Final answer:
The actuarial present value of a new 'Actuary Today' magazine subscriber is approximately $172.41, calculated using the formula for the present value of a perpetuity with declining cash flows. It is based on the $25 initial subscription fee, a renewal rate of 90%, and a discount factor of 0.95.
Step-by-step explanation:
The actuarial present value of a new subscriber for 'Actuary Today' magazine can be calculated by considering both the annual subscription fee and the renewal rate. Since subscribers would pay $25 at the start of each year, and the renewal rate is 90% with a discount factor of 0.95, it means that each subsequent year, only 90% of the subscribers are expected to renew. Hence, the cash flow from each subscriber would diminish accordingly.
To calculate the present value of the cash flow generated by a subscriber, we need to consider the entire expected duration for which the subscriber will renew the subscription. We use the formula for the present value of a perpetuity with declining cash flow, which is based on a geometric series. The formula is:
Here, PV represents the present value, P is the initial payment, g is the renewal rate, and r is the discount factor. Plugging in the values:
- PV = 25 / (1 - 0.9 * 0.95)
- PV = 25 / (1 - 0.855)
- PV = 25 / 0.145
- PV = 172.41
Therefore, the actuarial present value of a new subscriber is approximately $172.41. This value falls in the range of $170 but <$180.