Valuation of Common Stock

1
Valuation of Common Stock
Value of an asset PV of expected future
CFs Need to estimate (1) Stream of expected
CFs (2) The required rate of
return Valuation for one period
P0
P1 D1
R (P1 - P0 D1)/ P0 P0 (P1 D1) / (1 R)
2
Multi-period Valuation P1 (P2 D2) / (1
R) after successive substitutions, P0 ?Dt / (1
R)t Dividend Payment Patterns

time
3
Constant Dividends P0 D / R Constant
Growth Dt Dt-1(1 g) P0 D1 / (R -
g) Supernormal growth P0 ?Dt (1G)/ (1 R)t
Dm1/(R-g)(1R)m where G growth rate during
non normal growth period m non normal
growth period
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FUTURES

• The Futures contract
• Futures Markets
• CBT
• Chicago Mercantile Exchange
• CMX
• The Clearinghouse
• Initial margin
• marking to market
• Maintenance margin
• Reversing trades
• Open interest
• Basis spot price - futures price

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FINANCIAL FUTURES

• FX futures
• Interest rate futures
• Index futures
• Spot and future prices

F ---------- S - PV of dividends,
interest (1 Rf) where F is the futures price,
S is the spot price, Rf is the risk free rate
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Creating an Index Portfolio
Today At Delivery Buy t-bills -S0
S0(1 Rf) Buy Futures SdS0(1Rf) -D Net
CF -S0 Sd D You have replicated the
return on an index.
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Index Arbitrage
F ---------- S - PV of dividends,
interest (1 Rf) Suppose Rf 4, Dividend
yield 2 F 5500 S 5000
5500 5000x0.02 ------------ 5288.46 ?5000 -
------------ 4903.85 (1 0.04) (1
0.04) Purchase index at 5000 and sell them at
delivery. Sell index at F, and sell T bills for
5000 that mature on the delivery date. Net cash
flow is 0. At delivery date Sd 0.02x(5000)
(5500 - Sd) - 1.04(5000) 100 5500 - 5200
400 profit F must be 4903.85
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FX and Commodity Futures
FX Futures F RfFS ----------- S -
----------- (1 Rfd) (1
RfF) rearranging F (1 Rfd) ---
----------- S (1 RfF) Commodity Futures
F --------- S PV of storage costs - PV of
conv. (1 Rf) yield
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Synthetic Futures
1. Interest Rate Futures borrow for 1 yr, lend
for two years Borrow 90.91 _at_ 10 for 1
year Lend 90.91 _at_8 for 2 years Borrow _at_10
90.91 -100.00 Lend _at_ 8 -90.91
106.04 0
-100.00 106.04 Forward rate
(1.08)2/(1.10) - 1 0.0604
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2. FX Futures Borrow today, change into FX
and deposit. Equivalent to buying a forward
contract S DM 2 / R 8 RDM 6 Borrow
100 _at_ 8, Convert into DM 200, Deposit DM 200 _at_
6 and a year later withdraw your DM, pay your
debt Now
1 year later DM
DM Borrow 100.00 -108.00 Change
-100.00 200.00 Lend
-200.00 212.00 NCF 0 0
-108.00 212.00 Forward rate 212 / 108
DM 1.96 /