A machine costs P 20,000.00 today and has an estimated scrap value of P2,000.00 after 8 years. Inflation is 2% per year. The effective annual interest rate earned on money invested is 8%. How much money needs to be set aside each year to replace the machine with an identical model 8 years from now?
To find out how much money needs to be set aside each year to replace the machine, we need to calculate the future value of the machine's cost and subtract the future value of the scrap value.
First, we will calculate the future value of the machine's cost after 8 years. We will use the formula for future value with compound interest:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value (machine cost)
r = interest rate
n = number of years
PV = P20,000.00
r = 8% = 0.08
n = 8 years
FV= P20,000.00 * (1 + 0.08)^8 = P20,000.00 * 1.08^8 = P38806.95
Next, we will calculate the future value of the machine's scrap value after 8 years. We will also use the formula for future value with compound interest:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value (scrap value)
r = interest rate
n = number of years
PV = P2,000.00
r = 8% = 0.08
n = 8 years
FV = P2,000.00 * (1 + 0.08)^8 = P2,000.00 * 1.08^8 = P3,881.09
Now, we can calculate the annual amount that needs to be set aside to replace the machine:
Amount = (FV - Scrap Value) / (1 + Inflation Rate)^n
Where:
Amount = annual amount to be set aside
FV = future value of the machine's cost
Scrap Value = future value of the machine's scrap value
Inflation Rate = 2% = 0.02
n = number of years = 8
Amount = (P38,806.95 - P3,881.09) / (1 + 0.02)^8 = P34,925.86 / 1.02^8 = P27,994.65
Therefore, P27,994.65 needs to be set aside each year to replace the machine with an identical model 8 years from now.