PER CURIAM:
Defendant James Lee Cobb, III, appeals his 324-month sentence, imposed after pleading guilty to conspiracy to commit wire and mail fraud, aggravated identity theft, and possession of a firearm by a convicted felon. On appeal, Defendant challenges his sentence on numerous grounds. He argues that: (1) the district court clearly erred in estimating the loss amount and the number of victims for sentencing enhancement purposes, and in calculating the amount of restitution; (2) the district court erred by applying the vulnerable-victim enhancement; and (3) the district court plainly erred by imposing an enhancement for production of an unauthorized access device and by designating Defendant an armed career criminal. After careful review, we affirm.
I. BACKGROUND
A. Factual Background
Beginning in approximately 2011, and continuing until 2013, Defendant and his wife Eneshia Carlyle, stole identities from patients at the Department of Veterans’ Affairs (“VA”), ambulance services, hospitals, and clinics, to electronically file fraudulent tax returns. Defendant and his wife used prepaid debit cards to access the refunds produced by these fraudulent tax returns.
The investigation into Defendant began in August 2012, following a routine traffic stop by the Tampa .Police Department. Defendant consented to a search of his vehicle, and officers found receipts and debit cards imprinted with names other than Defendant’s.
Following a trash pull at Defendant’s residence—which revealed several debit cards with various names on them, a sheet containing personal identifying information, and a receipt for a cash-back transac
tion—officers executed a search warrant at the residence. Officers found over 300 debit cards, as well as medical records from the VA, ambulance services, and hospitals. These records contained approximately 7,000 pieces of personal identifying information. The search also revealed two firearms. In addition, officers found three keys to storage units inside of Defendant’s wife’s purse. A subsequent search of those storage units revealed trash bags filled with medical records containing personal identifying information, prepaid debit cards, and a Mercedes.
B. Procedural History
A federal grand jury subsequently issued a superseding indictment against Defendant, charging him with: (1) conspiracy to commit mail and wire fraud, in violation of 18 U.S.C. § 1349 (“Count 1”); (2) wire fraud, in violation of 18 U.S.C. § 1343 (“Counts 2 through 5”); (3) aggravated identity théft, in violation of 18 U.S.C. § 1028A (“Counts 6 through 9”); and (4) being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g) (“Count 10”). Defendant initially pleaded not guilty, but before trial was set to begin, he pled guilty to Counts 1 through 10.
Using the 2014' Sentencing Guidelines, the probation officer prepared a Presen-tence Investigation Report (“PSR”). Pursuant to U.S.S.G. § 3D1.2(d), the PSR grouped Counts 1 through 5 (mail and wire fraud offenses) and assigned Defendant a base offense level of 7. Defendant received the following enhancements: (1) an 18-level enhancement under U.S.S.G. § 2Bl.l(b)(l)(J), because the intended loss was more than $2,500,000; (2) a 6-level enhancement under § 2Bl.l(b)(2)(C), because the offense involved 250 or more victims; (3) a 2-level enhancement under § 2Bl,l(b)(10), because the offense involved sophisticated means; (4) a 2-level enhancement under § 2Bl.l(b)(ll)(B), because Defendant produced an unauthorized access device; (5) a 2-level enhancement under § 3Al.l(b)(l), because Defendant knew or should have known that a victim of the offense was a vulnerable victim; (6) a 4-level enhancement under U.S.S.G. § 3Bl.l(a), because Defendant was an organizer or leader of the conspiracy; and (7) a 2-level enhancement under § 3C1.1, for obstruction of justice. Defendant’s resulting adjusted offense level was 43.
As to Count 10 (possession of a firearm by a convicted felon offense), the PSR assigned Defendant a base offense level of 26, pursuant to U.S.S.G. § 2K2.1. The PSR also noted that Defendant faced a mandatory minimum of 24 months’ imprisonment for Counts 6 through 9 (aggravated identity theft offenses). Because Defendant’s offense level of 43 was greater than 26, the PSR determined that Defendant’s ' combined total offense level was 43.
