Question

5. Consider the following project data: A 2 million feasibility study will be conducted at t =0. If the study indicates potential, the firm will spend 10 million at t= 1 to build a prototype. The best estimate is that there is an 80% chance that the study will indicate potential and 20% chance that it will not. If reception of the prototype is good the firm will spend 350 million to build a production plant at t=2. The best estimate is that there is a 70% chance that the prototypes’ reception will be poor. If the plant is built, there’s a 60% chance of a t=3 cash inflow of 300 million and a 40% chance of 150 million cash inflow. If the inflow at t=3 is 300 million, there are 30% and 70% chances of 160 million and 90 million inflows respectively at t=4. If the inflow at t=3 is 150 million, there are 80% and 20% chances of 210 million and 140 million inflows respectively at t=4. The plant has a salvage value of 50 million at t=5. If the appropriate cost of capital is 15% what is the project’s expected NPV?

Answer 1

Time	Cash-flows
0	-2
1	-8
2	-105
3	240
4	145
5	50

At t=0

Investment of 2 million

At t=1

If the study indicates potential  the firm will spend 10 million

80% chance that the study will indicate potential

Expected cash-flow = 0.8 * (-10) = -$8 million

At t=2

If reception of the prototype is good the firm will spend 350 million and the best estimate is that there is a 30% (100%-70%) chance that the prototypes’ reception will be good

Expected cash-flow = 0.3*(-350) = -$105 million

At t=3

There’s a 60% chance of a t=3 cash inflow of 300 million and a 40% chance of 150 million

Expected cash-flow = 0.6*300+0.4*150 = $240 million

At t=4

If the inflow at t=3 is 300 million, there are 30% and 70% chances of 160 million and 90 million inflows
respectively at t=4.

If the inflow at t=3 is 150 million, there are 80% and 20% chances of 210 million and 140 million inflows respectively at t=4.

Expected cash-flow = (0.6*0.3*160)+(0.6*0.7*90)+(0.4*0.8*210)+(0.4*0.2*140) = $145 million

At t=5

Salvage value of 50 million

Time	Cash-flows (in $millions)
0	-2
1	-8
2	-105
3	240
4	145
5	50

We find the function NPV to find the Project's expected NPV

NPV = Initial investment + NPV(Cost of capital, Cash-flows from year 1-5)

Cost of capital = 15%

Time	Cash-flows (in $millions)
0	-2
1	-8
2	-105
3	240
4	145
5	50
NPV (in $millions)	177.2153464

Hence the project's expected NPV = $177.2153464 million = $177,215,346.4