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FTHC Ltd has forecast earnings per share in a year’s time of $2.50. FTHC Ltd has a policy of distributing 70% of earnings as an annual dividend. You forecast that dividends are expected to grow at a constant rate of 6% per annum each year following the dividend next year. If the required return from FTHC Ltd shares is 15% per annum, which of the following is closest to the present value of FTHC Ltd’s growth opportunities (measured on a per share basis)? (a) $2.78 (b) $4.50 (c) $19.44 (d) $27.00

Question

FTHC Ltd has forecast earnings per share in a year’s time of 2.50.FTHCLtdhasapolicyofdistributing70ataconstantrateof6fromFTHCLtdsharesis15FTHCLtdsgrowthopportunities(measuredonapersharebasis)?(a)2.50. FTHC Ltd has a policy of distributing 70% of earnings as an annual dividend. You forecast that dividends are expected to grow at a constant rate of 6% per annum each year following the dividend next year. If the required return from FTHC Ltd shares is 15% per annum, which of the following is closest to the present value of FTHC Ltd’s growth opportunities (measured on a per share basis)? (a) 2.78 (b) 4.50(c)4.50 (c) 19.44 (d) $27.00

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Solution

First, we need to calculate the dividend that will be paid out next year. FTHC Ltd has a policy of distributing 70% of earnings as an annual dividend. So, the dividend next year will be:

Dividend = Earnings per share * Dividend payout ratio Dividend = 2.500.70=2.50 * 0.70 = 1.75

Next, we use the Gordon Growth Model to calculate the total value of the stock. The formula for the Gordon Growth Model is:

Value = D1 / (r - g)

Where: D1 = Dividend expected next year r = Required rate of return g = Dividend growth rate

In this case: D1 = $1.75 r = 15% or 0.15 g = 6% or 0.06

So, the total value of the stock is:

Value = 1.75/(0.150.06)=1.75 / (0.15 - 0.06) = 19.44

The present value of FTHC Ltd's growth opportunities is the total value of the stock minus the earnings per share:

PVGO = Value - Earnings per share PVGO = 19.4419.44 - 2.50 = $16.94

None of the options provided (a) 2.78,(b)2.78, (b) 4.50, (c) 19.44,or(d)19.44, or (d) 27.00 are closest to the present value of FTHC Ltd's growth opportunities. The closest value based on the given information is $16.94.

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