The PSR also determined that Defendant qualified as an armed career criminal for purposes of U.S.S.G. § 4B1.4, based on his three prior Florida convictions for serious drug offenses: (1) a 2008 conviction for trafficking in cocaine; (2) a 2008 conviction for possession of cocaine with intent to sell/deliver; and (3) a 2008 conviction for attempted possession with intent to distribute and to possess with intent to distribute less than 50, kilograms of marijuana within 1,000 feet of a school. Nevertheless, Defendant’s offense level remained at 43, as it was greater than his offense level pursuant to the armed-career-criminal enhancement.
With a two-level reduction for acceptance of responsibility, Defendant’s total offense was 41. Based on a total offense level of 41 and a criminal history category of VI, Defendant’s guideline range was 360 months to life imprisonment. In addition, Defendant faced a mandatory minimum of
24 months’ imprisonment for Counts 6 through 9, to be imposed consecutively to any other sentence. The PSR also noted that Defendant owed restitution in the amount of $1,820,759. .
- Of relevance to this appeal, Defendant objected to the PSR’s calculation of restitution, as well as the enhancements corresponding to the loss amount and the number of victims. He further objected- to the imposition ' of thé vulnerable-victim enhancement, the production-of-an-unauthorized-access-device enhancement, and the armed-career-criminal enhancement.
At the sentencing hearing, Defendant withdrew his objections to the enhancements for production of an unauthorized access device, as well as to his designation as an armed career criminal. In light of Defendant’s numerous factual objections to the PSR, the Government called several witnesses to testify about the traffic stop and the trash pull.
Tampa Police Department Detective Sharia Canfield testified that she examined the evidence recovered from the trash pull and the search of Defendant’s residence. She stated that approximately 7,000 means of identification were found in Defendant’s residence, some of which were taken from patient medical records. The records included handwritten notations, such as “not good” or “zero.” Based on her experience investigating tax fraud, Detective Canfield interpreted these notations to mean that an attempt to do a fraudulent tax return was unsuccessful. She stated that Defendant used the means of identification in these records to file fraudulent tax returns for individuals between the ages of 28 days and 108 years old. Defendant knew the ages, arid in some cases serious medical conditions, of the individuals whose identities he was stealing.
The Government also called Glenn Hay-ag, an Internal Revenue Service (“IRS”) Special Agent, to testify about a spreadsheet he prepared for purposes of calculating the loss amount, the number of victims, and the. amount of restitution owed. Special Agent Hayag explained, that officers recovered more than 7,000 pieces of personal identifying information from the search warrant executed at Defendant’s residence. The investigation revealed that a total of 5,811 tax returns were fraudulently filed based on that personal identifying information during the years 2010, 2011, and 2012. The IRS paid out $12,407,679 in refunds based on those 5,811 tax returns.
While reviewing the evidence collected during the investigation of Defendant and his wife, Special Agent Hayag noticed a pattern of similar, addresses, e-mail addresses, Internet Protocol (“IP”) addresses, and characteristics on the tax .returns, related to interest income, dividend income, withholdings, and wages. He examined the 5,811 filings, looking for the factors he found common to Defendant’s scheme, and narrowed the filings to 805 victims. In doing so, he excluded any refunds that went to a regular bank or were prepared by paid tax preparers, given that Defendant’s scheme involved refunds deposited to debit cards. Based on the claimed and paid amounts for only those 805 tax returns, Special Agent Hayag calculated an intended loss amount of $5,613,514 and an actual loss amount of $1,822,759. He admitted that only about 60 or 70 electronically-filed tax returns were linked to the wireless hot spot device recovered from Defendant’s residence on the day of the search. However, the hot spot device was dynamic, meaning that the device assigns a new IP address each time it signs off the internet. Stated another way, all 5,811 of the tax returns could have come from the same device.
