Time-weighted Returns

While calculating the returns on financial assets, we will often look at the returns from multiple holding periods. For example, one may hold an asset for five years, and the asset may have earned total 150% returns over this period of 5 years. However, it is...

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Holding Period Return (Total Return)

For investments, the Holding Period Return (HPR) refers to the total return earned from an investment or an investment portfolio over the holding period, that is, the period for which the asset or portfolio was held by the investor. The holding period can be anything...

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Conflict Between NPV and IRR (And Problem with IRR)

When you are analyzing a single conventional project, both NPV and IRR will provide you the same indicator about whether to accept the project or not. However, when comparing two projects, the NPV and IRR may provide conflicting results. It may be so that one project...

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Internal Rate of Return

IRR is the case of a discount rate that equalizes the present value of cash inflows with present value of cash outflows. Within the context of a net present value analysis, when the cash inflows and outflows are known, IRR will be the rate that causes the NPV to equal...

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Net Present Value

The net present value is the most commonly used method to decide whether to invest in a project or not. The net present value of a project is equal to the sum of the present value of all after-tax cash flows from the project minus the initial investment. The...

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Using a Timeline to Solve Time Value of Money Problems

When solving a time value of money problem, it is sometimes easy to draw a timeline to present the cash flows on it. Once we have the timeline, we can easily understand the variables and visualize the present value or future value calculations. In the previous pages,...

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Annuities with Different Compounding Frequencies

In all the above examples for annuities, we assumed that the compounding frequency is annual. However, this may not always be the case and an annuity may have monthly, quarterly, or even semi-annual compounding. We can solve the time value of money problems for any of...

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Present Value and Future Value of Uneven Cash Flows

We have looked at the PV/FV calculations for single sums of money and for annuities in which all the cash flows are equal. However, there may be an investment where the cash flows are not equal. We will now look at how to calculate the PV and FV of such an uneven...

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Present Value of a Perpetuity

Perpetuity is a type of annuity that pays equal cash flows that occur periodically such as monthly, quarterly or annually for an infinite period of time. The present value of an annuity is calculated using the following formula: Assume that a perpetuity pays $500 per...

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