How to calculate the risk free rate? with explaination please. You are given the
ID: 2794758 • Letter: H
Question
How to calculate the risk free rate? with explaination please.
You are given the ordinary shares of company ABC with a market value of $1.50 at the 2015 financial year end. The following are extracts from the company’s published accounts at the 2015 financial year end.
Balance sheet at 31 December 2015
($m)
Capital and reserves
Share capital
512
Revaluation reserve
294
Retained earnings
1,306
Net borrowings
1,920
Income statement for the year ended 31 December 2015
($m)
Operating profit
952
Finance expenses
144
Profit before taxation
808
Income tax expense
202
Profit for the period
606
A summary of total dividends paid is shown below.
Year
2012
2013
2014
2015
Dividend per share (in Cents)
5.75
6.10
6.47
6.86
Note the following:
issued share capital consists only of ordinary 10 cents shares
the equity beta for the company is 1.125
the equity risk premium is 4%
borrowings were unchanged during 2015 and were all linked to the company’s bank’s base rate
the company incurs a credit risk premium of 1.5% over its bank’s base lending rate (also known as prime rate or minimum lending rate), which has not changed over the year
at the present time, bank base rates are 1% higher than the yield on short-term US Treasury debt
($m)
Capital and reserves
Share capital
512
Revaluation reserve
294
Retained earnings
1,306
Net borrowings
1,920
Explanation / Answer
Cost of Equity, Ke= D1/P0 + g
We find that the dividends are growing by (6.1-5.75)/5.75 * 100 = 6.06 % every year(approx 6% every year)
So D1 , Dividend in 2016 = 6.86*1.06 = 7.27 cents
So ke = 0.0727/1.5 + 6%
Ke = 4.84% + 6% = 10.84%
We also know by CAPM,
Ke = Rf + Beta* Risk premium
Equity beta = 1.125
Cost of Equity = Rf + Beta * Risk premium
10.84% = Rf + 1.125 * 4%
Rf= 10.84- 1.125*4% = 6.34 %
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