Question

Dernham Inc. is looking at investing in a production facility that will require an initial investment of $500,000. The facility will have a three-year useful life, and it will not have any salvage value at the end of the project’s life. If demand is strong, the facility will be able to generate annual cash flows of $260,000, but if demand turns out to be weak, the facility will generate annual cash flows of only $135,000. Dernham Inc. thinks that there is a 50% chance that demand will be strong and a 50% chance that demand will be weak.

If the company uses a project cost of capital of 11%, what will be the expected net present value (NPV) of this project?

A.) -$14,761

B.) -$11,288

C.) -$9,551

D.) -$17,366

Dernham Inc. could spend $510,000 to build the facility. Spending the additional $10,000 on the facility will allow the company to switch the products they produce in the facility after the first year of operations if demand turns out to be weak in year 1. If the company switches product lines because of low demand, it will be able to generate cash flows of $255,000 in years 2 and 3 of the project.

What is the expected NPV of this project if Dernham Inc. decides to invest the additional $10,000 to give themselves a flexibility option? (Note: Do not round your intermediate calculations.)

A.) $65,203

B.) $82,569

C.) $33,028

D.) $58,683

What will be the value of Dernham Inc.’s flexibility option?

A.) $33,028

B.) $65,203

C.) $58,683

D.) $74,312

E.) $82,569

Answer 1

1) Initial Investment = 500,000 | Strong demand Cashflows = 260,000 | Weak demand cashflows = 135,000

Probability of each state = 50% | Cost of capital = 11% | Time = 3 years

Expected Cashflows = Probability * Strong Demand Cashflow + Probability * Weak Demand cashflow

Expected Cashflows = 50% * 260,000 + 50% * 135,000 = 197,500

Using the Annuity formula, we can calculate Present Value of cashflows for 3 years and cost of capital of 11%.

PV of Annuity = (CF/R)*(1-(1+R)^-T)

PV of cashflows = (197,500 / 11%)*(1 - (1+11%)^-3)

PV of cashflows = $ 482,633.66

NPV = PV of cashflows - Initial cost

NPV of the project = 482,633.66 - 500,000 = -17,366.34 or - $17,366

Hence, NPV of the project is - $17,366 which is Option D.

2) Initial Cost = 510,000 | Cashflow for 2 and 3 years if weak demand = 255,000

Year 1 Expected Cashflow = 50% * Strong demand cashflow + 50% * Weak demand cashflow

Year 1 expected Cashflow = 50% * 260,000 + 50% * 135,000 = 197,500

Year 2 and 3 Expected Cashflow = 50% * Strong demand cashflow + 50% * New Cashflow in case of weak demand

Year 2 and 3 Expected Cashflow = 50% * 260,000 + 50% * 255,000 = 257,500

PV of Cashflows = 197500 / (1+11%) + 257,500 / (1+11%)² + 257,500 / (1+11%)³

PV of cashflows = 575,202.5

NPV = PV of cashflows - Initial Cost

NPV = ​​575,202.5 - 510,000 = $65,202.5 or $ 65,203

Hence, NPV of the project with additional 10,000 for flexibility is $ 65,203 which is Option A.

3) Value of Flexibility Option = NPV of Project with Flexibility - NPV of project without flexibility

Value of Flexibility Option = 65,203 - (-17,366) = 65,203 + 17,366

Value of Flexibility Option = $ 82,569

Hence, Value of flexibility Option is $ 82,569 which is Option E.