2. Introduction to Business Finance (Fall 2016)
Classification of returns
Dollar return on a financial asset can be divided into two categories:
1. Dollar income - income paid by the issuer of the financial asset
2. Capital gain/loss - the change in value of the financial asset in the
financial market
Dollar Return = dollar income + capital gain/loss
= dollar income + ending value – beginning value
Ending value represents the market value of the financial asset at the
end of the period.
Beginning value represents the market value of the financial asset at
the start of the period.
3. Introduction to Business Finance (Fall 2016)
Types of dollar income:
• If the financial asset is an equity, the income from
investment is dividend paid by a corporation
• If financial asset is a debt instrument, such as a bond, the
income from investment is the interest paid by the seller
of the bond
4. Introduction to Business Finance (Fall 2016)
Yield…
To determine an investment he stated dollar return as a
percentage of the dollar amount that was originally invested:
Yield =
𝒅𝒐𝒍𝒍𝒂𝒓 𝒓𝒆𝒕𝒖𝒓𝒏
𝐛𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠 𝒗𝒂𝒍𝒖𝒆
=
𝐃𝐨𝐥𝐥𝐚𝐫 𝐢𝐧𝐜𝐨𝐦𝐞+𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐠𝐚𝐢𝐧/𝒍𝒐𝒔𝒔
𝐁𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠 𝐯𝐚𝐥𝐮𝐞
Example: You bought a bond on January 1st, 2008 for $980.00 and
sold it on December 31st, 2008 for $990.25. If you receive $100 in
interest income on December 31st, 2008. What is your yield?
5. Introduction to Business Finance (Fall 2016)
Capital gains = 990.25-980 = $10.25
Dollar income = $100
Yield =
$𝟏𝟎𝟎+$𝟗𝟗𝟎.𝟐𝟓−$𝟗𝟖𝟎
$𝟗𝟖𝟎
= 0.1125 = 11.25%
Calculate the Current Yield??
$income/current price
=100/980*100= 10.2%
Calculate the Capital gains/loss yield?
=(Capital gain/loss)/beginning price
= (990.25-980)/980*100=1.05%
6. Introduction to Business Finance (Fall 2016)
The interest rate paid to investors depends on the
following four factors:
1. The rate of return that producers expect to earn on
their invested capital
2. Savers time preference for current versus future
consumption, differs from economy to economy
3. The riskiness of borrower
4. The expected future rate of inflation
7. Introduction to Business Finance (Fall 2016)
Moreover, Interest Rates are
determined through the
interaction of demand and
supply forces…
9. Introduction to Business Finance (Fall 2016)
Interest rates also move in line with the economic situation of the country. During
times of recession, interest rates fall. During boom interest rates rise.
13. Introduction to Business Finance (Fall 2016)
Term Structure of Interest Rates
The relationship between maturity profile of
bonds and interest rates is called the term
structure of interest rates.
Plotting of this relationship is called the yield
curve.
14. Introduction to Business Finance (Fall 2016)
Shape of yield curve
Upward sloping
Downward sloping
Flat
Humped
16. Introduction to Business Finance (Fall 2016)
There are 3 theories describing the
Term Structure of Interest Rates…
• Liquidity preference theory
• Unbiased expectation theory
• Market segmentation theory
17. Introduction to Business Finance (Fall 2016)
Term Structure of Interest Rates is
the relationship between the
interest rates and the time to
maturity i.e. the relationship
between long term and short term
rates…
18. Introduction to Business Finance (Fall 2016)
Why do yield curves differ?
When interest rates shift to substantially different levels, it
generally is because investors have changed either their
expectations concerning future inflation or their attitudes
concerning risk.
We will use a simple equation of interest rates on US Treasury
Securities to understand the affect of inflation on the shape of
yield curve:
R treasury = RRIR + MRP = [r* + IP] + MRP
In the equation for US Treasury securities the RP and LP are zero,
because we generally consider Treasury securities to be very liquid
and default free investments.
19. Introduction to Business Finance (Fall 2016)
• All else equal, investor generally prefer to hold short-term
securities because such securities are less sensitive to changes
in interest rate and provide greater investment flexibility than
long term securities. Thus, investors will accept lower yields
on short-term securities.
• While borrowers prefer long term debt because short-term
then exposes them to the risk of having to refinance the debt
under adverse condition for example higher interest rates.
• The interaction of demand and supply as discussed above
causes the borrower to offer a higher rate of return on higher
maturity securities.
• Thus it can be concluded that MRP increases with years to
maturity causing the yield curve to be upward sloping. The
theory that supports this conclusion is referred to as liquidity
preference theory.
20. Introduction to Business Finance (Fall 2016)
Assume that investors demand 0.1% maturity risk premium for
each year remaining until maturity for any debt with a term to
maturity greater than one year, with a maximum value of 1%.
a) Calculate MRP for a t-bill with one-year maturity =
b) Calculate MRP for a t-bond with five-year maturity=
c) Calculate MRP for a t-bond with ten-year maturity=
d) Calculate MRP for a t-bond with twenty-year maturity =
21. Introduction to Business Finance (Fall 2016)
IP(inflation premium) is the average of inflation rates that
are expected to occur during the life of the investment.
The expectations of the participant in the financial market,
that is investors and borrowers greatly impact interest
rates. The expectation theories states that the yield curve
depends on expectations concerning future inflation rate.
IP is the average of expected inflation of future years.
22. Introduction to Business Finance (Fall 2016)
Let’s consider the inflation expectation using two simple
examples, where r* is 2% :
1. inflation rate is expected to increase in the future
2. inflation rate is expected to decrease in the future
Calculate the IP for a 5-year security and a 10-year security.
Increasing inflation for 5-year security:
IP = (1 + 1.8 + 2 + 2.4 + 2.8)/5 = 2%
Decreasing inflation for a 10-year security:
IP = (5 + 4.2 + 4 + 3.4 + 3.2 + 2.4*5)/10 = 3.18 %
23. Introduction to Business Finance (Fall 2016)
Now calculate the rate of return on a US Treasury using the
following equation and MRP and IP from calculated in
previous slides for securities with maturity of:
1. 1 year
2. 5 years
3. 10 years
4. 20 years
R treasury = RRIR + MRP = [r* + IP] + MRP
Refer next slide for solution and graphs.
25. Introduction to Business Finance (Fall 2016)
The market segmentation theory suggests that, the slope
of the yield curve depends on demand supply conditions
in the long and short-term markets.
Thus, the yield curve could at any given time be flat,
upward sloping or downward sloping, or have humps and
dips.
27. Introduction to Business Finance (Fall 2016)
• According to expectations theory, there is no
reinvestment risk and there is no price risk.
• No matter in what way the investors invest for a
particular time horizon, the return is going to be the
same.
• For Eg: If the investor wants to invest for 10 years, no
matter if he invests for
– 10 years
– 5 years + 5 years
– 2 years+ 8 years
– 1 year +1 year+ 1year……
The return is going to be the same.
28. Introduction to Business Finance (Fall 2016)
• 1 year security 10%
• 2 years security 12%
• 3 years security 12.5%
What is the return on a 1 year security after 1 year?
• What is the return on a 1 year security after2
years?
• What is the return on a 2 year security after 1
year?
