Chapter 7
Common Stock: Characteristics, Valuation and Issuance
11. D0 = $1.50
D1 = $1.50(1.15) = $1.725
beginning of year 5, in present value terms.)
12. The dividend at the end of two years = $1 (FVIF0.20,2) = $1.44
D3 = $1.44(1.06) = $1.526
The price of the stock at the beginning of year 5 is the same as at
the end of year 4, or
b. Price at the beginning of year 3
of the intended holding period
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
14. Underwriting spread = Selling price to public – Proceeds to company
15. a. Number of shares = [(No. of directors desired)(No. of shares
outstanding)]/[(No. of directors being elected + 1] + 1
This number of shares will guarantee election. Consider the
following close race:
300,001
But you could be elected with fewer votes, e.g., 250,000 votes:
350,000
b. Number of shares = [(2)(1,500,000)]/[4 + 1] + 1 = 600,001
16. Present Value of First 4-Years’ Dividends:
Present Value
Year Dividend Interest Factor Present Value
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
1 $3.00 (1.15)1 = 0.806 2.781
$3.45
PV(First 4-Years’ Dividends)$10.104
Value of Stock at End of Year 4:
Present Value of P4:
PV(P4) = P4/(1 + ke)4 = $32.760 x PVIF(0.24,4)
Po = PV (First 4-Years’ Dividends) + PV (P4)
17. Present Value of First 5-Years’ Dividends:
Year Dividend Present Value Present Value
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
Interest Factor
t Dt = 2.00(1+g) PVIF(0.24,t) Dt x PVIF(0.24,t)
1 2.00(1.09)1 = $2.18 0.806 $1.757
Value of Stock at End of Year 5:
P5 = D6 / (ke – 0.04)
Present Value of P5:
PV(P5) = P5 / (1 + ke)5 = $15.42 x PVIF(0.24,5)
Value of Common Stock (Po):
Po = PV (First 5-Years’ Dividends) + PV (P5)
18. Present Value of First 4-Years’ Dividends:
Present Value
Year Dividend Interest Factor Present Value
t Dt PVIF0.18,t Dt x PVIF0.18,t
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
1 $0.00 0.847 $0.000
Value of Stock at End of Year 4:
P4 = D5/(ke – 0.05)
Present Value of P4:
PV(P4) = P4/(1 + ke)4 = $12.115 x PVIF(0.18,4)
Po = PV (First 4-Years’ Dividends) + PV(P4)
19. a. Present Value of First 3-Years’ Dividends:
Present Value
Year Dividend Interest Factor Present Value
t Dt PVIF0.16,t Dt x PVIF0.16,t
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
3.306
PV(First 3-Years’ Dividends) $ 6.410
Value of Stock at End of Year 3:
P3 = D4/(ke – 0.06)
Present Value of P3:
PV(P3) = P3/(1 + ke)3 = $35.04 x PVIF(0.16,3)
Po = PV (First 3-Years’ Dividends) + PV(P3)
b. Recall that, in present value terms, the beginning of year 2 is the same
as the end of year 1, however the year one dividend is not received.
P1 = D2(PVIF0.16,1) + D3(PVIF0.16,2) + P3(PVIF0.16,2)
20. D1 = $1.00 D2 = $2.00
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
P0 = PV(D1) + PV(D2) + PV (D3) + PV (P3)
21. P0 = $0.75(PVIF.2,1) + $0.863(PVIF.2,2) + $0.992(PVIF.2,3)
22. Earnings growth rate for ?rst 3 years = 50%, 25% for the following
3 years, and 8% thereafter. Required equity return = 20%. Payout
rate of 20% in years 2-4, and 50% thereafter.
Year Earnings Dividends
0 $1.00 $0.00
1 1.50 0.00
2 2.25 0.45
P0 = $0 + $0.45(PVIF0.2,2) +$0.675(PVIF0.2,3) + $0.844(PVIF0.2,4) + $2.637(PVIF0.2,5)
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
24. D0 = $3
P4 = 1.4(P0) – Note the beginning of year 5 is the same as the end
of year 4 in present value terms.
25. D0 = $0
D1 = $0
D2 = $2.00
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
P0 = $2(PVIF0.15,2) + $2.30(PVIF0.15,3) +$2.645(PVIF0.15,4)
26. a. The dividend yield for AT&T is 3.6%; for Boeing it is 1.6%;
b. These ?rms diFer with respect to expected earnings and dividend
c. P/E for Boeing = 31 times
d. Boeing’s higher expected growth rate more than oFsets the
a. $39.43 (assuming these data come from the Wall Street Journal,
27. a. Number of votes cast = 0.7 x 1,000,000 = 700,000
i. 350,000 + 1
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Chapter 7
Common Stock: Characteristics, Valuation and Issuance
28. No recommended solution.
29. P0 = 0.12(PVIF0.2,1) + .144(PVIF0.2,2) + .173(PVIF0.2,3)
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