Question

The B&B mineral Water Company is proposing to market a high fiber mineral water beverage. The product will be first test marketed for 3-years in various retirement communities in Florida at an initial (time zero) cost of $500,000. This test period is not expected to produce any profits, but will reveal consumer preferences. There is a 40% chance that demand will be good, a 30% chance that demand will be satisfactory, and a 30% chance that demand will be bad. If demand is good, B&B will spend $5 million to launch the product in certain regional markets and will receive expected annual profit (FCFF) of $700,000 in perpetuity. If demand is satisfactory, B&B will spend $2.5 million to launch the product in certain regional markets and will receive expected annual profit (FCFF) of $300,000 in perpetuity. In both good and satisfactory cases, the investment expenditure will be made at the end of year 3, and the first cash flow will be received at the end of year 4. If demand is bad, B&B will withdraw the product.Once consumer preferences are known (i.e., at the end of 3-years), the product will be subject to an average degree of risk, and therefore, B&B will require a return of 10% on their investment. However, the 3-year test-market phase is viewed by B&B as being riskier, and therefore, they will require a 30% return on their initial test market expenditure.What is the NPV of the high fiber mineral water project?

Answer 1

Solution:

First we will find the expected NPV for all the scenarios good, satisfactory and bad:

Expected NPV is the sum of the product of NPVs under different scenarios and their relevant probabilities.

It is given that once consumer preferences are known (i.e., at the end of 3-years), the product will be subject to an average degree of risk, and therefore, B&B will require a return of 10% or 0.1 on their investment

Under good demand Scenario:

B&B will spend $5 million i.e. $5,000,000 at the end of 3-years
B&B will receive expected annual profit (FCFF) of $700,000 in perpetuity and the first cash flow will be received at the end of year 4.
So, the present value of this perpetuity at the end of 3-years = 700000/(required return) = 700000/0.1 = 7,000,000
NPV under good demand scenario = 7,000,000 - 5,000,000 = 2,000,000

Under satisfactory demand Scenario:

B&B will spend $2.5 million i.e. $2,500,000 at the end of 3-years
B&B will receive expected annual profit (FCFF) of $300,000 in perpetuity and the first cash flow will be received at the end of year 4.
So, the present value of this perpetuity at the end of 3-years = 300000/(required return) = 300000/0.1 = 3,000,000
NPV under satisfactory demand scenario = 3,000,000 - 2,500,000 = 500,000.

Under bad demand Scenario:

There will be no additional investment and no cash-flows as If demand is bad, B&B will withdraw the product.
So, NPV under bad demand scenario = 0.

Finally, Expected NPV considering all the three scenarios = chance that demand will be good*NPV under good demand scenario + chance that demand will be satisfactory*NPV under satisfactory demand scenario + chance that demand will be bad*NPV under bad demand scenario
= 0.4*2,000,000 + 0.3*500,000 + 0.3*0
= 950,000

This expected NPV is the net expected cash flow at the end of 3-years.

It is given that the 3-year test-market phase is viewed by B&B as being riskier, and therefore, they will require a 30% return on their initial test market expenditure.

Value of the above net expected cash flow at year 0 = 950,000 / (1 + 0.3)^3 = 432,407.8289.

Initial (time zero) cost for this project for B&B = $500,000.

Therefore, the NPV of the high fiber mineral water project = 432,407.8289 - 500,000 = -$67,592.1711.

As the NPV is negative so this project should not be undertaken.