What is the Internal Rate of Return (IRR)

What is IRR

The Internal Rate of Return (IRR) is the rate of return you earn on your project.

The Internal Rate of Return (IRR) is the return such that NPV is zero.
An investment is worthwhile if IRR is greater than R, the next best competing alternative.

The rate of return is internal because it is the rate of return specific to the project. All that is needed is the cash flows for that project. Compared it to NPV, which requires cash flows and the discount rate, r.

Decision Making using IRR

IRR by itself doesn't mean anything.
IRR needs to be compared to r.
When IRR > r, then the idea/project is worth pursuing because NPV will be positive.

What is the NPV of an idea?

The Net Present Value of an idea is the value created by the idea.

Interest rate, R, in Net Present Value

Where does the interest rate, r, used in computing net present value come from?

• r comes from the next best use of your investment, or other people's investment on a similar project
• r does not belong to your project
• r is that return from investing in say a competitor

Simple and Continuously Compounded Returns

Time Value of Money

• Future Value
• Present Value
• Compound Annual Return
• Investment Horizon
• Continuous Compounding

Effective Annual Rate

• Effective Annual Rate
• Effective Continuous Compounding Annual Rate

Asset Return Calculations

• Simple Returns
• Multi-period Returns
• Simple k-month Return

Portfolio returns

• A portfolio of investment assets
• Define a portfolio by how much wealth (weight) is invested in each asset
• Rate of return on a portfolio
• A weighted average of the simple returns of individual assets
• Sum of weights add up to 1

Adjusting for Dividends

• Total Return = Capital Gain Return + Dividend yield (gross)

Adjusting for Inflation

• Deflate the nominal price by an index of the general price level 
• Compute returns in the usual way using the deflated prices
• Real Rate of Return =

Tips

Develop an intuition of the reasonable orders of magnitudes of  rates of return on different investments.
e.g. what is reasonable for a 1-month investment for Microsoft?
What is a typical rate of return in a year
What is a typical rate of return in a month

Ideas for Startup Engineering Project

Retirement Calculator

A calculator of how much one needs to save using the principles of Finance.
Additional ideas include:

1. Saving Reminders, 
2. Integration with precommitment websites
3. Gamification ideas

In Finance, always look forward

An interesting mindset of Finance is to always look forward - time travel if you have to.

A specific application is when calculating the amount owed at a point in time.
Instead of computing the entire loan amortization table to answer the question, it is easier to simply "time travel" to the point-in-time of interest and look forward to see how many payments are outstanding and do an PV calculation.

Simple Future Value and Present Value

Simple Future Value

FV = PV * (1 + r)^n

Simple Present Value

PV = FV / (1 + r)^n