■ Following Special Agent Hayag’s testimony, the district .court overruled Defen
dant’s objections to the calculation of the loss amount and the number of victims, concluding that ample evidence, including Special Agent Hayag’s testimony, showed that there were more than 250 victims who had their personal identifying information stolen and that $5,613,549 was a reasonable estimate of the intended loss. The district court also overruled Defendant’s objection to the PSR’s calculation of-restitution, concluding that Defendant owed restitution in the amount of $1,820,759, as this was the amount actually paid out by the IRS on the 805 tax returns attributed to Defendant.
As to the vulnerable-victim enhancement, the district court stated that:
The provision does provide if the defendant knew or should have known the victim of the offense was vulnerable as a result of the medical records. It’s clear from a review of the medical records that a number of them were vulnerable individuals just by virtue of the information and the source of the medical records.
Based on the district court’s determination regarding two enhancements not relevant to this appeal, the district court concluded that Defendant’s total offense level was 35, resulting in a guideline range of 292 to 365 months’ imprisonment. After considering the 18 U.S.C. § 3553(a) factors, the district court sentenced Defendant to a total of 324 months’ imprisonment. The district court also ordered Defendant to pay restitution in the amount of $1,820,759. This appeal followed.
II. DISCUSSION
A. Loss determination, calculation of the number of victims, and the amount of restitution
Defendant argues that the district court clearly erred by adopting Special Agent Hayag’s actual- and intended-loss determination and the calculation of the number of victims. In particular, Defendant argues that Special Agent Hayag’s calculations were speculative and did not reflect a reasonable estimate of the loss or the number of victims.
We review the district court’s loss determination, calculation of the number of victims, and the factual finding regarding the amount of restitution for clear error.
United States v. Rodriguez,
732 F.3d 1299, 1305 (11th Cir. 2013) (number-of-victims calculation);
United States v. Foley,
508 F.3d 627, 632 (11th Cir. 2007) (restitution);
United States v. Hernandez,
160 F.3d 661, 667-68 (11th Cir. 1998) (loss determination). “Although review for clear error is deferential, a finding of fact must be supported by substantial evidence.”
United States v. Robertson,
493 F.3d 1322, 1330 (11th Cir. 2007).
1. Loss Amount
Defendant first challenges the district court’s imposition of an 18-level enhancement based on its determination that the loss exceeded $2,500,000.
Section 2Bl.l(b)(l)(J) of the Sentencing Guidelines provides that a defendant is subject to an 18-level enhancement if the loss attributable to the defendant is more than $2,500,000. U.S.S.G. § 2Bl.l(b)(l)(J) (2014). The commentary states that “loss is the greater of actual or intended loss.”
Id.
§ 2B1.1, comment. (n.3(A)). More specifically, “actual loss” is the “reasonably foreseeable pecuniary harm that resulted from the offense” and “intended loss” is the “pecuniary harm that was intended to result from the offense.”
Id.
§ 2B1.1, comment. (n.3(A)(i)-(ii)).
The district court is only required to make a reasonable estimate of the loss,
and we defer appropriately to its determination.
See id.
§ 2B1.1, comment. (n.3(C)). To make the loss determination, the district court is permitted to use evidence from trial, undisputed PSR facts, and evidence from the sentencing hearing.
United States v. Bradley,
644 F.3d 1213, 1290 (11th Cir. 2011). Although reasonable estimates are permissible, speculation is not.
Id.
The Government must establish the facts by a preponderance of the evidence and support the loss calculation with reliable and specific evidence.
Id.
Here, the district court did not clearly err in finding that the Government proved by a preponderance of the evidence that the intended loss was more than $2,500,000. The Government provided reliable and specific evidence of the loss calculation and the district court made a reasonable estimate after reviewing the spreadsheet prepared by Special Agent Hayag and hearing his testimony at the sentencing hearing.
