
181 S.W.3d 66 (2005)
STATE of Missouri, Respondent,
v.
David Stanley ZINK, Appellant.
No. SC 86358.
Supreme Court of Missouri, En Banc.
November 22, 2005.
Rehearing Denied January 31, 2006.
*69 Rosemary E. Percival, Office of Public Defender, Kansas City, for Appellant.
Jeremiah W. (Jay) Nixon, Atty. Gen., Daniel N. McPherson, Deborah Daniels, Asst. Attys. Gen., Jefferson City, for Respondent.
RONNIE L. WHITE, Judge.

I.
A jury convicted Appellant, David Stanley Zink, of one count of first-degree murder and recommended the death sentence. Judgment was entered consistent with the jury's recommendation. Appellant seeks reversal raising twelve points of error. This Court has jurisdiction pursuant to Mo. Const. art. V, sec. 3. Affirmed.

II.
The facts, which this Court reviews in the light most favorable to the verdict,[1] are: In the early morning hours of July 12, 2001, police responded to the report of a traffic accident near Stafford, Missouri. Upon their arrival, they found Amanda Morton's car abandoned with the engine running, headlights and hazards lights on, and driver's side window down. The authorities would later learn that Appellant had rear-ended Ms. Morton's car and that they both left the accident scene in Appellant's vehicle.
After Ms. Morton's disappearance was broadcast on the evening news, the owner of a motel near Camdenton, Missouri, recognized Ms. Morton's picture as a woman who had checked into a room with Appellant. The motel owner provided the police with Appellant's registration card, and using this information the police were able to apprehended Appellant at his home. Ultimately, Appellant waived his Miranda rights and confessed to killing and burying Ms. Morton.
Appellant would testify at trial that after leaving the motel he drove Ms. Morton to a cemetery, bound her with twine, broke her neck and strangled her. Approximately ten minutes later he attempted to sever her spinal cord with a knife to ensure her *70 death. He further testified that it was his purpose to cause her death. The evidence also revealed that Appellant had sodomized Ms. Morton.
The jury found Appellant guilty of first-degree murder. During the penalty phase, the jury found the presence of three statutory aggravators to support its unanimous recommendation for a death sentence: (1) that Appellant had two prior convictions for aggravated rape; (2) that the murder was committed for the purpose of avoiding a lawful arrest; and (3) that the murder involved depravity of the mind and was outrageously and wantonly vile, horrible, and inhuman.

III.
In Appellant's points II, III, IV, and V, he claims trial court error in association with allowing him to represent himself and with failing to replace standby counsel appointed from the public defender's office. Specifically he contends that the trial court's failure to replace the public defender in the first instance forced him to represent himself; that his waiver of the right to counsel was not given voluntarily, knowingly and intelligently; and that standby counsel forced him to present conflicting defenses thereby canceling out any meaningful defense. Appellant presented the defense of lack of deliberation to support a conviction for voluntary manslaughter as opposed to first-degree murder. Standby counsel presented the defense of diminished mental capacity.
A defendant has a constitutional right to conduct his own trial when he knowingly, intelligently, and in a timely fashion exercises that right.[2] However, "[o]nce a pro se defendant invites or agrees to any substantial participation by (standby) counsel, subsequent appearances by counsel must be presumed to be with the defendant's acquiescence, at least until the defendant expressly and unambiguously ... requests that standby counsel be silenced."[3]
Appellant moved the trial court to allow him to proceed without legal counsel. The transcript of the hearing on Appellant's motion and the legal file both confirm that Appellant was fully informed of the charges; the potential penalties he faced if convicted, including confinement or death; his rights to appointed counsel and to a trial by jury; the perils of self-representation; and all potential consequences associated with the waiver of counsel. He was also informed that any sentencing recommendations by the prosecutor would not be binding on the judge and that he had the right to appeal.
The transcripts reveal that the trial judge read a prepared waiver of counsel form to Appellant that was in compliance with section 600.051, which codifies all of the requirements for waiver of counsel. Appellant signed this form, including a statement that he understood the full consequences of the waiver. Appellant's waiver was given voluntarily, knowingly and intelligently.
The court offered Appellant two opportunities to reconsider his decision prior to trial and Appellant declined. Prior to the introduction of evidence, the court extended an invitation that Appellant could change his mind on self-representation at any time during the trial by simply notifying the court. Appellant did not accept this invitation at any time during the guilt *71 phase of his trial, but he did turn his defense over to the public defenders for the sentencing phase of his trial.
The first day of trial, prior to the seating of the jury, Appellant gave his consent to allow standby counsel to address the defense of diminished capacity during opening statement. Appellant introduced standby counsel, stating, "Ah, the Public Defenders will put on their own defense. It's my defense technically. And he will speak to you about this defense." When the public defender addressed the jury, he outlined all of the evidence of the diminished mental capacity defense that he planned to present.
Appellant also consented to the introduction of evidence to support the diminished capacity defense, the submission of the diminished capacity jury instructions during the guilt and penalty phases of his trial, and the summation of this defense during closing arguments during the guilt and penalty phases of his trial. In fact, Appellant turned the penalty phase defense over to the public defenders, and at completion of the Appellant's case he stated to the court that it was his intent not to disrupt the diminished mental capacity defense and that this phase of the trial was the public defender's "ballgame." Appellant's alleged points of error have no merit.[4]

