Chapter 1 Introduction to Financial Management Chapter 6 Interest Rates

Tutorial One

Tutorial One - Review

Chapter 1 Introduction to Financial Management

Primary Financial Goals of the Corporation is shareholder wealth maximization, i.e.,

maximizing stock price.

Factors that affect stock price: 1) Projected cash flows to shareholders, 2) Timing of

the cash flow stream, 3) Riskiness (Volatility) of the cash flows.

Intrinsic value is an estimate of “true” value as calculated by a fully informed

analyst based on accurate risk and return data.

Market price is value based on perceived (possibly incorrect) information as seen by

the marginal investor.

Managers are inclined to act in their own best interests (which are not always the

same as the interest of stockholders).

Tutorial One - Review Chapter 6 Interest Rates

Determinants of interest rates: r = r* + IP + MRP + DRP + LP

r*: Real Risk-free Rate

IP: Inflation Premium

MRP: Maturity Risk Premium

DRP: Default Risk Premium

LP: Liquidity Premium

IPN = ∑ INFL t / N

Pure Expectations Hypothesis:

(1+0rt1+t2)t1+t2 = (1+0rt1)t1 x (1+t1rt1+t2)t2

Corporate Bond

Treasury Bond

Q 1-3

If most investors expect the same cash flows from Companies A and B

but are more confident that A’s cash flows will be close to their

expected value, which should have the higher stock price? Explain.

Investors will prefer the stock A rather than stock B, since they

have more confidence on the cash flow from company A, given

same expected value.

Consequently, high demand of stock A will drive a higher price of

stock A than that of stock B.

Q 1-3

What is a firm’s intrinsic value? Its current stock price? Is the stock’s “true long-run value” more closely related to its intrinsic value or its current price?

Intrinsic Value (Textbook, Page 8): An estimate of a stock’s “true” value based on accurate risk and return data.

Current stock price (Textbook, Page 10): The stock value based on perceived but possibly incorrect information as seen by the marginal investor.

From these two definitions, you can find that firm’s intrinsic value is more closely related to the stock’s “true long-run value”.

Q 1-12

What are some actions stockholders can take to ensure that

managements and stockholders’ interests are aligned?

Useful motivational tools include (Textbook, Page 16):

(1) reasonable compensation packages,

(2) direct intervention by shareholders, including firing managers

who don’t perform well,

(3) threat of takeover.

Q 6-3

Suppose you believe that the economy is just entering a recession.

Your firm must raise capital immediately, and debt will be used.

Should you borrow on a long-term or a short-term basis? Why?

You should borrow on a short-term basis, since the interest rate will

fall in future because of two reasons (Textbook, Page 177):

(1) Business borrowing will decrease during a recession. Thus,

the lower the demand of money, the lower the interest rate.

(2) Central bank (Federal Reserve in US) will increase money

supply to stimulate the economy. Thus, the higher the supply of

money, the lower the interest rate.

Q 6-7

It is a fact that the federal government (1) encouraged the development of the savings

and loan industry; (2) virtually forced the industry to make long-term, fixed-interest-

rate mortgages; and (3) forced the savings and loans to obtain most of their capital as

deposits that were withdrawable on demand. Would the savings and loans have

higher profits in a world with a “normal” or an inverted yield curve?

Savings and loan associations (Textbook, Page 150): Taking the funds from

individual (short term basis) and lending this money to commercial mortgage

borrowers (long term basis).

So the Income of S&Ls = Long term interest rate - Short term interest rate.

“Normal” Yield Curve (Textbook, Page 188): Upward-Sloping ( Long term interest

rate> Short term interest rate)

Inverted Yield Curve (Textbook, Page 188): Downward-Sloping Curve (Long term

interest rate< Short term interest rate)

Therefore, the profit of S&Ls will be higher in a world with “Normal” Yield Curve.

P 6-1

Yield curves. The following yields on US Treasury securities were taken from a recent financial

publication:

Term Rate

6 months 5.1%

1 year 5.5

2 years 5.6

3 years 5.7

4 years 5.8

5 years 6.0

10 years 6.1

20 years 6.5

30 years 6.3

a. Plot a yield curve based on these data

b. What type of yield curve is shown?

c. What information does this graph tell you?

P 6-1

b. The yield curve is mostly an upward sloping yield curve with slight inversion from

around 20 years.

c. In general, this upward curve implies (Textbook, Page 189) : either inflation is

expected to increase or there is an increasing maturity risk premium.

