Final answer:
To calculate the perpetual equivalent annual cost for the literacy program with a $220,000 initial cost and a recurring budget of $565,000 every 7 years at a 10% interest rate, we calculate the present value of the perpetuity and then find the equivalent annual cost, which is $3,978,000.
Step-by-step explanation:
The question asks to calculate the perpetual equivalent annual cost for a literacy program in Chiapas, Mexico, considering an initial cost and a recurring updated budget every 7 years, at an interest rate of 10% per annum. To determine this, we can use the formula for calculating the present value of a perpetuity:
PV = P / r
where PV is the present value of the perpetuity (what the equivalent cost is worth right now), P is the payment amount per period, and r is the interest rate per period.
However, in this scenario, we are asked for an equivalent annual cost, not just the present value. We must consider the initial cost of $220,000 as well as the perpetual cost of $565,000 that occurs every 7 years. The annual cost can be considered as an annuity that is received in perpetuity.
First, we calculate the present value of the $565,000 paid every 7 years as a perpetuity:
PV = $565,000 / (0.10/7) = $565,000 / (0.0142857) = $39,560,000
Now, we need to add the initial cost:
Total PV = $220,000 + $39,560,000 = $39,780,000
We then convert this present value into an equivalent annual cost (EAC) at 10% interest:
EAC = Total PV × annual interest rate
= $39,780,000 × 0.10
= $3,978,000
Therefore, the perpetual equivalent annual cost at a 10% interest rate is $3,978,000.