Question

The Rodriguez Company is considering an average-risk investment in a mineral water spring project that has an initial after-tax cost of $175,000. The project will produce 1,100 cases of mineral water per year indefinitely, starting at Year 1. The Year-1 sales price will be $146 per case, and the Year-1 cost per case will be $121. The firm is taxed at a rate of 25%. Both prices and costs are expected to rise after Year 1 at a rate of 5% per year due to inflation. The firm uses only equity, and it has a cost of capital of 12%. Assume that cash flows consist only of after-tax profits because the spring has an indefinite life and will not be depreciated.

1. What is the present value of future cash flows? (Hint: The project is a growing perpetuity, so you must use the constant growth formula to find its NPV.) What is the NPV? Do not round intermediate calculations. Round your answers to the nearest dollar. Negative values, if any, should be indicated by a minus sign.

   PV of future CFs:	$
   NPV:	$

2. Suppose that the company had forgotten to include future inflation. What would they have incorrectly calculated as the project's NPV? Do not round intermediate calculations. Round your answer to the nearest dollar. Negative value, if any, should be indicated by a minus sign.

   $  

Answer 1

Question a:

Year 1 Cash Flows  = 1,100 cases * ($146 - $121) = $27,500

Year 1 After Tax Cash Flows = $27,500 * (1 - 25%) = $20,625

g = inflation = 5%

r = cost of capital = 12%

>>>

Present value of future cash flows = Year 1 Cash Flows / (r -g)

= $20,625 / (12% - 5%)

= $20,625 / 0.07

= $294,642.857

Present value of Future cash flows is $294,642.86

>>>

NPV of the Project = Present value of Future cash flows - Initial Investment

= $294,642.86 - $175,000

= $119,642.86

Therefore, NPV of the Project with inflation is $119,642.86

Question b:

Year 1 Cash Flows  = 1,100 cases * ($146 - $121) = $27,500

Year 1 After Tax Cash Flows = $27,500 * (1 - 25%) = $20,625

r = cost of capital = 12%

>>>

Present value of future cash flows = Year 1 Cash Flows / Cost of Capital

= $20,625 / 12%

= $20,625 / 0.12

= $171,875

Present value of Future cash flows is $171,875

>>>

NPV of the Project = Present value of Future cash flows - Initial Investment

= $171,875 - $175,000

= -$3,125

Therefore, NPV of the Project without considering inflation is -$3,125