An initial investment of
3,411 thousand,
5,824 thousand, and
900 thousand. Calculate the net present value of the investment if the discount rate is 18%. Round your answer to the nearest thousand dollars.
The Correct Answer and Explanation is:
Net Present Value (NPV) Calculation
We are given three initial investments:
- 3,411 thousand
- 5,824 thousand
- 900 thousand
Since all are initial investments, they occur at time zero. To calculate the Net Present Value (NPV), we need the future cash inflows from these investments. However, the problem only mentions the investment amounts and the discount rate of 18 percent. If we assume the question is asking for the total present value of these outflows, then:
Total Investment = 3,411 + 5,824 + 900 = 10,135 thousand
Since these are initial investments made at time zero, their present value remains the same. Thus, if there are no future cash inflows mentioned, the NPV would just be the negative of this total investment:
NPV = –10,135 thousand
However, if you meant to calculate the present value of future returns from each investment (over a certain period), we would need those cash inflows and the time frame. For now, we’ll assume you’re referring to a series of annual cash flows that are equal to the amount invested for each, returned in one year. If we treat each amount as a single cash inflow to be received one year from now, we calculate the present value for each as follows:
Present Value Formula
PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}PV=(1+r)nFV
Where:
- FVFVFV is the future value (cash inflow)
- rrr is the discount rate (18 percent or 0.18)
- nnn is the number of years (assumed to be 1 year here)
So:
- PV of 3,411 = 3,411 ÷ (1 + 0.18) = 2,891
- PV of 5,824 = 5,824 ÷ (1 + 0.18) = 4,936
- PV of 900 = 900 ÷ (1 + 0.18) = 763
Now sum the present values:
Total PV = 2,891 + 4,936 + 763 = 8,590 thousand
Now subtract the total investment:
NPV = 8,590 – 10,135 = –1,545 thousand
Final Answer:
NPV ≈ –1,545 thousand dollars
Explanation
Net Present Value or NPV is a key financial metric used in capital budgeting to evaluate the profitability of an investment or project. It is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. The idea is to determine whether the investment will generate more value than it costs, once the time value of money is taken into account.
In this case, the investments total 10,135 thousand dollars. The discount rate given is 18 percent. We assume each investment returns an equal amount one year later. Using the present value formula, each future inflow is divided by one plus the discount rate. This gives the equivalent amount in today’s terms.
When we apply the formula, the present values of the individual investments come to 2,891, 4,936, and 763 thousand dollars respectively. Adding these gives a total present value of 8,590 thousand. Since the total amount invested is 10,135 thousand, the difference is negative 1,545 thousand. This means that, under the assumed conditions, the investment would result in a net loss of value when discounted at 18 percent.
A negative NPV suggests that the investment should be rejected, as it does not generate returns above the required rate. It would reduce value rather than create it. In capital budgeting decisions, firms typically accept projects with a positive NPV because they are expected to increase shareholder wealth. Thus, based on this analysis and assumption of returns in one year, this investment would not be financially favorable.
