What is the intrinsic value of a preference share that has been paying a semi-annual dividend of $0.9 per share, and has an equity cost of capital equal to 13.4% 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 $0.9 per share, and has an equity cost of capital equal to 13.4% p.a. compounding annually? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

BlackTom AI · Accepted Answer

Take the question as a valuation of a perpetual dividend-paying instrument. The share pays a fixed dividend of 0.9 dollars every half-year, i.e., 0.9 per period. Since the cost of equity capital is 13.4% per year with annual compounding, convert this to a per-half-year rate: 0.134 / 2 = 0.067 (or 6.7% per half-year).

This setup is a perpetuity with payments of 0.9 every half-year and a discount rate of 6.7% per half-year. The present value of a perpetual annuity (perpetuity) is Payment / rate per period. Therefore, the value V equals 0.9 / 0.067.

Carrying out the division: 0.9 ÷ 0.067 ≈ 13.432835...

Rounding to two decimals as requested gives 13.43.

As a cross-check, if you instead annualize the payments and use the annual cost of capital, the annual dividend is 1.8 dollars, and the annual rate is 0.134. The perpetuity formula gives V = 1.8 / 0.134 ≈ 13.4328, which confirms the same result when rounded to two decimals.

Therefore, the intrinsic value of the preference share, in dollars to two decimals, is 13.43.

FINC2011 (S1 2025) Regular Quiz 2 on Topics 5 & 6 - Due on 22 April

What is the intrinsic value of a preference share that has been paying a semi-annual dividend of $0.9 per share, and has an equity cost of capital equal to 13.4% 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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