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What is the intrinsic value of a preference share that has been paying a semi-annual dividend of $1.3 per share, and has an equity cost of capital equal to 11.2% 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 $1.3 per share, and has an equity cost of capital equal to 11.2% p.a. compounding annually? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

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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 periodic payments indefinitely. Preference shares are considered as perpetuities because they pay a fixed dividend indefinitely.

The formula for the present value of a perpetuity is:

PV = D / r

where:

  • PV is the present value or intrinsic value of the preference share
  • D is the dividend payment per period
  • r is the discount rate or cost of equity

Given in the problem, we have:

  • D = 1.3semiannualdividend2=1.3 semi-annual dividend * 2 = 2.6 annual dividend
  • r = 11.2% p.a. = 0.112

Substituting these values into the formula, we get:

PV = 2.6/0.112=2.6 / 0.112 = 23.21

Therefore, the intrinsic value of the preference share is approximately $23.21.

This problem has been solved

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