See United States v. Medina,
485 F.3d 1291, 1304 (11th Cir. 2007) (“A reasonable estimate of the loss amount is appropriate because often the amount of loss caused by fraud is difficult to determine accurately.” (quotations omitted)).
Special Agent Hayag explained that the IRS determined that the 7,000 pieces of personal identifying information found during the execution of the search warrant were used to file 5,811 fraudulent tax returns during the three-year period between 2010 and 2012. While reviewing the evidence obtained during the investigation of Defendant’s tax-fraud scheme, Special Agent Hayag noticed" a pattern of common addresses, IP addresses, and e-mail addresses, as well as similarities on the returns related to wages, interest income,- and dividends. Based on the patterns associated with Defendant’s tax-fraud- scheme, Special Agent Hayag attributed 805 of the 5,811 tax returns to Defendant. In arriving at this number, Special Agent Hayag also excluded any tax returns that were filed by a tax preparer, as well as returns that had a refund distributed to a bank, not a debit card. The intended loss (or amounts claimed) on those 805 tax returns was $5,613,549. Based on this testimony, the district court reasonably estimated the intended loss in the amount of $5,613,549.
Cf. Rodriguez,
732 F.3d at 1304-05 (concluding that the Government did not support the sentencing enhancement with rehable and specific evidence because no witness testified to authenticate the summaries of evidence presented at sentencing).
Defendant’s contention that Special Agent Hayag’s analysis was flawed because it used the 7,000 pieces of personal identifying information as a starting point misses the mark. Special Agent Hayag testified that the IRS determined that the 7,000 pieces of personal identifying information were associated with 5,811 fraudulent tax returns filed from 2010 to 2012. While Special Agent Hayag used those 5,811 tax returns as a starting point, he only attributed 805 of those returns .to Defendant based on the patterns he uncovered during his investigation of Defendant’s scheme. Defendant’s argument that it was unreasonable for Special Agent Hayag to use these common characteristics to attribute fraudulent tax returns to Defendant is without merit.
See United States v. Ford,
784 F.3d 1386, 1396-97 (11th Cir. 2015) (affirming district court’s loss calculation based on an IRS agent’s testimony that he narrowed the total number of tax returns attributable to the defendant using certain addresses linked to the defendant). Further, although Defendant asserts that Special Agent Hayag did not provide sufficient explanation regarding certain aspects of his analysis, Defendant had the opportunity to cross-examine
Special Agent Hayag on these points at the sentencing hearing.
We are also not persuaded by Defendant’s argument that he should only be held accountable for the loss amounts associated with the 60 to 70 tax returns linked to the IP address recovered from the hot spot device at his residence. As' Special Agent Hayag testified, the hot spot device recovered from Defendant’s residence was dynamic, meaning that it generated a new IP address each time that it disconnected from-the internet. In other words, the fact that the IP address could only be linked to 60 or 70 tax returns does not mean that the device was not used to file other tax returns.
Finally, we reject Defendant’s argument that the Government failed to establish that he had the ability to “rapid-file” tax returns, as he has pointed to no authority requiring the Government to submit proof that he had the ability to “rapid-file” tax returns. And indeed, the evidence put forth at the sentencing hearing showed that Defendant possessed 7,000 pieces of personal identifying information, in addition to over 300 debit cards. Because the Government presented reliable and specific evidence establishing by a preponderance of the evidence that the intended loss exceeded $2,500,000, the district court did not err in applying the 18-level enhancement under § 2Bl.l(b)(l)(J).
2. Number of Victims
Defendant further asserts that the district court’s finding that the offense involved more than 250 victims was speculative and unreasonable.
We do not agree. A defendant is subject to a 6-level enhancement when an offense involves, 250 or more: victims. U.S.S.G. § 2Bl.l(b)(2)(C) (2014). A victim is defined as “any person who sustained any part of the actual loss” of the scheme or “any individual whose means of identification was used unlawfully or without authority.”
Id.
§ 2B1.1, comment. (n.l
&
n.4(E)).
