If you want to take it out of context and go by metal value alone, that's pretty easy. Augustus reformed the coinage to make the Sestertius (HS) brass and revalue it to 1/100th of the gold Aureus, which at that time was about 8 grams. This would make the Augustan Sestertius notionally worth 80mg of gold. Today as of right now the USD gold spot price is $39.80/gram, so you're looking at $3.18 per notional Augustan Sestertius.

The value of the brass weight of the Sestertius in Augustan times may not have actually been 1/100th of an Aureus, as bi- or multi- metallist monetary systems are always susceptible to fluctuations in the true exchange values regardless of notional pegs. It also doesn't reflect the modern equivalence of today; that is to say the value of the 25-28 grams of brass in an Augustan Sestertius is, today, worth far less than the $3.18 cents I calculated above based on the ancient notional value. In fact, a pound (425 grams, or 17 HS' weight) of brass costs less than $1.25.

Most importantly, the current dollar value combined with the dollar's current purchasing power in relation to the value of metal in these ancient coins at today's rate do not provide you with an accurate estimate of the purchasing power of these coins under Augustus. The above back-of-the-napkin calculations simply tell you what you could do with a Sestertius' weight of brass or 1/100th an Aureus' weight of gold today.

So, for example, using this book's claims that under the early empire a modius of wheat cost 5-6 HS (=$15.90 per ~2 gallons by my $3.18 sestertius figure above), while the same amount of wheat today actually costs you about a $1.10 ($5.12/bushel spot price today).

What does all this nonsense I wrote actually tell you? Essentially, that prices, notional values, and government-dictated exchange rates and price controls are fleeting things and making useful, sensible comparisons through time and among differing markets in different worlds filled with different technology is incredibly difficult.

Edit: if you're interested in the answer to what /u/Feezec said you might want to consider instead, which is relative "purchasing power", here's a rough estimate based on the above and using wheat as the object. 4.5M HS could have bought 700,000 modii of wheat, which is about 1,400,000 gallons; about enough to make 6 and half million loaves of bread. That much wheat today would cost $770,000USD. Of course, this purchasing power example would be different if we didn't use wheat.

Edit2: I see the quoted amount is actually 43.5 M HS. Just multiply everything in that last paragraph by 9 and 2/3.

Well, let's first note, that the Romans notoriously had a tendency to round up numbers in prose; Walter Scheidel (1996) has shown that, irrespective of literary genres, the Latin literature is permeated by conventional or symbolic monetary valuations to an extent that seriously restricts the range even of tentative calculations and quantifying comparisons based on literary evidence. He has argued that between 90-100% of the numbers and prizes given in Roman literature were figures that were rounded up approximations, or exaggerated to give the number more emphasis and pomp (the Romans didn't really worry too much about sticking to the absolute truth when writing history). So, the 43 500 000 sestertii Tacitus gives might not be the original sum Augustus gave away at all.

All in all, ancient economy is a really difficult field to study and the literary evidence and e.g. numismatic evidence can often give completely different stories. For example, the economic imperialism of Classical Athens in the Greek world is the unanimous picture given by the literary sources, but actually, if we look at the coinage of the time (and this is something that has been noticed only recently), most of the Greek world during the Classical era did not adhere to Athenian coin weight standards and thus looks like the era is better described as an era of separate, detached micro-economies of city states that were trading mainly with their neighbors, and not an Mediterranean wide network where Athens acted as the ancient equivalent of Wall Street.

But, let's say we want to compare the number Tacitus gives regardless whether it's true or not. To answer your question we would require some sort of mass examination of coin weights, coin circulation, and the prices of basic goods at the end of Augustan era in Rome to get an idea of the value of sestertius that could be compared to modern US dollar. As long as I'm aware this hasn't been done yet in a convincing way (there's soooo much work to be done in Roman numismatics), and I'm not sure if there is enough data to actually make one - there might be, Roman economy isn't my absolute field of expertise (if there is an expert of Roman economy here, please chip in and all hail to you for devoting yourself to such an impossibly difficult field!). But, what I can do, is give you some other comparable numbers from Roman literature of the early and high Empire - so, even if Tacitus' number isn't correct, you'll get an idea what he was comparing the sum to. Here are some random things could have bought with 43 500 000 sestertii in Imperial Rome:

• Augustus set the property limit of the order of knights (equites) to 100,000 denarii. Sestertius is the quarter of denarius, so, with Augustus' will, you could have promoted almost 109 people to the equestrian order.

