Question

Find the intrinsic value of a share of stock XYZ using the two-stage dividend discount model. The data for the valuation model has been obtained from the Value Line Research Center. Because the report contains data from the end of 2014, we will use the end of 2014 (after the 2014 dividend has been paid) as t = 0.

(Need guide starting from part d, thank you so much)

a) (5 pts) The XYZ's beta from Value Line is 1.35. Assume that the risk-less rate of interest is 4% and the expected stock market return is 9%. Using the CAPM, what is XYZ's required rate of return?
b) (5 pts) XYZ's 2014 dividend as the t = 0 value is 0.32 and Value Line's forecast for XYZ's 5-year earnings growth is 17% for next 5 years, what will XYZ's dividend per share be at the end of 2019? (Assuming XYZ's plowback ratio remains constant and thus XYZ's dividend grows at the same rate as earnings).
c) (5 pts) Suppose that XYZ changes its payout policy in 2019 to pay 80% of its earnings as dividends. Using XYZ's 2014 earnings (2.03 per share) and the Value Line's 5-year growth forecast, what would XYZ's dividends per share be at the end of 2019? (Hint: what would be the earnings at 2019?)
d) (5 pts) After t = 5 (i.e., 2019), suppose XYZ's growth rate slows down to the commonly assumed long-run economic growth rate of 5%. Use the DDM and the required rate of return obtained in part a) to compute the expected intrinsic value of XYZ at the end of 2019. (Hint: what is the dividend at 2019? Use your answer in partc))
e) (5 pts) Under the payout assumption in (c) and Value Line's projected ROE=17% for XYZ in 2019, what
plowback ratio for XYZ would maximize its intrinsic value? (Hint: compare ROE and investors' required rate of
return)
f) Using the assumptions and results in (a), (b), (c) and (d), compute the intrinsic value of XYZ today (at t = 0). Assume XYZ's payout policy is unchanged until t = 5. (Hint: use two-stage DDM. The dividend level grows till 2019 following part b). The expected intrinsic value of XYZ at the end of 2019 following part c)&d))
g) If the price of XYZ at t = 0 is $41.19, how much is XYZ over- or underpriced?
h) If the market becomes efficient in 2015 (at t = 1), then what 1-year holding period return (HPR) would you expect from buying XYZ at its t = 0 price? How much is XYZ's alpha over that one year? (hint: alpha is the difference between the expected HPR and the required return)

i) Decompose the expected HPR in (h) into dividend yield and capital gain yield.

For part (j), (k), and (l), suppose that one year has passed (i.e. it is 2015 now) and there is an unexpected shock, such that XYZ's 2015 dividends become $4 per share and will grow at 3% forever. The market is efficient when the unexpected shock happens:

j) (5 pts) What's the actual price at 2015 after the shock?
k) (5 pts) What's the realized 1-year HPR?
l) (5 pts) Combine your answers in part (h) and (k), what's the unexpected 1-year HPR?

Answer 1

answer a

using CAPM, Re= Rf + B (Rm- Rf)

where Re is required rate of return on equity Rf is risk free rate Rm is market rate of return and B is beta

= 4 + 1.35(9-4)

= 4 + 6.75= 10.75% Or 0.1075

answer b

Do = dividend at t=0 is 0.32

g= growth rate =0.17 n= 5 years

D5= dividend at end of 5 years at 2019= Do(1+g)⁵

= 0.32(1 +0.17)⁵

=0.32 x 2.1`924= 0.70

answer c

E5= Eo (1+g)⁵

^{where E5 is earnings at end of year 5}

= 2.03 (1+0.17)⁵

= 2.03 x 2.1924= 4.45

Dividend= 80% of 4.45= 3.56

answer d

D5= 3.56 as per part c

required rate of return Ke= 0.1075

g2 = 0.05 = growth rate in the second stage

D6= dividend at end of year6= D5(1 +0.05)= 3.56(1+0.05)= 3.738

value of shares at end of year5= D6/(Ke-g2)

= 3.738/(0.1075-0.05)= 65

answer e

answer f

g1= 0.17 first stage growth

g2= 0.05= second stage growth

r= required rate of return = 0.1075 calculated in part a

n= 5 years

D1= dividend at end of year1= Do (1 + g1)= 0.32 x 1.17= 0.3744

intrinsic value of share today=D1 X    +       X

= 0.3744 X    + X           1/1+0.1075)⁵

0.3744 X (1-1.3156)/-0.0625         + 0.3744X1.05X1.8739/0.0575      x 1/1.6662

0.3744 X -0.3156/-0.0625 + 12.8116/1.6662

=1.8906 +7.6892= 9.5798

answer g

price at t=0 is $41.19 \

intrinsic value of 9.57 is less than market price , So overvalued

answer h

HPR= dividend + (end of period value- initial value)/initial value

=