IV.
Appellant also raises two points, points I and VI, claiming prosecutorial misconduct. Appellant maintains that the prosecutor failed to timely disclose, and the trial court failed to admit, a police report that may have provided evidence of Ms. Morton habitually violating her curfew. Appellant believes this evidence was relevant as to whether Ms. Morton left the accident scene with him voluntarily and that when the trial court excluded this evidence, pursuant to the State's objection, that it prejudiced his case.
Appellant further claims prosecutorial misconduct in relation to the State's cross-examination of witnesses Dr. Kenneth Benedict and Dr. Mark Cunningham. Appellant claims that the prosecutor inappropriately biased the jury against out-of-state witnesses by asking Dr. Benedict why the defense had to travel so far to find a witness to support his defense. Appellant contends that the prosecutor biased the jury against all expert witnesses when asking Dr. Cunningham if the defendant should receive the death penalty, a question that "no" witness could legally answer.[5] Appellant believes this left the jury with the impression that Dr. Cunningham was biased in favor of the defense.
In situations involving prosecutorial misconduct, the test is the fairness of the trial, not the culpability of the prosecutor.[6] "Where prosecutorial misconduct is alleged, the erroneous action must rise to the level of `substantial prejudice' in order *72 to justify reversal."[7] "The test for `substantial prejudice' is whether the misconduct substantially swayed the judgment."[8] With regard to the trial court's exclusion of the police report, "[t]rial courts have discretion to determine the relevancy of evidence, and appellate courts will reverse that determination only upon a showing of abuse of discretion."[9]
The record reveals that the prosecution disclosed the police report in question prior to trial and that the court found the evidence to be irrelevant. Appellant was being tried solely on the murder charge. Whether or not Ms. Morton left voluntarily with Appellant prior to his murdering her was irrelevant in the guilt phase of his trial because he admitted his guilt and intent to kill Ms. Morton. It was also irrelevant in the penalty phase because the jury found three statutory aggravators to support the sentence of death, none of which involved an allegation of the abduction or kidnapping of Ms. Morton. The trial court did not abuse its discretion when denying the introduction of this evidence, and even assuming, arguendo, that the court had erred with its exclusion, the evidence of Appellant's guilt was overwhelming, rebutting any presumption of prejudice associated with the exclusion of admissible evidence.[10]
With regard to the questions the prosecutor presented to defendant's experts, "[w]ide latitude is afforded the cross-examination of witnesses to test qualifications, credibility, skill or knowledge, and the value and accuracy of the expert's opinion."[11] "Cross-examination of a witness to determine possible bias or motive is permissible and its parameters are within the broad discretion of the trial court."[12] The prosecutor's questioning of Appellant's experts was directed at eliciting any bias favoring defendants or disfavoring the death penalty. These questions were appropriate subject matter for cross-examination and the trial court did not abuse its discretion in allowing them.

