Final answer:
The perpetual equivalent annual cost at an interest rate of 10% per year is $326,360.
Step-by-step explanation:
To determine the perpetual equivalent annual cost at an interest rate of 10% per year, we need to calculate the Present Value of the perpetual stream of cash flows. The first cost of $220,000 is a one-time payment, so we need to find the present value of that payment. The updated budget of $65,000 every 7 years forever is an annuity, so we need to find the present value of the annuity.
To find the present value of the one-time payment, we can use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. Plugging in the values, we get PV = $220,000 / (1 + 0.1)^0 = $220,000.
To find the present value of the annuity, we can use the formula PV = PMT * (1 - 1 / (1 + r)^n) / r, where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years. Plugging in the values, we get PV = $65,000 * (1 - 1 / (1 + 0.1)^7) / 0.1 = $65,000 * (1 - 1 / 1.1^7) / 0.1 = $65,000 * (1 - 1 / 1.1947) / 0.1 = $65,000 * (1 - 0.836) / 0.1 = $65,000 * 0.164 / 0.1 = $106,360.
The perpetual equivalent annual cost is the sum of the present value of the one-time payment and the present value of the annuity, which is $220,000 + $106,360 = $326,360. Therefore, the perpetual equivalent annual cost at an interest rate of 10% per year is $326,360.