The ASX 200 index is currently trading at 2325 points and is widely expected to pay a dividend (DPS1) equal to 135 points next year. At the same time, shares in MercedesF1 are trading at $78.55 and are expected to pay a dividend next year (DPS1) equal to $6.65. The consensus analyst forecast is that the growth rate of both MercedesF1 dividends and ASX 200 dividends will be 4.50% in perpetuity. The long-run risk-free rate is given as 5.25%. Assume that the market prices of the ASX 200 index and MercedesF1 are efficient.a) The cost of equity (re) for the ASX 200 is ?b) The market risk premium is ?c) The cost of equity (re) for MercedesF1 is ?d) The implied beta for MercedesF1 is ?
Question
The ASX 200 index is currently trading at 2325 points and is widely expected to pay a dividend (DPS1) equal to 135 points next year. At the same time, shares in MercedesF1 are trading at 6.65. The consensus analyst forecast is that the growth rate of both MercedesF1 dividends and ASX 200 dividends will be 4.50% in perpetuity. The long-run risk-free rate is given as 5.25%. Assume that the market prices of the ASX 200 index and MercedesF1 are efficient.a) The cost of equity (re) for the ASX 200 is ?b) The market risk premium is ?c) The cost of equity (re) for MercedesF1 is ?d) The implied beta for MercedesF1 is ?
Solution
a) The cost of equity (re) for the ASX 200 is:
We can use the Gordon Growth Model to calculate the cost of equity. The formula is:
re = D1 / P0 + g
Where: D1 = expected dividend per share one year from now P0 = current price of the stock g = growth rate of dividends
Substituting the given values into the formula, we get:
re = 135 / 2325 + 4.50% re = 5.80% + 4.50% re = 10.30%
b) The market risk premium is:
The market risk premium is the cost of equity minus the risk-free rate. So, the market risk premium is 10.30% - 5.25% = 5.05%.
c) The cost of equity (re) for MercedesF1 is:
Again, we can use the Gordon Growth Model to calculate the cost of equity. Substituting the given values into the formula, we get:
re = 78.55 + 4.50% re = 8.47% + 4.50% re = 12.97%
d) The implied beta for MercedesF1 is:
We can use the Capital Asset Pricing Model (CAPM) to calculate the implied beta. The formula is:
Beta = (re - Risk-free rate) / Market risk premium
Substituting the given values into the formula, we get:
Beta = (12.97% - 5.25%) / 5.05% Beta = 1.53
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