For my OOTA campaign I needed to get a handle on the value of slaves. It's a repugnant subject, but not one I believe we should avoid. Here is where I landed -
Slavery
Slavery is common in the Underdark, being most practiced by drow, duergar and fomorians. About 1/5 such creatures own on average 5 slaves, while 1/50 own on average 50. About 1/10 slaves are skilled, of whom 1/10 have tier 1 character-class equivalence. Old slaves are rare: most are young or adult. Slaves are priced on the basis of 2 years earnings from their labour.
Menzoberranzan (pop 20,000 free)
Type...........Slaves.........Usual Price
Unskilled......40,000.............150gp (based on 2sp earnings/day)
Skilled...........4,000...........1,500gp (based on 2gp earnings/day)
Tier 1...............400...........7,500gp (based on 10gp earnings/day)
Tier 2.................40........36,500gp (based on 50gp earnings/day)
Tier 3..................4.........priceless
Tier 4...............0-1.........priceless
Epic+..................0.........priceless
My assumptions are
1) based on large-scale slavery in the real world (US and UK) slaves are priced based on anticipated profits from their labour,
2) most slaves will remain in captivity for 5-10 years before dying or escaping,
2) owning a slave comes with costs and risks that more than halve their earnings for the purpose of calculating anticipated profits (hence they're valued on less than half their expected lifetime earnings). I based costs and earnings on
PHB 157-159. I believe some readers are going to feel here that my values are too high so I'd like to explain why I believe it is important that they
should be high. I based the slave population numbers on real world figures, bringing down the top end to reflect less efficient mythic-medieval logistics. Slaves are
in addition to the free population, i.e. in 1479DR Menzoberranzan contains perhaps 60,000 sentient beings, 2/3rds of whom are slaves. I used my "
order of magnitude fewer per tier" rule of thumb for slave skill levels. We know that there are at least
some tier 1 or above slaves in Menzoberranzan

Are there tier 3 or 4 slaves? As always that is up to each DM, but I feel we should raise the possibility: that could lead to interesting scenarios.
Your assumptions section doesn't state what interest rate you used to discount the future net income from the slave's labor to its net present value.
As it so happens, I've done some math here (big surprise from the tax accountant, I know).
An unskilled laborer earns 2 SP a day. PHB pg 159.
However, you also need to subtract the cost of living. While the conditions a slave lives in certainly qualifies as "inhumane," a term used to describe the wretched standard of living (PHB pg 158), the truth is that the remainder of the description fails to line up with what we'd expect for housing a slave. The squalid living condition (also PHB pg 158) is far more accurate, and that costs 1 SP a day.
So, we have a net income of 1 SP per day. And, that's ignoring any costs for hiring out the slave, or paying people to make sure the slave doesn't run away or otherwise try to fight for its freedom (perhaps by killing its owner).
Let's use your 10 year assumption for how long they can work. So, we have 1 SP per day, 365 days per year, for 10 years: that's 3,650 SP, or 365 GP.
But, that's future income. Now you have to discount that income stream. Since there really is no good way to determine the prevailing interest rate, our best bet is to use the desired rate of return as the discount rate so we can see what a willing buyer would pay in an arms'-length fair-market transaction.
Using the formula for the present value of an annuity, where the annual net income of 365 SP is the annual rents, 10 years is the number of periods, and 10% is the desired rate of return, we get 2,242.77 SP. That's a price of 224 GP, 2 SP, and 8 CP (actually 7.7 CP, but I rounded up). Which is actually equivalent to the PHB price for 4.5 draft horses (at 50 GP each). PHB pg 157.
To give that further perspective, examine that cost if paid in trade goods.
22,428 CP = 22,428 pounds of wheat. That's more than eleven tons of wheat!
22,428 CP = 4,485.6 pounds of salt. That's more than two tons of salt!
22,428 CP = 11,214 pounds of flour, or 11,214 chickens.
22,428 CP = 224 goats, or 112 sheep, or 112 pounds of cinnamon or pepper.
22,428 CP = 75 pigs.
22,428 CP = 15 oxen.
22,428 CP = an elephant and 1 mastiff (approximately).
22,428 CP = 448.4 pounds of copper, or 448.4 square yards of cotton cloth.
Edit: of course, all that changes if you tinker with the rate of return. And, naturally, rate of return is pegged to perceived risk of investment loss (escape, death, etc). So, it really wouldn't be outrageous for a buyer to expect a rate of return that would seem obscenely high to us in modern times. I could easily see a desire for a 25% to 50% rate of return being reasonable.
And, for the record, at increased levels of risk we're talking about the following prices:
20% = 15,302 CP
25% = 13,032 CP
30% = 11,284 CP
40% = 8,809 CP
50% = 7,173 CP