## How to Value Shares Using Investment Horizon

Price earnings ratio (PER) and price to book ratio (PBR) are the most commonly used indicators of share value. They are easy to calculate but individually tell only half the story.

### Price Earnings Ratio

PER = Price / Earnings per share

PER can be interpreted as the number of years it will take for the company to earn the current share price. Its drawback is that it only relates earnings to price and disregards the value of shareholder equity.

### Price to Book Ratio

PBR = Price / Book value per share

PBR is the multiple of shareholders equity that the market is willing to pay. Its drawback is the converse of PER in that it only relates shareholder equity to price and disregards earnings.

What if there was a simple value indicator that combines earnings and shareholder equity in a single number? There are many share valuation formulas available such as the discounted cash flow (DCF) or dividend discount models but they have the disadvantage that they can be complex and require predicting future cash flows or dividends. Investment horizon (IH) might be the answer. It is an indicator I use to help confirm whether share values calculated using DCF are in the right ball park or not.

### Investment Horizon

Investment horizon can be interpreted as the number of years it will take for a company’s book value per share to equal its current market price. This is based on the company’s current book value per share and return on equity and assumes all profits are reinvested and compounded. Its formula is straightforward and can easily be implemented in Excel (more Background on the formula can be found at the end of the post).

Investment Horizon (yrs) = log(Price/Book) / log(1 + ROE)

Where:

Price = Market price

Book = Book value per share

ROE = Return on equity

Given Investment Horizon we can then determine how well valued the share is in the market.

IH Range Yrs |
Valueness | IH Range Yrs |
Valueness |

IH < 0 | Below-Book | 4 <= IH < 5 | Fair-Value |

0 <= IH < 3 | Undervalued | 5 <= IH < 6 | Poor-Value |

3 <= IH < 4 | Good-Value | 6 <= IH | Overvalued |

#### Quick IH Calculator

To calculate investment horizon just enter the share price, net profit after tax (NPAT), shareholders equity, and shares on issue (SOI) for the company in the fields below then click the calculate button. Before using please read the Notes* below.

##### *Notes

*1. Share prices can be found on many financial web sites. The best source for NPAT, Equity, and SOI is the company annual report. NPAT is usually found towards the bottom of the income statement. Equity, or net assets, is found on the balance sheet, and SOI in the notes to financial statements. SOI can be listed under one of several different headings including: Contributed Equity, Issued Capital, or Share Capital.*

The following sample data is taken from the ANZ 2014 Annual Report. Copy and paste it into the corresponding fields to try out the calculator. Try different prices to see how it affects IH and valueness.

Price: | 31.92 | Closing price as at 28-Nov-2014 from http://www.shareholder.anz.com/ |

NPAT: | 7,283,000,000 | ANZ 2014 Annual Report page 78 (Income statement for year ended 30 September, Profit for the year) |

Equity: | 49,284,000,000 | ANZ 2014 Annual Report page 80 (Balance sheet as at 30 September, Total shareholders’ equity) |

Shares on Issue: | 2,757,127,771 | ANZ 2014 Annual Report page 123 (27: Share Capital, Total number of issued shares) |

*2. All input amounts must be non-negative. If the company made a loss then the calculator cannot be used.*

*3. Ensure the amounts entered in the calculator are the full amount including the effect of any multiplier, e.g., if profit after tax is given as 12,345.6 and the multiplier is thousands then enter 12,345,600 in the NPAT field. The multiplier is found in the column headings and is usually one, thousands, or millions.*

*4. Some companies report in a different currency than they trade in. In this case the share price must be converted into the reporting currency before being entered.*

*5. The calculator input values used must be annual numbers. If the latest report is a half year report the given equity and SOI can be used, however NPAT must be adjusted as below.*

*NPAT = Latest Full Year NPAT + Latest Half Year NPAT – Previous Corresponding Half Year NPAT*

*6. IH is relative to the date of the end of the period for which the annual report relates to. e.g., if the report is for the period ending 30th June 2014 then IH years is relative to that date.*

*7. Normally figures would be adjusted for any corporate actions, dividends, share splits, rights issues etc. For the purposes of keeping the calculator simple there are no adjustments available.*

*8. ROE is usually calculated as return on average equity. For example if a company provides six monthly reports then the equity used in the ROE calculation is the average of the last three reports. For simplicity the calculator uses only the latest reported equity. In most cases the this should not have a significant effect on the result.*

*9. Please remember that Investment Horizon only provides a ball park indication of how well valued a share is in the market and should not be read as a predictor of any future price movements.*

### Background

Here is some background on how Investment Horizon came about and how it is derived.

The formula is derived from the standard compound interest formula:

Future Value = Current Value x (1 + Return)^Years

Restated as:

Price = Book Value x (1 + Return on Equity)^Years

Then rearranged to solve for Years:

Investment Horizon Years = log(Price/Book Value) / log(1 + Return on Equity)

I discovered this formula in a eureka moment during 2006 while looking for a quick way to value stocks and have used it ever since. The Valueness interpretation came later when comparing Investment Horizon to Edge. Edge is a stock’s intrinsic value relative to its market price. It tells us the percentage profit or loss if we buy a stock at the current market price and price subsequently moves to intrinsic value.

Edge is calculated as:

Edge % = 100 x (Intrinsic Value / Price – 1)

Where:

Intrinsic Value = Valuation calculated using a proprietary derivative of the discounted cash flow formula closely related to the residual income valuation model.

Price = Current market price

Investment horizon and edge had been calculated for many hundreds of stocks and it was found that an edge close to zero, i.e., a market price close to intrinsic value, usually corresponded to an investment horizon of between four and five years. Therefore the investment horizon range between four and five years was labelled “Fair-Value”. Other Valueness ranges were labelled using a similar rationale where the more positive the edge the more undervalued the corresponding Valueness labels and vice versa.

The only other mention of the investment horizon formula I have encountered is in the Introduction to Computational Finance and Financial Econometrics course on Coursera run by Eric Zivot of the University of Washington.

#### How do you value stocks?

Do you have a simple formula you can share? How does it compare to Investment Horizon? Please share any comments in the form below. Please be aware of our comments policy.

Investment Horizon image Copyright: rolffimages / 123RF Stock Photo