When you are asked to find the net present worth of the following cash flow series at an interest rate of 10 %, you are determining the current value of all cash inflows and outflows discounted back to today. This process is essential in engineering economics and project evaluation because it converts future money into today’s terms using a 10 % interest rate as the benchmark for time value of money.
Understanding The Basic Concept Of Net Present Worth
Net present worth, or NPW, is the algebraic sum of the present values of all cash flows in a series, where each cash flow is adjusted for the 10 % interest rate. To find the net present worth of the following cash flow series at an interest rate of 10 %, you first identify each cash flow, its amount, and the exact timing in years when it occurs. Then you apply the present worth factor, which is one divided by one plus the interest rate raised to the power of the period number.
The general present worth formula is P = F / (1 + 0.10)^n, where F is the future cash flow and n is the year. Using this formula repeatedly for every inflow and outflow allows you to accumulate the total net present worth at 10 % and see whether the project adds value in today’s dollars.
Step By Step Calculation Procedure
To find the net present worth of the following cash flow series at an interest rate of 10 %, start by listing each year’s cash flow in chronological order, marking positive for inflows and negative for outflows. Next, calculate the discount factor for each year at 10 %, which becomes 1 for year zero, approximately 0.909 for year one, 0.826 for year two, and so on.
Multiply each cash flow by its corresponding discount factor to obtain the present worth of that year, then sum all these present worth values to arrive at the net present worth at 10 %. This systematic approach ensures that you consistently handle both positive and negative cash flows in the same terms.
Practical Example With Sample Cash Flows
Imagine a series with an initial outflow of 100 at year zero, an inflow of 150 at year one, and an inflow of 200 at year two. To find the net present worth of the following cash flow series at an interest rate of 10 %, you first recognize the 100 as a negative amount at time zero so its present worth remains 100. Then you discount the 150 at year one by 0.909 to get 136.35, and the 200 at year two by 0.826 to get 165.20. Summing 136.35 and 165.20 minus 100 gives a net present worth of 201.55, indicating a profitable project at 10 %.
Conclusion
In conclusion, to find the net present worth of the following cash flow series at an interest rate of 10 %, you consistently apply discounting to each cash flow and combine them into a single present value measure. Mastering this calculation helps you compare projects objectively and choose investments that truly generate value in today’s dollars.