V.
Appellant raises two evidentiary issues in points VII and IX. Appellant claims the trial court erred for allowing the prosecutor and the witnesses use the terms "murder," "kidnapping," "abduction," and "crime scene," because these terms were conclusory, invaded the province of the jury and prejudiced the verdict. Appellant also claims that the court erred when excluding excerpts from one police officer's deposition and an audiotape of a radio conversation between a sheriff and dispatcher. Appellant claims that this evidence is relevant to establishing that the police destroyed evidence, engaged in a cover-up to protect their image and attempted to make it appear there was a kidnapping.
"A trial court has broad discretion to admit or exclude evidence at trial."[13] "This standard of review compels the reversal of a trial court's ruling on the admission of evidence only if the court has *73 clearly abused its discretion."[14] "[T]hat discretion is abused when a ruling is clearly against the logic of the circumstances and is so unreasonable as to indicate a lack of careful consideration."[15] On direct appeal this Court reviews the trial court "for prejudice, not mere error, and will reverse only if the error was so prejudicial that it deprived the defendant of a fair trial."[16] Trial court error is not prejudicial unless there is a reasonable probability that the trial court's error affected the outcome of the trial.[17]
The State appropriately points out that the words Appellant objects to were minimally used and in a manner that did not constitute the dictating of a legal conclusion to the jury. The jury was fully instructed on the elements that it had to find beyond a reasonable doubt to support a conviction for first-degree murder, second-degree murder and voluntary manslaughter. Jurors are presumed to know and follow the instructions they are given when deciding the issue of a defendant's guilt or innocence.[18] Appellant offers nothing but speculation that the use of these words prejudiced his case and fails to demonstrate that he was denied a fair trial.
With regard to Appellant's second evidentiary claim, even assuming the trial court erred with the exclusion of the evidence in question, Appellant again fails to demonstrate any prejudice. Appellant admitted to intentionally killing Ms. Morton. He was only on trial for the murder, not kidnapping. Kidnapping was not an aggravating circumstance submitted to the jury to support a recommendation for the death penalty. There is no reasonable probability that the outcome of the trial would have been different had the evidence in question been admitted.

VI.
In point VIII, Appellant challenges the discharge of venireperson Byron Kronshage for hardship. Appellant contends that the discharge of Kronshage amounted to a tenth peremptory strike when only nine were statutorily allowed,[19] and that it prejudiced the outcome of the trial because Kronshage had stated in voir dire that it would be difficult for him to recommend a sentence of death.
Section 494.430.4 allows the trial court to excuse persons from jury service on the basis of hardship, and the court has substantial discretion with regard to juror excusals.[20] The record demonstrates that venireperson Kronshage was excused because he and his wife lived alone and both had heart ailments. Kronshage also had laboratory tests scheduled during the time period of the trial, the result of which might require adjustments in his medication. There is no evidence supporting Appellant's claim that Kronshage was excused because of his views on the death penalty. Nothing in the record of this case suggests that the tendered panel was not qualified, and the trial court did not abuse its discretion when excusing venireperson Kronshage.


