Question

Scenario: A new product manager presents to you, the Chief Financial Officer, a proposal to expand operations that includes the purchase of a new machine. The product manager is certain that the positive cash flows, which exceed the initial outlay by $20,000 by the end of year 4, will bring both praise and approval. You explain the company uses a 12% discount rate for cash flows and project related budgeting. You take the time to present the details of the Net Present Value (NPV) model used to assess product proposals. The data is below.

Project Outflows to Buy Machine      

Day 1 Cash Out                     -$70,000 12% discount rate applied.

End Year 1 Cash Repayment            $10,000

End Year 2 Cash Repayment            $20,000

End Year 3 Cash Repayment            $30,000

End Year 4 Cash Repayment            $30,000

To educate the new manager, and as CFO, you take the time to evaluate the following:

Checklist:

• Evaluate how the Time Value of Money concept results in a discounted cash flow in year 4 (an amount less than $30,000).
• Assess the investment option using a 12% cost of capital discount rate by applying the NPV model. Include values in your assessment. Provide the NPV at a 12% cost of capital discount rate. Include values in your assessment.
• Assess the investment option when a 7% cost of capital discount rate, versus a 12% cost of capital discount rate is applied. Include values in your assessment. Provide the NPV at a 7% cost of capital discount rate.

Answer 1

Net present value is the sum of all expected future cash flows discounted at the appropriate discount rate. The present value of a future cash flow can be calculated using the formula:

For example the present value of the cash flow to be received at the end of year 4 would be:

which is actually way less than 30,000.

Similarly, all cash flows need to be discounted and the sum of those discounted values would be the NPV. So, at a discount rate of 12%, NPV is:

or NPV=-4,708.6

Since, NPV is negative at 12% discount rate, the project should actually not be accepted.

If instead, the cost of capital was 7%, NPV would be:

or NPV = 4190.36

So, if the cost of capital was 7%, the project's NPV is positive and therefore, the project should be accepted.