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Stock-based Compensation Plans
 6 Months Ended
Mar. 31, 2021
Share-based Payment Arrangement, Noncash Expense [Abstract]  
Share-based Payment Arrangement [Text Block] Stock-based Compensation Plans
We granted 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 six months ended March 31, 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 
$11.6 
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 March 31, 2021, the outstanding Phantom Plan instruments had a fair value of $13.89 per instrument and our liability for Phantom Plan instruments was $2.0 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
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 March 31, 2021. We issued 103,058 shares of common stock during the six months ended March 31, 2021 to settle PRSUs during the period. Additionally, we issued 93,973 and 219,549 shares of common stock to settle restricted stock units vested and issued 45,517 and 108,950 shares of common stock to settle stock options exercised during the three and six months ended March 31, 2021, respectively.
Operating income included stock-based compensation expense of $2.5 million and $1.3 million during the three months ended March 31, 2021 and 2020, respectively, and $5.0 million and $3.2 million during the six months ended March 31, 2021 and 2020, respectively. At March 31, 2021, there was approximately $13.2 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 664,082 and 267,697 stock-based compensation instruments from the calculations of diluted earnings per share for the three months ended March 31, 2021 and 2020, respectively, and 447,086 and 184,296 for the six months ended March 31, 2021 and 2020, respectively, since their inclusion would have been antidilutive.