The district court did not clearly err when it determined that Defendant’s offense involved more than 250 victims. The district court based its determination on Special Agent Hayag’s testimony that 805 fraudulently-filed tax returns could be attributed to Defendant. For the same reasons explained above, the Government provided specific and reliable evidence to support the finding that the offense involved more than 250 victims, and thus warranted the six-level enhancement under § 2Bl.l(b)(2)(C).'
3. Restitution
Defendant likewise challenges the district court’s calculation of restitution in the amount of $1,820,759.
“The amount of restitution must be based on the amount of loss actually caused by the defendant’s conduct.”
United States v. Baldwin,
774 F.3d 711, 728 (11th Cir. 2014) (quotations omitted). The Government must establish the amount of restitution by a preponderance of the evidence.
Id.
“Because the determination of the restitution amount is by nature an inexact science, where difficulties arise, a district court may accept a reasonable estimate of the loss based oh the evidence presented.”
Id.
(citation and quotations omitted). ’
The .district court did not clearly err in determining that Defendant owed restitution in the amount of $1,820,759. Again, .the Government established by a preponderance of the evidence that Defendant was. accountable for 805 fraudulently-filed, tax returns. The actual loss, or amount paid out by the IRS, on those 805 tax returns was - $1,820,759.
See id.,
774
F.3d at 728. To the extent Defendant also challenges the forfeiture money judgment in the amount of $1,820,759, he does so for the first time on appeal. But regardless, for the reasons already explained, the forfeiture money judgment was based on the actual loss to the IRS as a result of the 805 fraudulently-filed tax returns attributed to Defendant.
B. Vulnerable-Victim Enhancement
Defendant next argues that the district court erred by applying the two-level vulnerable-victim enhancement under U.S.S.G. § 3Al.l(b)(l).
While the application of U.S.S.G. § 3Al.l(b) is a mixed question of law and fact that we review
de novo,
the district court’s determination that a victim is vulnerable is a factual finding to which we accord “due deference.”
United States v. Frank,
247 F.3d 1257, 1259 (11th Cir. 2001). We will reverse this factual finding only if we conclude that it is clearly erroneous.
Id,
Section 3Al.l(b)(l) of the Sentencing Guidelines provides for a two-level increase in a defendant’s offense level if “the defendant knew or should have known that a victim of the offense was a -vulnerable victim.” U.S.S.G. § 3Al.l(b)(l). The term “ ‘vulnerable victim’ means a person ... who is unusually vulnerable due to age, physical or mental condition, or who is otherwise particularly susceptible to - the criminal conduct.”
Id.
§ 3A1.1, comment. (n.2).
Defendant argues that the Government did not establish that he targeted his victims based on their vulnerability. However, we recently determined that § 3Al.l(b)(l) does not require a defendant to have targeted his victims based on their vulnerability, as it requires only that the defendant knew or should have known that a victim of the offense was vulnerable.
See United States v. Birge,
830 F.3d 1229, 1232-34 (11th Cir. 2016) (referring to language in our previous decisions stating that § 3A1.1 requires “targeting” a vulnerable victim as dicta). The district court found that Defendant knew or should have known that at least one of the victims of the offense was vulnerable, and Defendant does not appear to challenge that finding on appeal.
Instead, Defendant argues that the district court applied the vulnerable-victim enhancement based on the mere possession of medical records, but did not require proof that any personal identifying information from those records had actually been used. Because Defendant raises this argument for the first time on appeal, our review is for plain error.
See United States v. Massey,
443 F.3d 814, 819 (11th Cir. 2006) (explaining that a defendant fails to preserve an objection where he asserts the factual basis for the objection before the district court but asserts a different legal theory on appeal). Regardless, Defendant has failed to show error, plainly or. otherwise, because Defendant admitted at the guilty plea colloquy that he had used the information in the medical records to file fraudulent tax returns.
