Chapter 7: Model of Stock Prices
Dividend valuation model:
Equity = contractual agreement representing claim to a share in the income and assets of a corporation
Common stock is the principal form of equity.
Bundle of rights:
1. Right to vote on issues that are important to the company
2. Right to be the residual claimant – funds that remain after holders of debt are paid
Cashflows come in the form of dividends
Assume the stock sells at price Pt today (period t). The stock pays dividend Dt+1 next period, Dt+2 after
two-periods, Dt+3 after three-periods, and so on, out to the infinite future.
Fact: the dividend payments of the stock can be exactly replicated by a portfolio of discount bonds
having different maturities.
Consider the following investment strategy. Purchase:
a one-period discount bond with face value D t+1,
a two-period discount bond with face value Dt+2,
a three-period bond with face value D t+3
.
.
Which pays:
Dt+1 after one-period
Dt+2 After two periods
Price of bonds:
To formalize our argument, let
i1t = yield to maturity on a one-period discount bond
i2t = annualized yield to maturity on a two-period discount bond
i3t = annualized yield to maturity on a three-period discount bond
Let Qt+1 be the price of the one-period bond, then
Dt +1
Qt+1 =
1+i 1 t
,Price of two-period bond,
Dt +2
Qt+2 =
(1+i 2t )2
Price of three-period bond,
Dt +3
Qt+3 =
(1+i 3 t )3
Which means,
Pt = Qt+1 + Qt+2 + Qt+3 …..
What if
Pt < Qt+1 + Qt+2 + Qt+3 …..
So, it must be that:
Pt = Qt+1 + Qt+2 + Qt+3 ….. Equation (1)
Plug in what we already derived for bond prices.
D t +1 Dt +2 Dt +3
Pt = + + …..+….
1+i 1 t (1+i 2t )2 (1+i 3 t )3
∞
Dt + j
Pt =∑ equation (2)
j =1 ( 1+i jt ) j
, Dividend valuation model
How would we know the value of future dividends?
How do we know what interest to use to discount the dividend payments?
1. Write down the key assumption built into the dividend valuation model.
Dividends are growing at a constant rate
2. Write down the compact equation that summarizes the dividend valuation
model? Explain in words.
It is equal to the PV of future dividend payments
3. What information do we need to apply the dividend valuation model in
practice?
Dividend, interest rate
4. What assumptions are combined to the dividend valuation model to obtain the
Gordon growth model?
Constant growth rate, next year’s dividend
5. Write down the equation that summarizes the Gordon growth model?
D1/(k-g)
6. Assuming the Fed will raise rates in May, what impact will this decision have
on stock prices? Explain.
Stock prices will go down because the investors now have higher risk
Chapter 9: Banks
A L
Reserves Checkable Deposits
Securities Non-transaction deposits
Loans Borrowings
Physical Capital [Capital is the PLUG]
B/S of Bank:
A L
Uses Sources
Dividend valuation model:
Equity = contractual agreement representing claim to a share in the income and assets of a corporation
Common stock is the principal form of equity.
Bundle of rights:
1. Right to vote on issues that are important to the company
2. Right to be the residual claimant – funds that remain after holders of debt are paid
Cashflows come in the form of dividends
Assume the stock sells at price Pt today (period t). The stock pays dividend Dt+1 next period, Dt+2 after
two-periods, Dt+3 after three-periods, and so on, out to the infinite future.
Fact: the dividend payments of the stock can be exactly replicated by a portfolio of discount bonds
having different maturities.
Consider the following investment strategy. Purchase:
a one-period discount bond with face value D t+1,
a two-period discount bond with face value Dt+2,
a three-period bond with face value D t+3
.
.
Which pays:
Dt+1 after one-period
Dt+2 After two periods
Price of bonds:
To formalize our argument, let
i1t = yield to maturity on a one-period discount bond
i2t = annualized yield to maturity on a two-period discount bond
i3t = annualized yield to maturity on a three-period discount bond
Let Qt+1 be the price of the one-period bond, then
Dt +1
Qt+1 =
1+i 1 t
,Price of two-period bond,
Dt +2
Qt+2 =
(1+i 2t )2
Price of three-period bond,
Dt +3
Qt+3 =
(1+i 3 t )3
Which means,
Pt = Qt+1 + Qt+2 + Qt+3 …..
What if
Pt < Qt+1 + Qt+2 + Qt+3 …..
So, it must be that:
Pt = Qt+1 + Qt+2 + Qt+3 ….. Equation (1)
Plug in what we already derived for bond prices.
D t +1 Dt +2 Dt +3
Pt = + + …..+….
1+i 1 t (1+i 2t )2 (1+i 3 t )3
∞
Dt + j
Pt =∑ equation (2)
j =1 ( 1+i jt ) j
, Dividend valuation model
How would we know the value of future dividends?
How do we know what interest to use to discount the dividend payments?
1. Write down the key assumption built into the dividend valuation model.
Dividends are growing at a constant rate
2. Write down the compact equation that summarizes the dividend valuation
model? Explain in words.
It is equal to the PV of future dividend payments
3. What information do we need to apply the dividend valuation model in
practice?
Dividend, interest rate
4. What assumptions are combined to the dividend valuation model to obtain the
Gordon growth model?
Constant growth rate, next year’s dividend
5. Write down the equation that summarizes the Gordon growth model?
D1/(k-g)
6. Assuming the Fed will raise rates in May, what impact will this decision have
on stock prices? Explain.
Stock prices will go down because the investors now have higher risk
Chapter 9: Banks
A L
Reserves Checkable Deposits
Securities Non-transaction deposits
Loans Borrowings
Physical Capital [Capital is the PLUG]
B/S of Bank:
A L
Uses Sources
