Question

A smooth saleperson comes to visit your office with a proposal to sell your firm some new machinery to install in your vacant warehouse building on the property that has no alternative use. The salesperson claims that this technology produces products that should provide you with revenues next year of $7 million with a cost of goods to be $5 million. Both of these are expected to grow at a rate of 15% per year till year 6. Your firm faces a 35% tax rate, a 12% discount rate and you can depreciate your new investment using the straight line method over the six years, at which point the value of the venture moving forward will be $2 million. (This $2 million is the terminal value that is in year 6 dollars and is the PV of all cash flows year 7 and beyond.) The capital expenditure of this project is $6M. What is the NPV of the project? Assume that you have no significant working capital costs.(Enter just the number without the $ sign or a comma; round off decimals.) (You are strongly encouraged to use a spreadsh

Answer 1

In finance, the net present value (NPV) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity. In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, above the cost of funds.

NPV can be described as the "difference amount" between the sums of discounted: cash inflows and cash outflows. It compares the present value of money today to the present value of money in the future, taking inflation and returns into account.

$$\mathrm {N P V} (i, N) = \sum_ {t = 0} ^ {N} \frac {R _ {t}}{(1 + i) ^ {t}}$$