A machine is under consideration for investment. The cost of the machine is P25,000.00. Each year it operates, the machine will generate a savings of P15,000.00. Given the effective annual interest rate of 18%, what is the discounted payback period, in years, on the investment of the machine?
To determine the discounted payback period, we need to calculate the present value of the yearly savings generated by the machine and discount it using the effective annual interest rate.
First, let's calculate the present value factor using the formula:
Present Value Factor = 1 / (1 + i)^n
Where:
i = annual interest rate (in decimal form)
n = number of years
Given:
Annual interest rate = 18% = 0.18
Now, let's calculate the present value factor using the given effective annual interest rate. Since it is given in effective annual terms, we can directly use it as the annual interest rate.
Present Value Factor = 1 / (1 + 0.18)^n
Next, let's calculate the discounted savings for each year using the present value factor:
Year 1: P15,000 x Present Value Factor
Year 2: P15,000 x Present Value Factor^2
Year 3: P15,000 x Present Value Factor^3
...
We need to continue calculating until the discounted savings sum up to the initial investment cost of P25,000.
Let's compute the present value factor:
Present Value Factor = 1 / (1 + 0.18)^n
To find the discounted payback period, we need to calculate until the sum of the discounted savings is equal to or greater than the initial investment cost of P25,000.
Year 1:
Discounted savings = P15,000 x Present Value Factor
Year 2:
Discounted savings += P15,000 x Present Value Factor^2
Year 3:
Discounted savings += P15,000 x Present Value Factor^3
...
Continue calculating the discounted savings until the sum is equal to or greater than P25,000.
Once the sum is equal to or greater than P25,000, the discounted payback period is the number of years it takes to reach that point.