Question

Breakeven cash inflows and risk - 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 semi-conductor 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 $38.0 million to build. The second is for a "custom" plant which will cost $54.5 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 $12.9 million of product per year if the standard plant is constructed, but if the custom design is put in place, Boardman expects to sell $17.2 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 17.1%

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.

Range of cash inflows ($million)	Standard	Custom
0 - $5	0%	5%
$5 - $8	10%	10%
$8 - $11	60%	15%
$11 - $14	25%	25%
$14 - $17	5%	20%
$17 - $20	0%	15%
Above $20	0%	10%

What is the probability that each project will achieve the breakeven cash inflow found in part (b).

d. which project is more risky? What 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

Hi there, Thanks for posting the question. As per Q&A Guidelines, we should answer the first question when multiple questions posted under a single question. Hence, I have answered part a) below. Please repost the other questions separately. Thank you.

Answer :

Given:

plant	cost	cash inflow per year
standard plant	$38.0 million	$12.9 million
custom plant	$54.5 million	$17.2 million

NPV of both the plants can be calculated using the following formula :

Net Present value = ∑PV of cash inflows – initial cost

∑PV of cash inflows Can be calculated using Excel PV function as under :

Α B 2 Particulars 3 Cash Inflows per year 4 Rate 5 Life span 6 Cost Standard Plant Custom Plant 12.90 17.2. 17.1% 17.1% 10 38 54.5 10 8 ΣPV of cash inflows 9 NPV *59.88 * 21.88 *79.84 *25.34 70

1 Standard Plant 12.9 0.171 2 Particulars 3 Cash Inflows per year 4 Rate 5 Life span 6 Cost 7 8 ΣPV of cash inflows 9 NPV 10 Custom Plant 17.2 0.171 10 54.5 10 38 =PV(B4,B5,-B3,0,0) =B8-B6 =PV(C4,C5,-C3,0,0) =C8-C6

Note : please note that as cash inflow will be received per year in both the projects so it will be considered as annuity so applying =PV function put cashflow values as pmt.

The default value of pmt is always negative as per =PV function so used -pmt.

PV of cash inflows can be calculated manually by multiplying cash inflow with PV factor formula as cash inflows are in annuity:

(1+r)" PVofanmuity=-

Answer : as per the NPV both projects are acceptable as both having positive NPV.