a 70% probability that cash flows will be $1,000 per year and a 30% probability that cash flows will be $400 per year. Which cash flow scenario will occur will be known with certainty following the feasibility study. What is the NPV of the project if the appropriate discount rate is 15%?

1. $411.20
2. $627.40
3. $747.25
4. $1,110.57
5. $1,950.00

Answer 1

In case of 70% probability that cash flows will be $1,000 per year

NPV after one year =-1500+ 1000/1.15^1+1000/1.15^2+.....+1000/1.15^5

= -1500+1000/0.15*(1-1/1.15^5)

=1852.16

So, NPV today= -500+1852.16/1.15 = 1110.57

In case of 30% probability that cash flows will be $400 per year

NPV after one year =-1500+ 400/1.15^1+400/1.15^2+.....+400/1.15^5

= -1500+400/0.15*(1-1/1.15^5)

= -159.138

As the scenario will be known after feasibility study, the investment of 1500 will not be made in this case

Hence NPV today = -500

Expected NPV = 1110.57*70%+(-500)*30% = $627.40 (option b)