101 Concepts for the Level I Exam Show Concept 1: Calculating PV and FV of Different Cash FlowsPresent value is the current value of a future cash flow.
Future value is the value to which an investment will grow after one or more compounding periods.
The future value and the present value of a single sum of money can be calculated by using the formulae given below or by using the TVM keys on a financial calculator (recommended approach for the exams). FV = PV (1 + I/Y)N PV = FV / (1 + I/Y)N You invest U$100 today at an interest rate of 10% for 5 years. How much will you receive after five years? Solution: Plug the following values in the calculator. N = 5; I/Y = 10; PV = 100, PMT = 0; CPT FV = $161.05 An ordinary annuity is series of finite but equal cash flows which occur at the end of each period. How much should you invest today at an interest rate of 10% to receive $100 at the end of each year for 5 years? Using the calculator: N = 5; I/Y = 10; PMT = 100; FV = 0; CPT PV = $379.08 An annuity due is a series of finite but equal cash flows which occur at the start of each period. How much should you invest today at an interest rate of 10% to receive $100 at the beginning of each year for 5 years? Solution: Put the calculator in BGN mode and plug the following values. (Remember to exit the BGN mode once you are done with your calculations.) N = 5; I/Y = 10; PMT = 100, FV = 0; CPT PV = $416.98 A perpetuity is a series of equal cash flows at regular intervals occurring forever. The present value of perpetuity can be calculated as:
 How much should you invest today at an interest rate of 10% to receive $100 at the end of each year forever? Solution: PV = 100/0.1 = $1,000 The present (future) value of any series of cash flows is equal to the sum of the present (future) values of the individual cash flows. What is the future value of the following series of cash flows, given an interest rate of 10%? $1,000 at the end of year 1, $2,000 at the end of year 2, $3,000 at the end of year 3, $4,000 at the end of year 4 and $5,000 at the end of year 5. Solution: The future value is 5000 + 4000 x 1.1 + 3000 x 1.12 + 2000 x 1.13 + 1000 x 1.14 = $17,156 New: CRASH COURSE for the Nov-2022 Exam. Revise and Practice in our Live/Zoom Class. This is default text for notification bar Learn how Net Present Value works What is the NPV Formula?The NPV formula is a way of calculating the Net Present Value (NPV) of a series of cash flows based on a specified discount rate. The NPV formula can be very useful for financial analysis and financial modeling when determining the value of an investment (a company, a project, a cost-saving initiative, etc.). Below is an illustration of the NPV formula for a single cash flow. Screenshot of CFI’s Corporate Finance 101 Course. NPV for a Series of Cash FlowsIn most cases, a financial analyst needs to calculate the net present value of a series of cash flows, not just one individual cash flow. The formula works in the same way, however, each cash flow has to be discounted individually, and then all of them are added together. Here is an illustration of a series of cash flows being discounted: Source: CFI’s Free Corporate Finance Course. What is the Math Behind the NPV Formula? Here is the mathematical formula for calculating the present value of an individual cash flow. NPV = F / [ (1 + i)^n ] Where, PV = Present Value F = Future payment (cash flow) i = Discount rate (or interest rate) n = the number of periods in the future the cash flow is How to Use the NPV Formula in ExcelMost financial analysts never calculate the net present value by hand nor with a calculator, instead, they use Excel. =NPV(discount rate, series of cash flow) (See screenshots below) Example of how to use the NPV function: Step 1: Set a discount rate in a cell. Step 2: Establish a series of cash flows (must be in consecutive cells). Step 3: Type “=NPV(“ and select the discount rate “,” then select the cash flow cells and “)”. Congratulations, you have now calculated net present value in Excel! Download the free template. Source: CFI’s Free Excel Crash Course. If you need to be very precise in your calculation, it’s highly recommended to use XNPV instead of the regular function. To find out why, read CFI’s guide to XNPV vs NPV in Excel. Video Explanation of the NPV FormulaBelow is a short video explanation of how the formula works, including a detailed example with an illustration of how future cash flows become discounted back to the present. DCF ModelingThe main use of the NPV formula is in Discounted Cash Flow (DCF) modeling in Excel. In DCF models an analyst will forecast a company’s three financial statements into the future and calculate the company’s Free Cash Flow to the Firm (FCFF). Additionally, a terminal value is calculated at the end of the forecast period. Each of the cash flows in the forecast and terminal value are then discounted back to the present using a hurdle rate of the firm’s weighted average cost of capital (WACC). Below is an example of a DCF model from one of CFI’s financial modeling courses. Screenshot: CFI financial modeling courses. Why do we calculate present value of cash flows?Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Present value takes the future value and applies a discount rate or the interest rate that could be earned if invested.
What is the formula for calculating present value?The present value formula is PV = FV/(1 + i) n where PV = present value, FV = future value, i = decimalized interest rate, and n = number of periods. It answers questions like, How much would you pay today for $X at time y in the future, given an interest rate and a compounding period?
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