
480 N.W.2d 28 (1992)
Kurtis L. BRADHAM, Appellant,
v.
STATE of Iowa, Appellee.
Robert A. DAVIS, Appellant,
v.
STATE of Iowa, Appellee.
Timothy G. LYON, Appellant,
v.
STATE of Iowa, Appellee.
No. 90-1502.
Supreme Court of Iowa.
January 22, 1992.
Rehearing Denied February 19, 1992.
Philip B. Mears of Mears Law Office, Iowa City, for appellants.
Bonnie J. Campbell, Atty. Gen., and R. Andrew Humphrey, Asst. Atty. Gen., for appellee.
Considered by HARRIS, P.J., and CARTER, LAVORATO, NEUMAN, and SNELL, JJ.
LAVORATO, Justice.
In this consolidated postconviction relief action, three applicants challenge the way the Iowa Men's Reformatory administers the work bonus day credits program at the institution under Iowa Code chapter 903A (1989). We affirm in part, reverse in part, and remand with directions.

I. Factua1 Background.

Kurtis L. Bradham, Robert A. Davis, and Timothy G. Lyon are inmates at the Iowa Men's Reformatory. All three were employed *29 at the facility in various jobs. Their evaluations for work performance ranged from above average to outstanding.
Based on their performance evaluations, each applicant earned two or three work bonus day credits per month. These work bonus day credits reduced their time served by one to one and one-half days per month rather than by the two or three work bonus day credits earned.
The applicants challenge two particular policies on how the work bonus program is administered. They complain because the reformatory cuts their work bonus day credits earned in half when calculating their discharge date. They think the reformatory's method of calculation violates the plain meaning of Iowa Code section 903A.2, the controlling statute on good conduct time and work bonus day credits. And they complain that as inmates living and working in the institution the maximum bonus day credits they can earn is three days a month. They think this policy likewise violates the plain meaning of section 903A.2 which allows "up to five days a month." Iowa Code § 903A.2.

II. Procedural Background.

Each applicant filed an administrative grievance challenging the way the work bonus day credits are administered. After exhausting their administrative remedies, each applicant filed for postconviction relief. See Iowa Code § 663A.2(6). The district court denied them relief. Each applicant then appealed to this court. Because the issues in each case are the same, we ordered the three separate appeals consolidated.
III. Whether the Way the Reformatory Calculates Work Bonus Day Credits Violates Iowa Code Section 903A.2.
Iowa Code section 903A.2 allows an inmate to reduce the inmate's sentence in two ways: through good conduct time credits and through work bonus day credits. Specifically, the statute pertinently provides:
Each inmate of an institution under the Iowa department of corrections, is eligible for a reduction of sentence of one day for each day of good conduct of the inmate while committed to one of the department's institutions. In addition to the sentence reduction of one day for each day of good conduct, each inmate is eligible for an additional reduction of sentence of up to five days a month if the inmate participates satisfactorily in employment in the institution....
Iowa Code § 903A.2 (emphasis added).
As they did in the district court, the applicants challenge the way the reformatory calculates work bonus day credits for purposes of section 903A.2.
Section 903A.2 authorizes a day-for-day reduction in an inmate's sentence for good conduct. That means an inmate earns an extra day reduction in sentence for each day the inmate serves. The net effect of the credit is that the sentence is cut in half.
According to the reformatory's method of computation, an inmate is given all of the good conduct day-for-day reduction against the entire sentence immediately upon the inmate's commitment. This results in a projected reduction of sentence rather than an actual reduction. The computation produces what the reformatory calls a projected discharge date (PDD), which forecasts the actual time to be served. The calculation is based on the assumption that the inmate will serve the entire projected sentence.
Because the PDD is calculated before an inmate has completed even one day of the actual sentence, the PDD is subject to change. For example, loss of good conduct time because of a rule infraction can extend the PDD. But logically the loss of good conduct time must be computed by taking into account the day-for-day credit for each day served. For example, a loss of sixteen days of good conduct time extends the PDD or the actual time to be served by eight rather than sixteen days. The sixteen days is like an additional sentence that must be reduced by the day-for-day credit the inmate receives upon commitment. *30 In this example the day-for-day credit is eight days.
According to the State, the following example shows how the reformatory's method of calculation works:


