human
n o t e s t o c o n s o l i d a t e d f i n a n c i a l s t a t e m e n t s (continued) ace limited and subsidiaries share-based compensation expense for stock options and shares issued under the employee stock purchase plan (espp) amounted to $24 million ($22 million after tax or $0.07 per basic and diluted share), $23 million ($21 million after tax or $0.06 per basic and diluted share), and $20 million ($18 million after tax or $0.05 per basic and diluted share) for the years ended december 31, 2008, 2007, and 2006, respectively. for the years ended december 31, 2008, 2007 and 2006, the expense for the restricted stock was $101 million ($71 million after tax), $77 million ($57 million after tax), and $65 million ($49 million after tax), respectively. during 2004, the company established the ace limited 2004 long-term incentive plan (the 2004 ltip). once the 2004 ltip was approved by shareholders, it became effective february 25, 2004. it will continue in effect until terminated by the board. this plan replaced the ace limited 1995 long-term incentive plan, the ace limited 1995 outside directors plan, the ace limited 1998 long-term incentive plan, and the ace limited 1999 replacement long-term incentive plan (the prior plans) except as to outstanding awards. during the company 2019s 2008 annual general meeting, shareholders voted to increase the number of common shares authorized to be issued under the 2004 ltip from 15000000 common shares to 19000000 common shares. accordingly, under the 2004 ltip, a total of 19000000 common shares of the company are authorized to be issued pursuant to awards made as stock options, stock appreciation rights, performance shares, performance units, restricted stock, and restricted stock units. the maximum number of shares that may be delivered to participants and their beneficiaries under the 2004 ltip shall be equal to the sum of: (i) 19000000 shares; and (ii) any shares that are represented by awards granted under the prior plans that are forfeited, expired, or are canceled after the effective date of the 2004 ltip, without delivery of shares or which result in the forfeiture of the shares back to the company to the extent that such shares would have been added back to the reserve under the terms of the applicable prior plan. as of december 31, 2008, a total of 10591090 shares remain available for future issuance under this plan. under the 2004 ltip, 3000000 common shares are authorized to be issued under the espp. as of december 31, 2008, a total of 989812 common shares remain available for issuance under the espp. stock options the company 2019s 2004 ltip provides for grants of both incentive and non-qualified stock options principally at an option price per share of 100 percent of the fair value of the company 2019s common shares on the date of grant. stock options are generally granted with a 3-year vesting period and a 10-year term. the stock options vest in equal annual installments over the respective vesting period, which is also the requisite service period. included in the company 2019s share-based compensation expense in the year ended december 31, 2008, is the cost related to the unvested portion of the 2005-2008 stock option grants. the fair value of the stock options was estimated on the date of grant using the black-scholes option-pricing model that uses the assumptions noted in the following table. the risk-free inter- est rate is based on the u.s. treasury yield curve in effect at the time of grant. the expected life (estimated period of time from grant to exercise date) was estimated using the historical exercise behavior of employees. expected volatility was calculated as a blend of (a) historical volatility based on daily closing prices over a period equal to the expected life assumption, (b) long- term historical volatility based on daily closing prices over the period from ace 2019s initial public trading date through the most recent quarter, and (c) implied volatility derived from ace 2019s publicly traded options. the fair value of the options issued is estimated on the date of grant using the black-scholes option-pricing model, with the following weighted-average assumptions used for grants for the years indicated:.
|  | 2008 | 2007 | 2006 |
| --------- | --------- | --------- | --------- |
| Dividend yield | 1.80% | 1.78% | 1.64% |
| Expected volatility | 32.20% | 27.43% | 31.29% |
| Risk-free interest rate | 3.15% | 4.51% | 4.60% |
| Forfeiture rate | 7.5% | 7.5% | 7.5% |
| Expected life | 5.7 years | 5.6 years | 6 years |
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Please answer the following question with expressions if necessary.
what percentage change does this represent?
assistant
subtract(3.15, 4.51), divide(#0, 4.51)