MHB How Many Shares to Buy to Achieve a Target Average Price?

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The discussion focuses on calculating the number of shares needed to achieve a target average price using a Python script. A user owns 250,000 shares at $0.005 and wants to buy additional shares at $0.03 to reach an average price of $0.02. The initial brute force method suggested yields a result of 375,000 shares. A more efficient approach using a weighted average formula is also presented, confirming the calculation of 375,000 shares needed. The conversation emphasizes the importance of simplifying the formula for clarity and efficiency in calculations.
Grimmet
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Writing a small python script...
If one owns 250000 shares at 0.005
and buys shares at 0.03.
How many shares would one buy for the average price to equal 0.02.

My attempt so far as used brute force looping to get close to a figure.
For example, the script gives the answer 375000 shares.
... I'm sure there's a more elegant way.

exitPrg = "y"

def LowBracket(buyP, targetP, currentA, ownedS, lim):
nX = 0
while nX <= limit:
nm = round(((nX * buyP)+currentA)/(nX+ownedS),5)
if nm == targetPrice:
break
nX += 1
return nX

def HighBracket(buyP, targetP, currentA, ownedS, lim):
nY = lim
while nY > 0:
nn = round(((nY * buyP)+currentA)/(nY+ownedS),5)
if nn == targetP:
break
nY -= 1
return nY

while ( exitPrg == "y" or exitPrg == "Y"):
ownedShares = input("\nShares owned: ")
boughtPrice = input("Price bought: ")
buyPrice = input("New price: ")
targetPrice = input("Target price: ")
limit = input("Share limit: ")

ownedShares = int(ownedShares)
boughtPrice = float(boughtPrice)
buyPrice = float(buyPrice)
targetPrice = float(targetPrice)
limit = int(limit)

currentAmount = ownedShares * boughtPrice

numberA = LowBracket(buyPrice, targetPrice, currentAmount, ownedShares, limit)

numberB = HighBracket(buyPrice, targetPrice, currentAmount, ownedShares, limit)

print("\nNumber of shares: %i\n" % ((numberB+numberA)/2))

exitPrg = input("Continue? (y/n) ")

Thanks.
 
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You could use what's called a weighted average to determine the answer:

$$\frac{250000\cdot0.005+X\cdot0.03}{250000+X}=0.02$$

Simplify:

$$\frac{1250+0.03X}{250000+X}=0.02$$

Multiply through by $250000+X$:

$$1250+0.03X=5000+0.02X$$

Rearrange:

$$0.01X=3750$$

Multiply through by 100:

$$X=375000$$
 
Therefore:
Shares = ownedShares*targetPrice - ownedShares*boughtPrice / buyPrice - targetPrice

Thanks for the help.

Grimmet
 
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