   Length of sentence (2 years x 365 days)                              730 days
   Less maximum good conduct time credit available                      365 days
                                                                        ____
   Initial PDD                                                          365
                                                                        ====
   Loss of good conduct time for rule infraction                         16 days
   Less maximum good conduct time day-for-day credit available because
     of increase in confinement                                           8 days
                                                                         ____
       Total increase to PDD                                              8 days
       Add initial PDD                                                  365 days
                                                                        ____
       New PDD                                                          373 days
                                                                        ====

As we said, work bonus day credits also reduce an inmate's sentence. These credits are earned if the inmate "participates satisfactorily in employment in the institution." Iowa Code § 903A.2.
Under the reformatory's method, a calculation of work bonus day credits rests on the same logic that applies in calculating the loss of good conduct time. Like the latter calculation, the calculation of work bonus day credits must take into account the day-for-day credit originally given the inmate at the time of commitment. Again, this is because the day-for-day credit was projected on the assumption the inmate would serve the entire projected sentence. Once work bonus day credits are earned, the inmate will not be serving the entire projected sentence and so will not be earning all of the day-for-day credits originally projected. The PDD must therefore be adjusted to reflect work bonus day credits and the reduction in day-for-day credits.
Unless the reduction in day-for-day credits is made, the inmate would receive a windfall: a double reduction in sentence. This double reduction would result from (1) the original day-for-day credit given at commitment and (2) a day-for-day credit given the inmate for time not served. Logically, then, because the original day-for-day credits reduced the sentence by one-half, the work bonus day credits must likewise be reduced by one-half.
According to the State, the following example shows how thirty days of work bonus day credits would affect a two-year sentence:


   Length of sentence (2 years x 365 days)                               730 days
   Less maximum good conduct time credit available                       365 days
                                                                         ___
   Initial PDD                                                           365
                                                                         ===
   Total days of work bonus credit                                        30 days
   Less good conduct time credit no longer earnable because inmate will
     serve only one-half of these thirty days due to day-for-day credit
     originally given inmate at commitment                                15 days
                                                                         ___
   Work bonus credit available                                            15 days
                                                                         ===
   Initial PDD                                                           365 days
   Less work bonus credit                                                 15 days
                                                                         ___
   New PDD                                                               350 days
                                                                         ===

The applicants think that the total work bonus day credits of thirty daysrather than one-half of those creditsshould be applied to the PDD. Under the applicants' method of calculation, the new PDD in the above example would be 335 days (365 - 30) rather than 350 days.
*31 The bone of contention between the applicants and the State is the "good conduct time forecast" the institution makes under section 903A.2 at the time of commitment. This projection isas we saidmade before any time is actually served and before an inmate's eligibility for employment and work bonus day credits is determined.
What section 903A.2 does require is a day-for-day reduction of sentence by good conduct time an inmate earns while committed to one of the department's institutions. Iowa Code § 903A.2. This means that an inmate cannot actually receive good conduct time for days not actually served. We agree with the district court that
if the time served is reduced by work bonus credits and thereby reduces the amount of time the inmate is actually in the institution, an adjustment must be made in the good conduct time that has already been projected ahead of time. While the institution once presumed the inmate was going to be there for a set period of time, that presumption is no longer true in that the period of time an inmate will serve has been reduced because of the work bonus credits. Therefore, the good time already figured must be adjusted.
(Emphasis added.)
We think the district court correctly concluded that the current method of computation employed by the reformatory complies with section 903A.2.
IV. Whether Inmates Who Live and Work Within the Institution Are Entitled to Earn More Than Three Days Per Month Under Iowa Code Section 903A.2.
The applicants also contend that they each should be able to earn more than three work bonus day credits per month under section 903A.2. On this point, section 903A.2 provides that

