Mobius Antiques has a beta of 1.4, the annual riskk-free rate is 10% and the req
ID: 2665890 • Letter: M
Question
Mobius Antiques has a beta of 1.4, the annual riskk-free rate is 10% and the required return of the market is 16%. The firm expects future dividends will grow at CAGR consistent with that experienced over the 1999-2003 period. Over the past 5 years the annual common stock dividends have been as follows:Year Dividend/share
2003 3.60
2002 3.40
2001 3.10
2000 2.85
1999 2.46
Note: The next dividend(2004) has not been provided
a. Estimate the value of Mobius Antiques : You must round any dividend growth rate to a whole percentage. byou must compute K1 to 3 decimals, prices must be in dollars and cents.
Explanation / Answer
Annual risk-fre rate = 10%
Required rate of return of the market = 16%
Stock Beta = 1.4
Dividend payment in 1999 = $2.46
Dividend payment in 2000 = $2.85
Dividend payment in 2001 = $3.10
Dividend payment in 2002 = $3.40
Dividend payment in 2003 = $3.60
Dividend growth rate (g) = [($3.60 - $3.40) / $3.40]
Dividend growth rate (g) = 5.88%
Dividend payment in 2004 = $3.60 (1+5.88%)
Dividend payment in 2004 = $3.81
According to CAPM:
Calculate Rate of Return (Re):
Rate of Return (Re) = Rf + B (Required Rate of return on market - Rf)
Rate of Return (Re) = 10% + 1.4 (16% - 10%)
Rate of Return (Re) = 0.10 + 1.4 (0.06)
Rate of Return (Re) = 0.184 (or) 18.4%
Rate of Return (Re) = 18.4%
Calculating Stock Value:
Stock value in 2004 = [Dividend in 2005 / R – g]
Dividend payment in 2005 = [$3.81 * (1+5.88%)]
Dividend payment in 2005 = $4.03
Stock Value in 2004 = [$4.03 / 0.184 – 0.0588]
Stock Value in 2004 = [$4.03 / 0.1252]
Stock Value in 2004 = $32.1885
Stock Value of Mobius Antiques = [$2.46 / (1+0.184)1] + [$2.85 / (1+0.184)2 ] + [$3.10 /(1+0.184)3] + [$3.40 / (1+0.184)4] + [$3.60 / (1+0.184)5] + [$3.81 / (1+0.184)6] + [$32.1885 / (1+0.184)6]
Stock value of Mobius Antiques = [$2.07 + ($2.85 / 1.401856) + ($3.10 / 1.65979) + ($3.40 / 1.9652) + ($3.60 / 2.3267) + ($3.81 / 2.7549) + ($32.1885 / 2.7549)]
Stock Value of Mobius Antiques = [$2.07 + $2.03 + $1.87 + $1.73 + $1.55 + $1.38 + $11.68]
Stock value of Mobius Antiques = $22.31