A share of preferred stock of MXT Ltd. is expected to pay $1.5 per quarter into indefinite future. The current annual expected rate of return (k) is 12%. Suppose that an investor buys 10 shares today and holds them for two years. Find his/her cash flows on a timeline in each of the following situations:
a. Interest Rates don't change
b. The required annual expected ROR on the preferred stock becomes 8% bu the end of year 2.
To determine the cash flows on a timeline for each situation, we need to calculate the dividends received by the investor for each quarter.
a. In this situation, where the interest rates don't change, the investor will receive $1.5 per share as quarterly dividends indefinitely. To calculate the cash flows for two years, we'll consider 8 quarters.
Cash flows for each quarter:
Quarter 1: 10 shares x $1.5 = $15
Quarter 2: 10 shares x $1.5 = $15
Quarter 3: 10 shares x $1.5 = $15
Quarter 4: 10 shares x $1.5 = $15
Quarter 5: 10 shares x $1.5 = $15
Quarter 6: 10 shares x $1.5 = $15
Quarter 7: 10 shares x $1.5 = $15
Quarter 8: 10 shares x $1.5 = $15
Therefore, the cash flows for two years would be:
Year 1: $60 (sum of the first four quarters)
Year 2: $60 (sum of the last four quarters)
b. In this situation, the required annual expected rate of return (ROR) on the preferred stock becomes 8% by the end of year 2. Since the ROR affects the value of the dividend payment, we need to calculate the dividend for each quarter at the new ROR.
Assuming the investor still holds the shares for two years, we'll once again consider 8 quarters.
First, we need to calculate the new dividend per share for each quarter based on the new ROR.
New dividend per share = Annual dividend payment / Annual expected rate of return
For the first four quarters (Year 1), the dividend per share remains the same as in situation a:
New dividend per share = $1.5 / 12% = $12.50
Cash flows for each quarter:
Quarter 1: 10 shares x $1.5 = $15
Quarter 2: 10 shares x $1.5 = $15
Quarter 3: 10 shares x $1.5 = $15
Quarter 4: 10 shares x $1.5 = $15
For the last four quarters (Year 2), we'll calculate the new dividend per share using the new ROR of 8%:
New dividend per share = $1.5 / 8% = $18.75
Cash flows for each quarter:
Quarter 5: 10 shares x $18.75 = $187.50
Quarter 6: 10 shares x $18.75 = $187.50
Quarter 7: 10 shares x $18.75 = $187.50
Quarter 8: 10 shares x $18.75 = $187.50
Therefore, the cash flows in Year 1 would be $60, and in Year 2, it would be $750 (sum of the last four quarters).