Preferred stock question. I need help with part b.
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 solve part b of the question, we need to calculate the cash flows of the investor when the required annual expected rate of return (ROR) on the preferred stock becomes 8% by the end of year 2.
Let's break down the steps to find the cash flows:
Step 1: Calculate the cash flows for the first two years assuming the interest rates don't change:
Since the preferred stock is expected to pay $1.5 per quarter, the annual cash flow for one share would be 4 * $1.5 = $6.
Therefore, the cash flow for 10 shares each year would be $6 * 10 = $60.
Year 1: The investor receives $60 in cash flows.
Year 2: The investor receives another $60 in cash flows.
So, if the interest rates don't change, the cash flows for the first two years are $60 and $60, respectively.
Step 2: Calculate the cash flows at the end of year 2 when the required annual expected ROR on the preferred stock becomes 8%.
To find the cash flows when the ROR changes, we need to consider the new rate and the remaining years.
The new rate is 8% or 0.08, and the remaining period is 2 years. We'll then calculate the present value of the future cash flows using the formula:
Present Value = Cash Flow / (1 + ROR)^n
Where ROR is the rate of return and n is the number of years.
For year 3, the cash flow will be $6 * 10 = $60. We'll discount it back to the present time using the new ROR:
Present Value = $60 / (1 + 0.08)^1 = $60 / 1.08 = $55.56
For year 4, the cash flow will also be $6 * 10 = $60. We'll discount it using the new ROR:
Present Value = $60 / (1 + 0.08)^2 = $60 / 1.1664 = $51.51
So, at the end of year 2, the cash flows will be $55.56 and $51.51 for years 3 and 4, respectively.
In summary, the cash flows on a timeline in situation b (where the required annual ROR becomes 8% by the end of year 2) are:
Year 1: $60
Year 2: $60
Year 3: $55.56
Year 4: $51.51