• 031 07/14/2015

Context: I recently received a question from an entrepreneur in the process of negotiating the sale of a control equity position in his business where he would remain post transaction as CEO and a minority shareholder. Most everything detailed in the offer was clear except for a footnote explaining that IRR's referenced in the term sheet would be calculated using the =XIRR formula in Excel. This was of particular interest because his ownership had the potential to grow substantially post transaction if the business generated certain "hurdle" IRRs at exit. (As a crude example, imagine that at an IRR of 15% the entrepreneur would be entitled to an additional X number of shares, and at an IRR of 30% an additional 2X shares, etc.)

What perplexed him was that attempts to recreate the IRR schedules in the document generated different outcomes if the =XIRR formula or =IRR formula was used. Why did it differ at all?

Q: Why do =XIRR and =IRR calculate different IRRs in some scenarios?

A: It helps to distinguish between the Internal Rate of Return ("IRR") and the Excel formulas =IRR and =XIRR. The Internal Rate of Return ("IRR") is the rate ("r") at which the Net Present Value ("NPV") of all future cash inflows and outflows ("CF") for a project is zero.

The Excel formulas, =IRR and =XIRR, are designed to calculate the IRR under different scenarios. What differs between the two formulas is what you are communicating to Excel by selecting one over the other.

With the =IRR formula you are telling Excel to expect equal time periods between cash flows (months, years, etc.), and to calculate the rate of return per period. The =XIRR formula, however, was designed to be more flexible. By using this formula you are communicating to Excel that time periods may be incongruous, and that this needs to be taken into account. It helps to look at the equation behind the formula:

The difference is that "t" (time period) in the =IRR forumla is substituted by the quotient of the difference in days between the first cash flow and a particular cash flow over 365.

So the primary difference between the two is that the =XIRR formula provides some additional flexibility, and has been adjusted to accommodate incongruous time periods. If the =IRR formula is used in any scenario where the time periods between cash flows are not equivalent, it will return an incorrect value. But the =XIRR formula will be correct in both scenarios.

The reason the results differ when measuring the internal rate of return over a number of years is that every fourth year is a leap year. You can test this by building two schedules and measuring the internal rate of return with both the =XIRR and =IRR formula. For years 2017, 2018 and 2019 the results will match, but once 2020 is included you will notice a difference if you include enough decimal places (next leap day: February 29, 2020). The video in the follow up post elaborates on this.

See follow up post: Excel: =IRR() vs. =XIRR() (continued)

See related video: Net Present Value.

Note: This is an abridged overview of the principal difference between the two Excel formulas. The unique characteristics of each could be discussed in much greater detail.

• 030 01/27/2015

This question made me realize that I should add some material demonstrating how dividends flow through the three financial statements. In the interim please see the Q&A that follows:

Q: If net income is \$10 for four months, retained earnings grows by \$10 each month. However, if dividends were paid out in the second month, would net income equal the change in retained earnings over the four month period less the dividend?

A: The statement of retained earnings is affected by any transaction that affects net income and dividends.

Starting with net income:

Retained earnings will grow by net income in each period. So if net income is \$10 in one month retained earnings will grow by \$10 that same month. If over four months net income is \$10 each month retained earnings will grow by \$10 each month or \$40 over the four month period.

Dividends:

Retained earnings must also reflect any dividends paid out in that period. For example, if for any period you had a beginning balance for retained earnings of \$100, and in that period recorded net income of \$10 and paid dividends of \$5:

Retained Earnings = \$100 + \$10 - \$5 = \$105

Net income, however, is not impacted by dividends.

The balance sheet remains balanced (Assets = Liabilities + Stockholders’ Equity) by reducing cash by the same amount paid out in dividends. This works because your cash flow statement starts with net income at the top, and then makes adjustments to net income to arrive at cash flow for that period at the bottom. One of those adjustments is the payment of dividends (made under cash flow from financing activities). The cash flow calculated on the cash flow statement is the sum that grows your cash balance on the balance sheet. So on your balance sheet both cash and retained earnings get reduced by the dividends paid out.

IMAGE: screencap from the video titled Income Statement

• 029 11/13/2014

A friend of mine recently emailed asking for help with a formula. In an effort to build a dashboard that would provide information on the buildings and apartments he manages, he was looking for a formula that could return the number of units he had a available for rent within a certain time period.

The problem was that the software he was using did not always generate a uniform response for an "unrented" unit. The solution provided was to use the =CountIf formula and an asterisk.

Models are:

A) really boring
B) pretty sweet
C) super important
D) somewhat easy
E) kind of hard
F) fun
G) all of the above

*Answers a, b, c, d, e, f and g are all correct.