Improvement to batteries is constantly improving. A 20 k Wh battery purchased 20
ID: 387725 • Letter: I
Question
Improvement to batteries is constantly improving. A 20 k Wh battery purchased 20 years ago at a cost of $100.000. A) What will a 50 k Wh battery cost today if the power-sizing exponent is 0.57 and the cost index has increased from 180 to 200 over the last 20 years? B) When making the economic decision to replace the battery today. would you be concerned with your previous expenditure on the 20 kWh battery Explain C) Determine the breakeven volume (number of units sold) for the 50 k Wh battery. Fixed Cost 1.5 Billion Materials and Labor $95.000 unitExplanation / Answer
20KWH battery purchased 20 years ago at a cost of $100,000
Cost of 50KWH today: ??
Power sizing exponent: 0.57
Cost index increased from 180 to 200 over 20 years
We know that:
C1/C2 = (Q1/Q2)^x
Where
C1 = cost of 20KWH battery: 100,000
C2 = cost of 50KWH battery: Need to find
Q1 = capacity / 20KWH: 20 kWh
Q2 = capacity / 50KWH: 50kwh
x = power-sizing exponent: 0.57
C2 = C1/ ((Q1/Q2)^x)
= 10000/((20/50)^0.57)
=168587 $
As this price would be 20 years old, let us look at given cost index to normalize it.
Cost of 50 kwh bulb: Cost 20 years back X (Cost index now/ cost index before)
: 168587 X (200/180)
: 187,319 $
Therefore present cost of 50KWH battery is 187,319$