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 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 $39.3 million to build. The second is for a "custom" plant which will cost $53.4 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 $17.9 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 16.8%. 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)? 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? a. The NPV for project "standard" is $ . (Round to the nearest cent.)

Answer 1

Solution:

a. Net Present Value and acceptability of projects

Net Present Value, NPV = PVA_n - I

PVA_n = Present value of n cash inflows = A x [(1+r)ⁿ - 1] / r(1+r)ⁿ where A is the annual cash inflow, n is the period and r is discount rate or cost of capital

I = Initial Outlay

NPV of standard plant = {12.9 x [(1+0.168)¹⁰-1] / 0.168 x (1+0.168)¹⁰ } - 39.3 = 60.54 - 39.30 = $ 21.24 mn

NPV of custom plant = {17.9 x [(1+0.168)¹⁰-1] / 0.168 x (1+0.168)¹⁰ } - 53.4 = 84 -53.40 = $ 30.60 mn

(1.168¹⁰ = 4.7253)

Both projects are acceptable as they have a positive NPV.

b. Breakeven cash inflow for the projects

Breakeven is when the NPV is 0 or the PV of inflows equals initial outlay

Breakeven inflows A_S of standard plant:

{A_S x [(1+0.168)¹⁰-1] / 0.168 x (1+0.168)¹⁰ } = 39.3

So A_S x 4.6927 = 39.30 and A_S = 39.30 / 4.6927 = $ 8.37 mn

Breakeven inflows A_C of custom plant:

{A_C x [(1+0.168)¹⁰-1] / 0.168 x (1+0.168)¹⁰ } = 53.4

So A_C x 4.6927 = 53.40 and A_C = 53.40 / 4.6927 = $ 11.38 mn

c. Probability of each project reaching the breakeven cash inflow

As standard plant project has cash inflow of 8.37 mn, it falls in the range of $ 8 to $ 11 mn, so there is a 60% probability that the project will reach the breakeven cash inflow.

As custom plant project has cash inflow of 11.38 mn, it falls in the range of $ 11 to $ 14 mn, so there is a 25% probability that the project will reach the breakeven cash inflow.

d. Riskier of the two, higher NPV and risk-return trade-off

The custom plant project is more riskier than the standard one since it involves a higher initial investment. However, it has a potentially higher NPV as can be seen from answer part a.

The standard plant has a lower investment and has lower cash inflows and hence is less risky as it has a lower chance of failure. Further, it has a greater probability of achieving cash inflows in the range of $ 8 to $ 11 mn, hence it results in a lower return than the custom one.

The custom plant has a higher investment and has higher cash inflows and hence is more risky as it has a higher chance of failure. Further, it has a greater probability of achieving cash inflows in the range of $ 11 to $ 14 mn, hence it results in a higher return than the standard one.

e. Minimise losses and maximise NPV

If the firm wishes to minimize the losses i.e when NPV < 0, the firm should select the standard one since the maximum loss will not be more than $ 39.3 mn (the initial investment) against $ 53.4 mn (that of the custom one). If the goal was to achieve a higher NPV the custom project would have to be selected as it has higher inflows of $ 17.9 mn against $ 12.9 mn od the standard plant.