Lecture 4
1
Bond valuation
Exercise 1.
A Treasury bond has a coupon rate of 9%, a face value of $1000 and matures 10 years from today. For a
treasury bond the interest on the bond is paid in semi-annual installments. The current riskless interest rate
is 12% (compounded semi-annually).
1. Suppose you purchase the Treasury bond described above and immediately thereafter the riskless interest
rate falls to 8%. (compounded semi-annually). What would be the new market price of the bond?
2. What is your best estimate of what the price would be if the riskless interest rate was 9% (compounded
semi-annually)?
Exercise 2.
Suppose you are trying to determine the interest rate sensitivity of two bonds. Bond 1 is a 12% coupon bond
with a 7-year maturity and a $1000 principal. Bond 2 is a ‘zero-coupon’ bond that pays $1120 after 7 year.
The current interest rate is 12%.
1. Determine the duration of each bond.
2. If the interest rate increases 100 basis points (100 basis points = 1%), what will be the capital loss on
each bond?
Exercise 3.
A $100, 10 year bond was issued 7 years ago at a 10% annual interest rate. The current interest rate is 9%.
The current price of the bond is 100.917. Use annual, discrete compounding.
1. Calculate the bonds yield to maturity.
Exercise 4.
A two-year Treasury bond with a face value of 1000 and an annual coupon payment of 8% sells for 982.50.
A one-year T bill, with a face value of 100, and no coupons, sells for 90. Compounding is discrete, annual.
Given these market prices,
1. Find the prices d(0, 1) and d(0, 2) of one dollar received respectively one and two years from now.
2. Find the corresponding interest rates.
Exercise 5.
Suppose you want to invest $1000 for two years. The current term structure looks like the following:
Year
1
2
Spot rate
6%
7%
1. If you want to be certain of the amount you will have after two years, what is the amount you get in
year 2?
2. Suppose you only invest for one year, and enter into a contract that guarantees the interest rate you
will get one year from now, the forward rate. What must this forward rate be?
2
Common Stock Valuation.
Exercise 6.
1
Expected return = Expected dividend yield + Expected capital gain return.
E[r] =
E[D1 ] E[P1 ] − P0
+
P0
P0
In equilibrium, the price of the stock (P0 ) will adjust so that the expected return E[r] equals the required
return of investors, r. The required return, r, is sometimes called the opportunity cost of capital or market
capitalization rate.
Show that this implies the following expression for the current stock price
P0 =
∞
X
E[Dt ]
(1 + r)t
t=1
Exercise 7.
Consider the following valuation formula for stock prices:
P0 =
∞
X
E[Dt ]
(1 + r)t
t=1
where P0 is todays stock price, Dt the dividend payment on date t, and r the required rate of return on the
stock.
• Under what circumstances does this collapse into the valuation formula
Po =
D1
r−g
Exercise 8.
The common stock of the Handy Dandy Hardware store chain is currently selling for $30 per share. Last
year’s dividend per share was $4.00. Earnings and dividends per share are expected to grow at a constant
rate of 5% per year for the indefinite future.
1. Estimate the market capitalization rate for Handy Dandy.
2. What is the expected price of the stock one year from now?
3. What are the expected dividend and capital gain returns over the next year?
Exercise 9.
The Handy Dandy Hardware Store chain is expected to benefit greatly from the recent interest in ‘do-ityourself’ home repair. Analysts are forecasting that Handy Dandy will experience two years of abnormally
high growth of 20% in earnings and dividends before settling down to a normal growth rate of 5% in year
3 and beyond. Last year’s dividend per share was $4.00. Assume that the appropriate opportunity cost of
capital is 19%.
1. Determine the market price of Handy Dandy’s common stock.
2