C. Production-of Unauthorized-Access-Device Enhancement
Defendant argues that the district court plainly erred by imposing a two-level en
hancement for the production of an unauthorized access device under U.S.S.G. § 2Bl.l(b)(ll)(B)(i). In particular, he asserts that the use of personal identifying information to file fraudulent tax returns does not constitute production of an unauthorized access device.
Under § 2Bl.l(b)(ll)(B)(i), a defendant is subject to a two-level increase in his offense level if the offense involved the production of an unauthorized access device. U.S.S.G. § 2Bl.l(b)(ll)(B)(i). The commentary defines “production” to mean “manufacture, design, alteration, authentication, duplication, or assembly.”
Id.
§ 2B1.1, comment. (n.lO(A)).
Defendant initially objected to the PSR’s application of this enhancement, but subsequently withdrew the objection at the beginning of the sentencing hearing. As a result, the Government contends that the doctrine of invited error precludes appellate review of Defendant’s argument challenging this enhancement. “The doctrine of invited error is implicated when a party induces or invites the district court into making an error. Where invited error exists, it precludes a court from invoking the plain error rule and reversing.”
United States v. Silvestri,
409 F.3d 1311, 1327-28 (11th Cir. 2005) (citation and quotations omitted). In a similar vein, we have held that a defendant waives a sentencing objection where he expressly withdraws the objection before the district court.
See United States v. Horsfall, 552
F.3d 1275, 1283-84 (11th Cir. 2008);
see also United States v. Masters,
118 F.3d 1524, 1526 (11th Cir. 1997) (concluding that plain-error review did not apply where a defendant withdrew his objection, despite knowing that the district court would commit error).
Based on the record before us, we conclude that Defendant waived any argument he may have had challenging the district court’s imposition of the two-level enhancement under § 2Bl.l(b)(ll)(B)(i).
See Horsfall, 552
F.3d at 1283-84;
Masters,
118 F.3d at 1526. Because Defendant expressly withdrew his objection to the enhancement at the sentencing hearing, we are precluded from addressing his arguments challenging the enhancement on appeal.
See Horsfall, 552
F.3d at 1283-84.
In any event, even if Defendant had not waived this argument, it would still fail under plain-error review. Defendant has not pointed to any on-point precedent, in which our Court or the Supreme Court has concluded that duplicating stolen Social Security numbers on tax returns for the purpose of obtaining fraudulent refunds loaded onto debit cards does not qualify as production of unauthorized access devices.
See United States v. Lejarde-Rada,
319 F.3d 1288, 1291 (11th Cir. 2003) (“It is the law of this circuit that, at least where the explicit language of a statute or rule does not specifically resolve an issue, there can be no plain error where there is no precedent from the Supreme Court or this Court directly resolving it.”).
D. Armed-Career-Criminal Enhancement
Finally, Defendant asserts that his 2008 Florida conviction for possession of cocaine with intent to sell or deliver does not qualify as a serious drug offense for purposes of the armed-career-criminal enhancement.
At the sentencing hearing, Defendant withdrew his objection to the armed-career-criminal enhancement. Defense counsel stated that he had reviewed Defendant’s underlying convictions and believed the enhancement applied. When the district court asked Defendant to confirm that he did not contest his designation as an armed career criminal, Defendant re
sponded: “That’s what .the- record states, yes.”
Based on Defendant’s express and voluntary withdrawal of his objection to the armed-career-criminal enhancement, Defendant has waived any challenge he may have had to this enhancement.
See Horsfall,
552 F.3d at 1283-84. But even if we determined that Defendant had not waived this challenge, his argument would likewise fail under plain-error review. As Defendant readily concedes, his argument that his conviction for possession of cocaine with intent to sell or deliver under Florida Statute § 893.13(1) does not qualify as a serious drug offense is foreclosed by
United States v. Smith,
775 F.3d 1262, 1264-68 (11th Cir. 2014).
III. CONCLUSION
For all of the above reasons, Defendant’s 324-month sentence is
AFFIRMED.