Unformatted text preview: rs g n This is the price of the stock 5 years from now. The PV of this price, discounted back
5 years, is as follows:
Ö
PV of P5 = $52.80(PVIF12%,5) = $52.80(0.5674) = $29.96.
Step 3
The price of the stock today is as follows:
Ö
P0 Ö
= PV dividends Years 1 through 5 + PV of P5
= $9.46 + $29.96 = $39.42. This problem could also be solved by substituting the proper values into the following
equation: Answers and Solutions: 7  11 Ö
P0 = 5 §
t !1 t
0 (1 g s ) ¨
6
©
©r g
t
(1 rs )
n
ªs 5 ¸¨ 1 ¸
¹©
¹
¹ ©1 r ¹ .
sº
ºª Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash
flow register, input I = 12, PV = ? PV = $39.43.
c. First Year
D1/P0 = $2.01/$39.42
Capital gains yield
Expected total return = 5.10%
= 6.90%
= 12.00% Sixth Year
D6/P5 = $3.70/$52.80
Capital gains yield
Expected total return = 7.00%
= 5.00
= 12.00% *We know that r is 12 percent, and the dividend yield is 5.10 percent; therefore, the
capital gains yield must be 6.90 percent.
The main points to note here are as follows:
1. The total yield is always 12 percent (except for rounding errors).
2. The capital gains yield starts relatively high, then declines as the supernormal
growth period approaches its end. The dividend yield rises.
3. After t=5, the stock will grow at a 5 percent rate. The dividend yield will equal 7
percent, the capital gains yield will equal 5 percent, and the total return will be 12
percent. Answers and Solutions: 7  12 a. Part 1. Graphical representation of the problem:
Supernormal
growth
1 0
 2  D0
PVD1
PVD2
PV
P0  Ö
(D2 + P2 ) D1 Normal
growth
3

 D3 D ¤
¥ 2 D1 = D0(1 + gs) = $1.6(1.20) = $1.92.
D2 = D0(1 + gs)2 = $1.60(1.20)2 = $2.304.
Ö
P2 =
Ö
P0 D3
=
rs g n 2 (1 g n ) rs g n $2.304 (1 .06)
= $61.06.
0.10 0.06 = Ö
= PV(D1) + PV(D2) + PV( P )
Ö
P2
D1
D2
=
(1 rs ) (1 rs ) 2 (1 rs ) 2
= $1.92(0.9091) + $2.304(0.8264) + $61.06(0.8264) = $54.11. ¦ 718 Calculator solution: Input 0, 1.92, 63.364(2....
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 Spring '12
 jamnadas
 Valuation, Dividend yield

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