*74 VII.
In Appellant's point X, he alleges trial court error with submitting the prosecutor's penalty phase jury instructions 19 and 21, claiming that they diminished the State's burden to establish that he was death-eligible. Instruction 19 was based upon MAI-CR3d 313.44A, and it required the jury to determine whether there were facts or circumstances in mitigation of punishment that were sufficient to outweigh the facts or circumstances in aggravation. Instruction 21 was based upon MAI-CR3d 313.48A, and it instructs the jury in how to complete the verdict form, based upon the jury's findings, to pronounce the recommended punishment.
On a claim of instructional error, "[a]n appellate court will reverse only if there is error in submitting an instruction and prejudice to the defendant."[21] MAI instructions are presumptively valid and, when applicable, must be given to the exclusion of other instructions.[22]
Appellant's specific claim relates to the statutory requirement in section 565.030.4(3) requiring the jury to determine if mitigating circumstances exist that sufficiently outweigh the evidence in aggravation of punishment. Appellant claims that the instructions, as given, improperly raised his burden to obtain a unanimous jury decision that evidence in mitigation of punishment was sufficient to outweigh the evidence in aggravation. Appellant also claims that Instruction 19 improperly lacks a limitation on the use of aggravating evidence when performing this balancing test.
This Court has previously rejected these and similar arguments concerning these MAI patterned instructions, and these instructions in no way preclude the jury from giving proper effect to the mitigating evidence. Having ruled on these issues previously, and having examined this claim thoroughly and finding no error of law, an extended opinion on these issues would have no precedential value.[23]

VII.
In point XI, Appellant contends that the jury failed to make the proper factual finding to support, beyond a reasonable doubt, the "depravity of mind" aggravator and this failure resulted in prejudice. The jury found the presence of three statutory aggravators beyond a reasonable doubt. Even assuming, arguendo, that the "depravity of mind" aggravator was invalid, "a defendant is `death eligible' where, as here, at least one valid statutory aggravator was found."[24]

VIII.
In point XII, Appellant finally argues that the trial court lacked jurisdiction and authority to sentence him because the state failed to charge him with "aggravated *75 first-degree murder." Appellant claims that failure to plead facts, as listed in section 565.030, creates a charge of murder whereby the maximum penalty was life in prison.
This Court has addressed this claim numerous times before, and the omission of statutory aggravators from an indictment or information charging the defendant with first-degree murder does not deprive the sentencing court of jurisdiction to impose the death penalty.[25] Missouri's statutory scheme recognizes a single offense of murder with maximum sentence of death, and the requirement that aggravating facts or circumstances be present to warrant imposition of death penalty did not have the effect of increasing the maximum penalty for the offense.[26] Having examined this claim thoroughly and finding no error of law, an extended opinion on these issues would have no precedential value.[27]

IX.
This Court independently reviews the proportionality of all death sentences. Under section 565.035.3, RSMo 2000, this Court is required to determine whether:
(1) the sentence of death was imposed under the influence of passion, prejudice, or any other arbitrary factor;
(2) Whether the evidence supports the jury's or judge's finding of a statutory aggravating circumstance as enumerated in subsection 2 of section 565.032 and any other circumstance found;
(3) the sentence of death is excessive or disproportionate to the penalty imposed in similar cases, considering both the crime, the strength of the evidence, and the defendant.
Having thoroughly reviewed the record, this Court concludes that there is no evidence to suggest that the punishment imposed was a product of passion, prejudice, or any other arbitrary factor.
The trial court's findings are next reviewed to determine if the evidence supports, beyond a reasonable doubt, the existence of an aggravating circumstance and any other circumstance found. In this case, the jury unanimously found three statutory aggravating circumstances as a basis for considering the death sentence. The evidence supports, beyond a reasonable doubt, a finding that the Appellant had two prior serious assaultive convictions for aggravated rape; that he committed the murder of Ms. Morton for the purpose of avoiding a lawful arrest; and that the murder involved depravity of mind and was outrageously and wantonly vile, horrible and inhuman.[28]
Finally, this Court has upheld sentences of death in similar cases where the defendant committed a prior murder and/or a serious assaultive offense and then murdered again.[29] The death sentence in this case is neither excessive nor disproportionate to the penalty imposed in similar cases, considering the crime, the strength of the evidence, and the defendant.


