3
mon stock of GE is expctd 2 pay a dividend of $1.25 nxt yr & crrntly sells for $25. Assume that the firm's future dividend pymnts are expctd to grow @ a cnstnt rate for the frsable future. Determine the implied growt rate of GE dvdnds (and earnings), assmng that the rqrd RofR of investors is 12%.
Po = $25 D1 = $1.25 ke = .12
ke = D1/Po + g
.12 = 1.25/25 + g
g = .07 (or 7%)
6. S currently pays a $2.50 dividend/share. Next yr's dividend is expected to be $3/share. After next yr, dividends are expected to increase at a 9% AR for 3 yrs and a 6% AR thereafter.
a. what is the CV of a share of S stock to an investor who requires a 15% return on his investment?
Po = D1/(1 + ke) + Σ [D1(1 + g1)t-1/(1 + ke)t]
t=2
+ [D5/(ke - g2)]/[(1 + ke)4]
ke = .15 Do = $2.50 D1 = $3.00 g1 = .09 g2 = .06
Present Value of First Year Dividend
PV(D1) = 3.00/(1 + .15) = 3.00(PVIF.15,1)
= 3.00(.870) = $2.610
Present Value of Next 3-Years' Dividends
Year Dividend P.V. Interest Factor Present Value
t Dt = 3.00(1 + .09) t-1 PVIF.15,t Dt x PVIF.15,t
2 3.00(1 + .09)1 = .756 $2.472
$3.270
3 3.00(1 + .09)2 = .658 2.345
$3.564
4 3.00(1 + .09)3 = .572 2.222
$3.885
PV(Next 3-Years' Dividends) $7.039
Value of Stock at End of Year 4
D5 = D4(1 + g2) = 3.885(1 + .06) = $4.118
P4 = D5/(ke - g2) = 4.118/(.15 - .06) = $45.756
Present Value of P4
PV(P4) = P4/(1 + ke)4 = P4 x PVIF.15,4
= 45.756 x .572 = $26.172
Value of Common Stock:
Po = PV(D1) + PV(Next 3-Years' Dividends) + PV(P4)
= $2.610 + $7.039 + $26.172 = $35.82 (tables)
b. If the dividend in yr 1 is expected to be $3 and the growth rate over the following 3 yrs is expected to be only 7% and then 6% thereafter, what will the new stock price be?
ke = .15 Do = $2.50 D1 = $3.00 g1 = .07 g2 = .06
Present Value of First Year Dividend
PV(D1) = $2.610 (same as part (a))
Present Value of Next 3-Years' Dividends
Year Dividend P.V. Interest Factor Present Value
t Dt=3.00(1 + .07)t-1 PVIF.15,t Dt x PVIF.15,t
2 3.00(1 + .07)1 = .756 $2.427
$3.210
3 3.00(1 + .07)2 = .658 2.260
$3.435
4 3.00(1 + .07)3 = .572 2.102
$3.675
PV(Next 3-Years' Dividends) $6.789
Value of Stock at End of Year 4
D5 = 3.675(1 + .06) = $3.896
P4 = 3.896/(.15 - .06) = $43.289
Present Value of P4
PV(P4) = 43.289 x .572 = $24.761
Value of Common Stock:
Po = $2.610 + $6.789 + $24.761 = $34.16 (tables)
12. Piedmont crrntly pays a dvdnd of $1/share. Dvdnd is expctd 2 grow at 20%/yr rate 4 the next 2 yrs, after which it is expctd to grow at 6%/yr for the foreseeable fut. U rqre 15% RofR, what price do U expt 2 sell at bgning of yr 5?
The dividend at the end of two years = $1 (FVIF0.20,2) = $1.44
D3 = $1.44(1.06) = $1.526
D4 = $1.53(1.06) = $1.618
D5 = $1.62(1.06) = $1.715
The price of the stock at the beginning of year 5 is the same as at the end of year 4, or
P4 = $1.715/(0.15 - 0.06) = $19.06
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