E-Eyes.com Bank just issued some new preferred stock. The issue will pay a $9 annual dividend in perpetuity, beginning 11 years from now. If the market requires a 0.08 return on this investment, how much does a share of preferred stock cost today? Enter the answer with 2 decimals (The answer should look something like 45.45).

If you struggle with this problem, here is a video where I solve a similar problem. If you find yourself relying a lot on these video solutions, it means that you have NOT learned the material, and likely you will struggle in the exam. Make sure to go back and re-watch the lecture videos. Anyways, here is the video solution: https://streaming.uww.edu/#/videos/e6a0d9ce-6312-4e2f-9530-4d9ac8896579 Links to an external site.

Question

E-Eyes.com Bank just issued some new preferred stock. The issue will pay a $9 annual dividend in perpetuity, beginning 11 years from now. If the market requires a 0.08 return on this investment, how much does a share of preferred stock cost today? Enter the answer with 2 decimals (The answer should look something like 45.45).

If you struggle with this problem, here is a video where I solve a similar problem. If you find yourself relying a lot on these video solutions, it means that you have NOT learned the material, and likely you will struggle in the exam. Make sure to go back and re-watch the lecture videos. Anyways, here is the video solution: https://streaming.uww.edu/#/videos/e6a0d9ce-6312-4e2f-9530-4d9ac8896579 Links to an external site.

BlackTom AI · Accepted Answer

The question asks for the present value today of a preferred stock that pays a fixed dividend of 9 every year forever, with the first payment occurring 11 years from now, and the required return (discount rate) is 8% per year.

First, recognize the structure: this is a perpetuity that starts one year from year 11, i.e., the first cash flow occurs at t = 11 and continues indefinitely thereafter. To value a perpetuity that starts in the future, you can think of its value one period before the first payment as the standard perpetuity value, then discount that value back to today.

Step 1: Value of the perpetuity at the moment right before the first payment (time t = 10). For a perpetuity with annual payment C = 9 and discount rate r = 0.08, the value one period before the first payment is C/r = 9 / 0.08 = 112.50. This is the value at time t = 10, because the first payment occurs at t = 11.

Step 2: Discount that value back to today (time t = 0). The number of years to discount is 10 years (from t = 10 to t = 0), so you divide by (1 + r)^10 = 1.08^10. Compute 1.08^10 ≈ 2.1589.

Step 3: Present value today = 112.50 / 2.1589 ≈ 52.12.

If someone were to check alternative interpretations, such as discounting 11 years or treating the first payment differently, they would end up with a different numeric result (for example, using 11 years would further reduce the value). The correct approach here is to value just before the first payment (time 10) and then discount back 10 years.

Note on the given context: there are no answer choices provided in the prompt, only the computed result is sought. The calculation steps above show how to arrive at the price using standard perpetuity and time-value-of-money reasoning.

FNBSLW 344-23 Chapter 7 HW-Part 1

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