To determine the current share price of Burnett Corp.'s stock, we need to calculate the present value of the dividend payments, given that the dividends are constant for 13 years and then cease. This is a finite series of cash flows, which can be valued using the formula for the present value of an annuity.
The formula for the present value of an annuity is:
\[ PV = C \times \left(1 - (1 + r)^{-n}\right) / r \]
where:
- \( PV \) is the present value of the annuity.
- \( C \) is the cash flow per period (the dividend in this case, which is \$8.25).
- \( r \) is the discount rate (the required return, which is 11.2% or 0.112).
- \( n \) is the number of periods (13 years).
Plugging in the values:
\[ PV = 8.25 \times \left(1 - (1 + 0.112)^{-13}\right) / 0.112 \]
First, calculate \((1 + 0.112)^{-13}\):
\[ (1 + 0.112)^{-13} = (1.112)^{-13} \approx 0.2472 \]
Now, substitute back into the formula:
\[ PV = 8.25 \times \left(1 - 0.2472\right) / 0.112 \]
\[ PV = 8.25 \times 0.7528 / 0.112 \]
\[ PV = 8.25 \times 6.7232 \]
\[ PV \approx 55.47 \]
Therefore, the current share price of Burnett Corp.'s stock is approximately \$55.47.