P6-17

Interest rate premium. A 5-year Treasury bond has a 5.2 percent yield. A 10-year Treasury bond

yields 6.4 percent, and a 10-year corporate bond yields 8.4 percent. The market expects that

inflation will average 2.5 percent over the next 10 years (IP10 = 2.5%). Assume that there is no

maturity risk premium (MRP = 0), and that the annual real risk-free rate, r*, will remain constant

over the next 10 years. (Hint: Remember that the default risk premium and the liquidity

premium are zero for Treasury securities: DRP = LP = 0.) A 5-year corporate bond has the same

default risk premium and liquidity premium as the 10-year corporate bond described above.

What is the yield on this 5-year corporate bond?

Applying the formula (Textbook, Page 180): r = r* + IP + MRP + DRP + LP

rT5 = r* + IP5 +MRP5 5.2 = r* + IP5 + 0

rT10 = r* + IP10 +MRP10 6.4 = r* + 2.5 + 0

rC5 = r* + IP5 +MRP5 + DRP5 + LP5 rC5 = r* + IP5 + 0 + (DRP5 + LP5)

rC10 = r* + IP10 +MRP10 + DRP10 + LP10 8.4 = r* + 2.5 + 0+ (DRP5 + LP5 )

Four Variables : r*, IP5, rC5, (DRP5 + LP5) and Four Equations. We can solve for rC5 = 7.2%

P6-20

a. What effect would each of the following events likely have on the

level of nominal interest rates?

1. Households dramatically increase their savings rate

2. Corporations increase their demand for funds following an

increase in investment opportunities

3. The government runs a larger than expected budget deficit

4. There is an increase in expected inflation.

1. Money supply increases: interest rate decreases.

2. Money demand increases: interest rate increases.

3. Money demand increases: interest rate increases.

4. Inflation premium increases: interest rate increases.

P6-20

b. Suppose you are considering two possible investment opportunities for a 12-year

Treasury bond and a 7-year, A-rated corporate bond. The current real risk-free rate

is 4 percent, and inflation is expected to be 2 percent for the next 2 years, 3 percent

for the following 4 years, and 4 percent thereafter. The maturity risk premium is

estimated by this formula: MRP = 0.1 (t -1) %. The liquidity premium for the

corporate bond is estimated to be 0.7 percent. Finally, you may determine the

default risk premium, given the company’s bond rating, from the default risk

premium table in the text. What yield would you predict for each of these two

investments?

Answer: b.

rT12 = r* + IP12 + MRP12 = 4 + (2*2+3*4+4*6)/12 + 0.1(12-1) = 8.433%

rC7 = r* + IP7 + MRP7 + DRP7 + LP7 = 4 + (2*2+3*4+4*1)/7 + 0.1(7-1) + 1.13 + 0.7

= 9.287%

(Note: DRP for A-rated corporate bond is 1.13, see page 183 of the Textbook)

P6-20

c. Given the following Treasury bond yield information from a recent financial

publication, construct a graph of the yield curve.

Maturity Rate

1 year 5.37

2 years 5.47

3 years 5.65

4 years 5.71

5 years 5.64

10 years 5.75

20 years 6.33

30 years 5.94

d. Based on the information above about the corporate bond that was given in part b,

calculate yields and then construct a new yield curve graph that shows both

Treasury and the corporate bonds.

We can estimate the rate of corporate bonds rC = r* + IP + MRP + DRP + LP.

DRP = 1.13 and LP = 0.7, which are the same as in part b.

rT = r* + IP + MRP, which are the same as in part c.

Therefore, we are able to estimate rC in year 1, 2, 3, 4, 5, 10, 20, and 30.

P6-20

e. Which part of the yield curve (the left side or right side) is likely to be the most

volatile over time?

The left side of the yield curve (short-term rates) is more volatile over time,

because (Textbook, Page 197-198):

1. The Fed in US operates mainly in the short-tem sector, so its intervention has the

strongest effect in the short-tem sector.

2. Long-term rates reflect the average expected inflation rate over the next 20 to 30 years,

and this expectation generally does not change much.

P6-20

f. Using the Treasury yield information in (c) above, calculate the following rates:

3. The 10-year rate, 10 years from now

4. The 10-year rate, 20 years from now

(Textbook, Page 194)

3. (1+r20)20 = (1+r10)

10 x (1+10r20)10

(1+0.0633)20 = (1+0.0575)10 x (1+10r20)10

10r20 = 6.91%

4. (1+r30)30 = (1+r20)

20 x (1+20r30)10

(1+0.0594)30 = (1+0.0633)20 x (1+20r30)10

20r30 = 5.16%

Note: Pure Expectations Hypothesis ---- (1+0rt1+t2)t1+t2 = (1+0rt1)

t1 x (1+t1rt1+t2)t2

P6-20

Maturity Rate

1 year 5.37

2 years 5.47

3 years 5.65

4 years 5.71

5 years 5.64

10 years 5.75

20 years 6.33

30 years 5.94