Valuation of Financial Assets
Lecture 5
25 September 2010
Valuation of financial assets: steps
z
z
z
Understanding the taxonomy of financial
instruments;
Understanding “no difference” idea when
evaluating real and financial assets;
Specific techniques
Taxonomy of financial assets
The two major types of financial assets are:
z Primary instruments
contain a claim on some real asset
z Derivatives
contain a claim on some contract
related to real assets
Primary instruments
Primary assets are sub-divided into
z Currencies
a right to purchase a certain
amount of goods and services
within a given territory
z Securities
a right on some part of property,
owned by a legal or physical entity
Securities
z
Debt securities (Bonds, bills, notes)
–
z
Equity securities (Stocks/shares)
–
z
a paper that promises to pay some periodic
payments for a specified period of time;
a security that represents a share of ownership in
legal entity, also a claim on a part of future cash
flows
Hybrid securities
Stocks Vs. Bonds
z
z
Stocks give a right to take part in decisionmaking process concerning the company’s
actions, and to share all the benefits and
risks of these decisions.
Debt securities are more certain (they offer
fixed income), but their upside opportunities
are limited as well. Debt owners do NOT
normally make decisions about the firm.
Financial assets valuation
z
z
Fundamentally, valuation techniques of real
and financial assets could not differ at all:
otherwise an investor would not be able to
compare them.
Definition: Financial asset is a claim on
some future cash flow (or expected future
cash flow)
Financial assets valuation:
key principles
z
z
z
Take all the cash flows of a security you’re
planning to invest in;
Find an appropriate discount rate that would
reflect the risks of the security (opportunity
cost of capital);
Find the “fair price” of the security – the
today’s equivalent of the future cash flows
(i.e., the price that reflects all future CFs).
Financial assets valuation: Bonds
z
Value a 5-year bond with a par value of
$1000 and a promised coupon rate of 9%
p.a. Assume similar projects require a return
of 11%.
PV =
+
90
(1 + 0.11)
1
90
(1 + 0.11)
4
+
+
90
(1 + 0.11)
1090
(1 + 0.11)
5
2
+
90
(1 + 0.11)
= 926.08
3
+
Financial assets valuation: Bonds
Discount rate =
Year
11%
Coupon
payment
+
Notional
amount
=
CF
*
Discount
factor
=
DCF
1
90
0
90
0,9009
81,0811
2
90
0
90
0,8116
73,0460
3
90
0
90
0,7312
65,8072
4
90
0
90
0,6587
59,2858
5
90
1000
1090
0,5935
646,8619
P=
926,0821
Bonds valuation: special case
z
z
Previously we considered a coupon bond – a
bond that pays a certain amount of money
each pre-specified period.
There is one more type of bond – zerocoupon bond, i.e., the one that brings no
interim cash flows but is sold at a discount to
its par value instead (also called discount
bonds for obvious reasons).
Bonds valuation: special case
z
Assume a zero-coupon bond will bring you $1000 in
5 years. What should be the price of this bond if the
discount rate is 10%?
Discount rate =
PV =
1000
(1 + 0.1)
... = 620.9
5
=
10%
Year
CF
*
DF
=
DCF
1
0
0,909
0
2
0
0,826
0
3
0
0,751
0
4
0
0,683
0
5
1000
0,621
620,9
P=
620,9
Notion of returns: YTM
z
z
Yield to maturity (YTM) – is the return per
annum that the investor would get holding
this instrument till maturity.
Example: a 3-year bond with 9% coupon rate
is priced at 95.0%. Find YTM.
(
c× P
c× P
1 + c)× P
+
+
Pmrkt =
1
2
(1 + y )3
(1 + y ) (1 + y )
950 =
90
(1 + y )
1
+
90
(1 + y )
2
+
1090
(1 + y )
3
=> y = 11.05%
Notion of returns: YTM
z
z
11.05% means that an investor who
purchases this bond and will hold this
instrument till maturity will obtain an annual
return of 11.05%.
Note that:
–
–
YTM is very similar to the IRR concept
YTM is an average yield over the investment
horizon
Financial assets valuation: Stocks
z
z
Current forecasts are for XYZ company to
pay dividends for $3.00, $3.24 and $3.50 per
share over the next three years, respectively.
At the end of this period you anticipate
selling your stock at a market price of $94.48.
What is the price of this stock if the
opportunity cost of investing in it is 12% for
you?
3.00
3.24
3.50 + 94.48
PV =
+
+
1
2
(1 + 0.12) (1 + 0.12 ) (1 + 0.12 )3
Financial assets valuation: Stocks
Discount rate =
12%
+
Sale
proceeds
Dividend
1
3,00
0
3,00
0,8929
2,6786
2
3,24
0
3,24
0,7972
2,5829
3
3,50
94,48
97,98
0,7118
69,7402
P=
75,0017
PV = 75.00
+
CF
*
Discount
factor
Year
=
DCF
Stocks valuation: special case 1
z
z
Current forecasts are for XYZ-2 company to
pay dividends of $6.00 every year forever.
Suppose you do not plan to sell this stock.
What is the price of the stock if expected
return on comparable alternative projects is
12%?
PV =
6.00
(1 + 0.12)
1
+
6.00
(1 + 0.12 )
2
6.00
+ ... =
= 50
0.12
Stocks valuation: special case 2
z
z
Current forecasts are for XYZ-3 company to
pay dividends of $5.00 next year, which will
then grow by 7% every year forever.
Suppose you do not plan to sell this stock.
What is the price of the stock if expected
return on comparable alternative projects is
1
5 . 00 × (1 + 0 . 07 )
12%? PV = 5 . 00
+
+
+
(1 + 0 . 12 )1
2
5 . 00 × (1 + 0 . 07 )
(1 + 0 . 12 )3
(1 +
+ ... =
0 . 12
)2
5 . 00
= 100
0 . 12 − 0 . 07
Notion of returns
z
z
By definition, return is an increase in the
value of investment.
From your investment you expect to receive
two types of cash flows:
–
–
Periodic (coupon payments or dividends);
Final (capital gain or par value at maturity).
D1 + ∆P D1 + (P1 − P0 )
=
r=
P0
P0
Notion of returns: Example
z
Suppose you purchase shares of a JSC
Company on 24.09.2010 at RUB 80. Your
dividend payment in a year will be RUB 20. if
the market price on 24.09.2011 is expected
to be RUB 85, what is the return on your
investment?
20 + (85 − 80 ) 25
r=
=
= 31.25%
80
80
Notion of returns: Example
z
Return on a stock = dividend yield + capital
appreciation
–
–
z
Dividend yield = Div / P0
Capital appreciation = ∆P / P0 = (P1 - P0) / P0
From the previous example:
–
–
Dividend yield = 20 / 80 = 25%
Capital appreciation = (85 – 80) / 80 = 6.25%
Financial markets: key information
z
All financial markets are driven by
demand and supply, like all the others!!!
z
Assuming that others are as smart as we are,
market prices should reflect all information
relevant to a particular instrument. Therefore,
we can assume that
market prices = fair prices
Financial markets: key information
z
z
Market price:
Supply = Demand
As market price = fair price =>
fair price is the maximum price you
are willing to pay for a certain financial
claim, and the minimum price that the
seller would accept.
Summary
z
Bonds valuation: general case
n
PV = ∑
t =1
z
c× N
(1 + r )
t
+
N
(1 + r )
n
Stocks valuation: general case
∞
PV = ∑
t =1
∞
Div t
(1 + r )
t
=∑
t =1
Div1 × (1 + g )
t −1
(1 + r )
t
Div1
=
r−g