Chapter 7
Common Stock: Characteristics, Valuation and Issuance
6. a. 4
Po = D1/(1 + ke) + [D1(1 + g1)t-1/(1 + ke)t]
t=2
+ [D5/(ke – g2)]/[(1 + ke)4]
Present Value of First Year Dividend
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
$3.885
PV(Next 3-Years’ Dividends) $7.039
Value of Stock at End of Year 4
Present Value of P4
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
Value of Common Stock:
Po = PV(D1) + PV(Next 3-Years’ Dividends) + PV(P4)
Present Value of First Year Dividend
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
$3.675
PV(Next 3-Years’ Dividends) $6.789
Value of Stock at End of Year 4
Present Value of P4
Value of Common Stock:
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
7. P0 = D/ke
8. Present Value of First 4-Year’s Dividends:
4
[Do(1 + g1)t/(1 + ke)t]; Do = $1.50; g1 = .11; ke = .14
t=1
Present Value
Year Dividend Interest Factor Present Value
t Dt = 1.50(1 + .11)t PVIF.14,t Dt x PVIF.14,t
1 1.50(1 + .11)1 = .877 1.460
$1.6650
Value of Stock at End of Year 4:
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
Present Value of P4:
PV(P4) = P4/(1 + ke)4 = $26.567/(1 + .14)4
Value of Common Stock (Po):
Po = PV(First 4-Years’ Dividends) + PV(P4)
3 6
9. Po = [Do(1 + g1)t/(1 + ke)t] + [D3(1 + g2)t-3/(1 + ke)t]
t=1 t=4
Present Value of First 3-Years’ Dividends
Year Dividend P.V. Interest Factor Present Value
t Dt = 1.50(1 + .15)t PVIF.18,t Dt x PVIF.18,t
1 1.50(1 + .15)1 = .847 $1.461
$1.725
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
Present Value of Next 3-Years’ Dividends
Year Dividend P.V. Interest Factor Present Value
t Dt = 2.281(1 + .075)t-3 PVIF.18,t Dt x PVIF.18,t
Value of Stock at End of Year 6
Present Value of P6
PV(P6) = P6/(1 + ke)6 = P6 x PVIF(0.18,6)
Value of Common Stock
Po = PV(First 3-Years’ Dividends) +
PV(Next 3-Years’ Dividends) + PV(P6)
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
10. a. FVn = PVo(1+ g)n
The term (1 + g)6 represents the future value interest factor
(FVIFg,6) in Table I at the back of the book. Reading across
b. Dt = Do(1 + g)t; Do = $2.00
Year Dividend*
t Dt = 2.00(1 + g)t
1 2.00(1 + .12)1 = $2.240
2 2.00(1 + .12)2 = $2.509
*Note: The (1 + 0.12)t factors can be obtained from Table I, i.e.,
Earnings per year will be exactly two times the projected dividends.
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
c. Po = D1/(ke – g)
d. The =rm’s earnings and dividends probably cannot continue to
e. Present value of First 6-Years’ Dividends:
6
[Do(1 + g1)t/(1 + ke)t]
t=1
Year Dividend P.V. Interest Factor Present Value
t Dt PVIF.18,t Dt x PVIF.18,t
1 $2.240 .847 $1.897
Value of Stock at End of Year 6:
7-2
Chapter 7
Common Stock: Characteristics, Valuation and Issuance
Present Value of P6:
PV(P6) = P6/(1 + ke)6 = $34.875/(1 + 0.18)6 = $34.875 x PVIF(0.18,6)
Value of Common Stock (Po)
Po = PV(First 6-Year’s Dividends) + PV(P6)
7-2