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Stock-based Compensation Plans
 9 Months Ended
Jun. 30, 2021
Share-based Payment Arrangement, Noncash Expense [Abstract]  
Share-based Payment Arrangement [Text Block] Stock-based Compensation Plans
We grant various forms of stock-based compensation, including market-based restricted stock units (“MRSUs”), restricted stock units, stock options and performance-based restricted stock units (“PRSUs”) under our Amended and Restated 2006 Mueller Water Products, Inc. Stock Incentive Plan (the “2006 Stock Plan”), Phantom Plan instruments under our Mueller Water Products, Inc. 2012 Phantom Plan, and Employee stock purchase plan instruments under our 2006 Employee Stock Purchase Plan. Grants during the nine months ended June 30, 2021 are as follows:
Units grantedWeighted average grant date fair value per instrumentTotal grant date fair value
(in millions)
Quarter ended December 31, 2020
    MRSUs234,199 $15.39 $3.6 
    Phantom Plan instruments180,987 11.86 2.1 
    Restricted stock units129,081 11.86 1.5 
    Non-qualified stock options423,405 3.05 1.3 
    PRSUs: 2020 award60,019 11.86 0.7 
                  2019 award84,483 11.86 1.0 
    Employee stock purchase plan instruments40,286 1.92 0.1 
Quarter ended March 31, 2021
    MRSUs4,187 $14.26 $0.1 
    Phantom Plan instruments1,254 11.94 — 
    Restricted stock units82,565 12.81 1.1 
    Non-qualified stock options8,115 3.08 — 
    Employee stock purchase plan instruments35,325 2.24 0.1 
Quarter ended June 30, 2021
    Phantom Plan instruments3,567 $14.29 $0.1 
    Restricted stock units7,127 13.32 0.1 
    Employee stock purchase plan instruments32,916 2.52 0.1 
$11.9 

An MRSU award represents a target number of units that may be paid out at the end of a three-year award cycle based on a calculation of our relative total shareholder return (“TSR”) performance as compared with a selected peer group's TSR. Settlements, in our common shares, will range from zero to two times the number of MRSUs granted, depending on our TSR performance relative to that of the peer group.
Compensation expense attributable to MRSUs is based on the fair value of the awards on their respective grant dates, as determined using a Monte Carlo model. The assumptions used to determine the grant date fair value are indicated below.
January 27, 2021December 2, 2020
Variables used in determining grant date fair value:
Dividend yield1.84 %1.77 %
Risk-free rate0.16 %0.21 %
Expected term (in years)2.672.83

The expected dividend yield is based on our estimated annual dividend and our stock price history at the grant date. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield in effect at the grant date with a term equal to the expected term. The expected term represents the average period of time the units are expected to be outstanding.
At June 30, 2021, the outstanding Phantom Plan instruments had a fair value of $14.42 per instrument and our liability for Phantom Plan instruments was $2.7 million and is included within Other current liabilities and Other noncurrent liabilities.
Stock options generally vest on each anniversary date of the original grant ratably over three years. Compensation expense attributed to stock options is based on the fair value of the awards on their respective grant dates, as determined using a Black-Scholes model. The assumptions used to determine the grant date fair value are indicated below.
January 27, 2021December 2, 2020
Variables used in determining grant date fair value:
Dividend yield2.01 %2.01 %
Risk-free rate0.66 %0.66 %
Expected term (in years)6.006.00

The expected dividend yield is based on our estimated annual dividend and our stock price history at the grant date. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield in effect at the grant date with a term equal to the expected term. The expected term represents the average period of time the options are expected to be outstanding.
A PRSU award consists of a number of units that may be paid out at the end of a three-year award cycle consisting of a series of annual performance periods coinciding with our fiscal years. After we establish the financial performance targets related to PRSUs for a given performance period, typically during the first quarter of that fiscal year, we consider that portion of a PRSU award to be granted. Thus, each award consists of a grant in the year of award and grants in the two following years. Settlements, in our common shares, will range from zero to two times the number of PRSUs granted, depending on our financial performance relative to the targets.
We did not issue any shares of common stock during the three months ended June 30, 2021. We issued 103,058 shares of common stock during the nine months ended June 30, 2021 to settle PRSUs during the period. Additionally, we issued 2,324 and 221,873 shares of common stock to settle restricted stock units vested and issued zero and 108,950 shares of common stock to settle stock options exercised during the three and nine months ended June 30, 2021, respectively.
Operating income included stock-based compensation expense of $3.4 million and $1.8 million during the three months ended June 30, 2021 and 2020, respectively, and $8.4 million and $5.0 million during the nine months ended June 30, 2021 and 2020, respectively. At June 30, 2021, there was approximately $11.5 million of unrecognized compensation expense related to stock-based compensation arrangements and there were 199,994 PRSUs that have been awarded for the 2021 and 2022 performance periods for which performance goal achievement cannot yet be determined.
We excluded 131,178 and 474,423 stock-based compensation instruments from the calculations of diluted earnings per share for the three months ended June 30, 2021 and 2020, respectively, and 566,666 and 274,009 for the nine months ended June 30, 2021 and 2020, respectively, since their inclusion would have been antidilutive.