Question

Boardman Gases and Chemicals is a supplier of highly purified gases to semiconductor manufacturers. A large chip producer has asked Boardman to build a new gas production facility close to an existing semiconductor plant. Once the new gas plant is in​ place, Boardman will be the exclusive supplier for that semiconductor fabrication plant for the subsequent 10 years. Boardman is considering one of two plant designs. The first is ​ Boardman's "standard" plant which will cost ​$39.1 million to build. The second is for a​ "custom" plant which will cost ​$54.1 million to build. The custom plant will allow Boardman to produce the highly specialized gases required for an emergency semiconductor manufacturing process. Boardman estimates that its client will order​$12.3 million of product per year if the standard plant is​ constructed, but if the custom design is put in​ place, Boardman expects to sell ​$16.7 million worth of product annually to its client. Boardman has enough money to build either type of​ plant, and, in the absence of risk​ differences, accepts the project with the highest NPV. The cost of capital is 17.2%.

a. Find the NPV for each project. Are the projects​ acceptable?

b. Find the breakeven cash inflow for each project.

c. The firm has estimated the probabilities of achieving various ranges of cash inflows for the two​ projects, as shown in the table. What is the probability that each project will achieve the breakeven cash inflow found in part ​(b​)​?

	Probability of achieving cash inflow in given range
Range of cash inflow​ ($ millions)	Standard Plant	Custom Plant
​$0 to​ $5	0%	5%
​$5 to​ $8	10	10
​$8 to​ $11	60	15
​$11 to​ $14	25	25
​$14 to​ $17	5	20
​$17 to​ $20	0	15
Above​ $20	0	10

d. Which project is more​ risky? Which project has the potentially higher​ NPV? Discuss the​ risk-return trade-offs of the two projects.

e. If the firm wished to minimize losses​ (that is, NPV < $0​), which project would you​ recommend? Which would you recommend if the goal was achieving a higher​ NPV?

Answer 1

a) NPV of standard plant = -39.1 +12.3/1.172 +12.3/1.172^2+...+12.3/1.172^10

=-39.1+12.3/0.172*(1-1/1.172^10)

=17.7864

So the NPV of standard plant is $17.7864 Million

NPV of Custom plant = -54.1 +16.7/1.172 +16.7/1.172^2+...+16.7/1.172^10

=-54.1+16.7/0.172*(1-1/1.172^10)

=23.1361

So the NPV of Custom plant is $23.1361 Million

As NPV is positive for both projects, both projects are acceptable. But Custom project must be selected as it has higher NPV

b) Breakeven cash inflow (A) of Standard plant is given by

A/0.172*(1-1/1.172^10) = 39.1

=> A*4.62491 =39.1

=> A = $8.4542 million

Breakeven cash inflow (A) of Custom plant is given by

A/0.172*(1-1/1.172^10) = 54.1

=> A*4.62491 =54.1

=> A = $11.6975 million

c) Assuming linear distribution of probability within intervals

For Standard plant

Pr(CF>8.4542)

= Pr(8<CF<11)*(11-8.4542)/(11-8) + Pr(11<CF<14)+ Pr(14<CF<17)+ Pr(17<CF<20)+ Pr(20<CF)

= 60%*2.5458/3+25%+5%+0+0

=80.916% which is the probability of achieving the breakeven Cashflows

For Custom plant

Pr(CF>11.6975)

= Pr(11<CF<14)*(14-11.6975)/(14-11) + Pr(14<CF<17)+ Pr(17<CF<20)+ Pr(20<CF)

= 25%*2.3025/3+20%+15%+10%

=64.1875% which is the probability of achieving the breakeven Cashflows

d) As per the probabilities of achieving the breakeven cashflows, the Custom project is more risky as it has less probability to achieve breakeven cashflows as compared to Standard project

The Custom Project also has higher potential NPV . Thus the Custom project is a high risk, high reward project as compared to standard project which has a less risk and less reward.

e. If the goal is to minimise losses. the Standard project with high probabilities of achieving breakeven cashflows. However, if the goal is to achieve a higher NPV , the Custom project with a potential higher NPV is better.