What is the intrinsic value of a preference share that has been paying a semi-annual dividend of $1.0 per share, and has an equity cost of capital equal to 10.0% p.a. compounding annually? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Question
What is the intrinsic value of a preference share that has been paying a semi-annual dividend of $1.0 per share, and has an equity cost of capital equal to 10.0% p.a. compounding annually? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
The intrinsic value of a preference share can be calculated using the formula for the present value of a perpetuity. A perpetuity is a type of annuity that pays dividends indefinitely. The formula is:
Intrinsic Value = D / r
where: D = Dividend per period r = Discount rate per period
In this case, the dividend (D) is $1.0 per semi-annual period, and the discount rate (r) is 10.0% per annum. However, since the dividend is paid semi-annually, we need to adjust the discount rate to a semi-annual rate.
The semi-annual discount rate is (1 + annual rate)^(1/2) - 1, which is (1 + 0.10)^(1/2) - 1 = 0.0488 or 4.88%.
So, the intrinsic value of the preference share is:
Intrinsic Value = 20.49
So, the intrinsic value of the preference share is approximately $20.49.
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