Final answer:
To calculate the present value of the described perpetuity, we must discount each of the first 23 increasing payments to present value, then calculate the present value of a level perpetuity from year 24 onward and discount that to present value as well. This requires the sum of a series and the perpetuity present value formula.
Step-by-step explanation:
To find the present value of the described perpetuity with an annual effective interest rate of 0.06, we must calculate the present value of the first 23 payments individually and then use the formula for a level perpetuity for the payments from year 24 onward. The perpetuity formula is PV = R / i, where R is the periodic payment and i is the interest rate per period.
The first portion requires discounting each of the increasing payments (1 to 23) back to the present value using the formula PV = Payment / (1 + i)^t, where t represents the time in years. So, we must calculate the sum of 1/(1.06)^1 + 2/(1.06)^2 + ... + 23/(1.06)^23.
Next, for the level perpetuity starting after year 23, the present value in year 23 would be PV = 23 / 0.06. Since this is the value in year 23, we then need to discount it back to present value by dividing by (1.06)^23.
By summing the present values of the individual increasing payments and the discounted perpetuity, we arrive at the total present value of the perpetuity. This is a somewhat complex calculation that requires either careful manual summation or the use of financial software or a programmable calculator. It should be noted that the present values we obtain are impacted by the discounting effect; the earlier payments are worth more in today's terms than those further in the future due to the time value of money principle.