*76 X.
The judgment is affirmed.
All concur.
NOTES
[1]  State v. Taylor, 134 S.W.3d 21, 24 (Mo. banc 2004).
[2]  Faretta v. California, 422 U.S. 806, 835, 95 S.Ct. 2525, 45 L.Ed.2d 562 (1975).
[3]  United States v. Swinney, 970 F.2d 494, 498 (8th Cir.1992), quoting, McKaskle v. Wiggins, 465 U.S. 168, 183, 104 S.Ct. 944, 79 L.Ed.2d 122 (1984).
[4]  Appellant also fails to articulate or cite any authority to support the proposition that the two defenses, i.e., inability to deliberate and diminished mental capacity, were in fact conflicting or why they could not be submitted to the jury in the alternative.
[5]  State v. Taylor, 944 S.W.2d 925, 938 (Mo. banc 1997). It should be noted that defendant's citation to Taylor is incorrect. In Taylor this Court held that the "[testimony] of a victim's family members' characterizations and opinions about the appropriate sentence are inadmissible." The Court did, however, delineate that an expert's function was not to recommend punishment in State v. Nickens, 403 S.W.2d 582, 587 (Mo. banc 1966).
[6]  State v. Williams, 922 S.W.2d 845, 851 (Mo.App.1996); Smith v. Phillips, 455 U.S. 209, 220, 102 S.Ct. 940, 71 L.Ed.2d 78, (1982).
[7]  State v. Peterson, 833 S.W.2d 395, 398 (Mo.App.1992).
[8]  Id.
[9]  State v. Wolfe, 13 S.W.3d 248, 258 (Mo. banc 2000).
[10]  State v. Barriner, 111 S.W.3d 396, 401 (Mo. banc 2003).
[11]  Middleton v. State, 103 S.W.3d 726, 741 (Mo. banc 2003).
[12]  State v. Leisure, 796 S.W.2d 875, 880 (Mo. banc 1990).
[13]  State v. Madorie, 156 S.W.3d 351, 355 (Mo. banc 2005).
[14]  Id.
[15]  State v. Gonzales, 153 S.W.3d 311, 312 (Mo. banc 2005).
[16]  State v. Middleton, 995 S.W.2d 443, 452 (Mo. banc 1999).
[17]  Barriner, 111 S.W.3d at 401.
[18]  State v. Madison, 997 S.W.2d 16, 21 (Mo. banc 1999).
[19]  Section 494.480.2(1).
[20]  State v. Murray, 744 S.W.2d 762, 770 (Mo. banc 1988).
[21]  Id.
[22]  Rule 28.02(c); State v. Whalen, 49 S.W.3d 181, 188 (Mo. banc 2001).
[23]  Rule 30.25. See State v. Gill, 167 S.W.3d 184, 2005 WL 1620412*7(Mo. banc 2005); State v. Glass, 136 S.W.3d 496, 520-21 (Mo. banc 2004); Taylor, 134 S.W.3d at 30; State v. Tisius, 92 S.W.3d 751, 770 (Mo. banc 2002); State v. Cole, 71 S.W.3d 163, 176 (Mo. banc 2002).
[24]  Section 565.032; Gill, 167 S.W.3d 184, 193. To support the determination of the depravity of mind aggravator, the jury instruction required the jury to find "that the defendant committed repeated and excessive acts of physical abuse upon Amanda L. Morton and the killing was therefore unreasonably brutal." The verdict form for aggravating circumstances may have been inartfully completed by the jury, but this does not negate the fact that the necessary findings were made to support this aggravator.
[25]  Cole, 71 S.W.3d at 171.
[26]  Id. See also Tisius, 92 S.W.3d at 766.
[27]  Rule 30.25.
[28]  Section 565.032.2.
[29]  Storey v. State, 175 S.W.3d 116 (Mo. banc 2005); Gill, 167 S.W.3d 184; State v. Strong, 142 S.W.3d 702 (Mo. banc 2004); State v. Mayes, 63 S.W.3d 615 (Mo. banc 2001); Skillicorn v. State, 22 S.W.3d 678 (Mo. banc 2000); State v. Middleton, 998 S.W.2d 520 (Mo. banc 1999).