• According to a graffiti in Pompeii (might be c. 60-70 years later than Augustus' death, though), we know that the going rate for a pitcher of wine was 2 asses. As was a quarter of a sestertius, so you could buy 87 000 000 pitchers of wine.

• Also, again thanks to graffiti in Pompeii, we know you could hire the prostitute Attice for 4 sestertii; so you could hire 10 875 000 average prostitutes.

• According to Martial's poem 12.61, a purple cloak - purple was especially expensive dye - went for 10 000 sestertii, so you could clothe yourself with 4350 of those. Alternatively, you could buy 4350 donkeys which also went for 10 000 according to Elder Pliny (c. 77AD) and Varro (1st century BC).

• According to elder Pliny, an estimated price for a decent villa with furnishings was 3 000 000 sestertii, so you could buy 14 and a half of those.

• A decent aristocratic dowry, according to Martial and Juvenal, would be 1 000 000 so you could marry off 43 of your daughters to a gentleman.

• A legionary's yearly pay at the time of Augustus was 900 sestertii (Augustus actually also left 300 sestertii to all soldiers in his will), so you could have hired an army of 48 333 trained legionaries for a year, granted that you paid for their food and accommodation as well.

Note that most of these figures I use are also suspiciously neat and thus probably rounded up according to the conventions of Latin literature and do not really reflect reality! I got these figures, aside from the graffiti, from Walter Schneidel's handy lists.

We could try to make some rough estimation of the value of sestertii and dollars on the basis of the price of basic goods and your relative purchasing power, such as the price of wheat in ancient Rome, which has been used in the past to examine inflation etc. in ancient Rome, e.g. by Rickman. Here's an interesting survey of Roman wheat prices. During the early Empire, a modius, so about two gallons, of wheat would have cut you back by about 7 sestertii in Pompeii, according to the graffiti. But, note that you could get it for a fraction of that price in the provinces, showing you how difficult it is to even use this method to make comparisons between ancient and modern currencies! Anyway, using the prices in Rome (and if my maths is correct) you could buy 6 214 285 modii of wheat, so ~12 428 571 gallons or ~391 393 metric tons of wheat. According to Index Mundi, a ton of wheat currently costs 188.12 US$. So, from that we get a sum of 73 628 851,16 US$ from 43 500 000 sestertii.

I think there's lot of obvious difficulties with this method and don't quote me on that answer because I don't have the head for maths and economics, but I guess it's fair to say that we're talking about a lot of money.

Edit: looks like u/dontVoteBarack2016 beat me to using wheat as a point of comparison, and gave a much more math savy answer!

These currency-to-currency comparisons over such periods are unrewarding because the two economies underlying the respective currency units are so vastly unalike. Pretty much every attempt to quantify Roman living standards starts out with the price of wheat, which might have accounted for a quarter of the economy and was certainly the biggest product: in today's US even at 60m tons it's worth under a thousandth of total annual national output, making any economy-wide comparison - which the relative value of money is - unreliable.

It's far more useful to think about these values in terms of what they were worth at the time. Recent estimates of the Empire's per capita GDP have ranged from HS260 to 380 (1): on that basis HS43½m might support 230-330,000 people for a year at half the average income level. In the US at today's incomes that would take $6.4-9.3bn, but if we just use the wheat price - about $1.2 per modius in the US today against HS2½-3, the total is only about $17-20½m, perhaps 1/300 as much, reflecting a hundred-fold income difference and sectoral earnings & price shifts that have left grain prices at a historic low relative to incomes.

That's why in my experience these conversions don't work. Better to say it was perhaps the combined annual earnings of a provincial territory of maybe 120-170,000 inhabitants. That tells me something useful.