[i]n addition to the sentence reduction of one day for each day of good conduct, each inmate is eligible for an additional reduction of sentence of up to five days a month if the inmate participates satisfactorily in employment in the institution, in Iowa state industries, in an inmate employment program established by the director, or in an inmate educational program approved by the director.
(Emphasis added.)
The applicants strenuously urge this language plainly mandates that inmates who work should receive five days of work bonus day credits per month in addition to good conduct time if their work performance is acceptable. The inmates maintain that the department rule limiting inmates living and working within each institution to earn up to four days of work bonus day credits a month is contrary to the plain language of the statute. Andthey point outthe reformatory's rule further compounds the error because it only allows such inmates to earn up to three days per month.
A. The department's rule. The Iowa department of corrections' rule is set out in a written document identified as "policy number IN-V-98." It provides that
[i]nmates who demonstrate satisfactory performance in work assignments or educational programs are eligible for [work bonus credits] which shall not exceed four (4) additional days per month for those inmates in maximum, medium, or minimum status during the entire month. Inmates living and working in minimum live-out status or work release can receive up to five (5) days additional good time credit. The granting of this additional credit shall be at the discretion of the housing institution and shall be based upon such factors as performance, number of hours devoted to the activity, supervision requirements, the skill level necessary to perform the activity, and the inmate's status within any level system.
We think the department's rule meets the requirements of section 903A.2 for several reasons.
Iowa Code section 903A.4 authorizes the Iowa department of corrections to develop policy and procedural rules to implement *32 section 903A.2. That authority plus the permissive language ("up to five days") in section 903A.2 vests considerable discretion in the department to decide how to allocate work bonus day credits. The burden is on the applicants to establish that the department's exercise of this discretion is arbitrary or capricious.
In addition, the department's implementing rule recognizes the maximum five day allowance provided in section 903A.2. Inmates living and working in minimum live-out status or work release can receive up to the maximum five days additional work bonus day credits per month. Inmates in maximum, medium, or minimum status who perform satisfactorily in work assignments or educational programs can receive up to four days of credit. We do not think this is an arbitrary or capricious determination by the department. In this regard, we, like the district court, find the policy behind such differentiation persuasive:
[T]he rationale behind more work bonus credits for those outside the walls of the prison is the increased trust placed in those individuals. Those job assignments are ones [in which] there is little supervision and security provided. Offering more credits for these occupations provides an added incentive for the inmate[s].
B. The reformatory's rule. The reformatory's rule presents a closer question. The rule is found in general order # 48 and pertinently provides:
Inmates classified as maximum or medium custody who demonstrate average performance for the entire month and have not missed work may be awarded a maximum of one day [work bonus credit].
Inmates who demonstrate above average performance for the entire month and have not missed work may be awarded a maximum of two days [work bonus credit].
Inmates who demonstrate outstanding performance for the entire month and have not missed work may be awarded a maximum of three days [work bonus credit].
Inmates classified as medium out, minimum or minimum overnight who demonstrate at least average performance and have not missed work may be awarded up to four days [work bonus credit]. Only inmates in minimum live-out or work release status are eligible to receive a maximum of five days [work bonus credit].
As these inmates urge, there is one glaring difference between the department's rule and the reformatory's rule. Under the department's rule, inmates living and working inside the institution can earn up to four days of work bonus credits per month. In contrast, under the reformatory's rule the maximum credits such inmates can earn are three. (Evidence was introduced showing that the Iowa State Penitentiary at Ft. Madison allows inmates living and working in the institution to earn up to four days of credit.) To this extent, the reformatory's rule conflicts with the department's rule and is therefore invalid. Consistent with the department's rule, the reformatory must allow inmates living and working within the institution to earn up to four days of work bonus credits per month.

V. Disposition.

The Iowa department of corrections' method of calculating work bonus day credits meets the requirements of Iowa Code section 903A.2. In addition, section 903A.2 and Iowa Code section 903A.4 vest wide discretion in the department on how to allocate work bonus day credits. The department's rule implementing section 903A.2 on this point is not arbitrary nor capricious. The district court reached the right decision on both issues. So we affirm its ruling on them.
But the reformatory's rule conflicts with the department's rule allocating work bonus day credits to inmates living and working in the institution. To that extent, the reformatory's rule is invalid. The district court's ruling to the contrary was error. So we reverse on this issue. Because of this reversal, we remand to the district court for further proceedings to determine *33 what, if any, additional work bonus day credits the applicants should receive.
Costs are taxed one-half to the applicants and one-half to the State.
AFFIRMED IN PART, REVERSED IN PART, AND REMANDED WITH DIRECTIONS.
