Solutions for Chapters 12: Questions and Problems
CHAPTER 12
THE ANALYSIS AND VALUATION OF BONDS
Answers to Questions
1. The present value equation is more useful for the bond investor largely because the bond
investor has fewer uncertainties regarding future cash flows than does the common stock
investor. By investing in bonds with relatively no default risk (i.e., government securities)
the investor can value a bond based primarily on expected cash flows (coupon rate and
2. The most crucial assumption in both cases that the investor makes is that cash flows will
be received in full and reinvested at the promised yield. This assumption is crucial
because it is implicit in the mathematical equation that solves for promised yield. If the
4. The expectations hypothesis imagines a yield curve that reflects what bond investors
expect to earn on successive investments in short-term bonds during the term to maturity
of the long-term bond. The liquidity preference hypothesis envisions the generally
upward-sloping yield curve owing to the fact that investors prefer the liquidity of
Solutions for Chapters 12: Questions and Problems
6. You should select portfolio A because it has a longer duration (5.7 versus 4.9 years) and
greater convexity (125.18 versus 40.30), thereby offering greater price appreciation.
Portfolio A is also noncallable, therefore there is no danger of the bonds being called in
by the issuer when interest rates decline (as you expect they will).
7(a). Call-adjusted duration takes into account the probability of a call and its impact on the
actual duration of a bond. If a bond is noncallable, duration is based on all cash flows up
7(c). If rates fall to 4%, call becomes highly probable, so call-adjusted duration will drop to the
low end. (Remember here that duration to call is now greater than 2.1 years because of
the inverse relationship between duration and yield to maturity).
Solutions for Chapters 12: Questions and Problems
– 90 –
CHAPTER 12
Answers to Problems
1(a). Assuming annual compounding
1(b). Using a financial calculator: PV= -1000, FV = 1100, PMT = 35, n= 8 as the bonds were
purchased 4 years ago. The resulting periodic return is 4.564% or 9.13% annually.
1(c). Using a financial calculator: FV = 1000, PMT = 35, n= 42 as the bonds mature in 21
years. If the periodic interest rate is 5%/2 or 2.5%, the price of the bonds is $1,258.21.
3. (1) (2) (3) (4) (5) (6)
Cash PV PV PV as %
Period Flow at 5% of Flow of Price (1) × (5)
1 $ 40 .9524 $ 38.10 .04014 .04014
2 40 .9070 36.28 .03822 .07644
Solutions for Chapters 12: Questions and Problems
– 91 –
The bond price should increase by 1.294% in response to a drop in the bonds YTM from
10% to 9.5%. If the price of the bond before the decline was $949.23, the price after the
decline in the YTM should be approximately $949.23 × 1.01294 = $961.51.
4. Assuming semiannual compounding, 10 years, zero coupon, $1,000 par value, 12% YTM
Purchase Price = $1,000 (.31180) = $311.80
where .31180 is (1 / 1.06)20 , namely the present value factor for 6% interest
5(a). Assuming semiannual interest payments
5(b). Percentage change in price = -5.442 × -3% = + 16.33%
The 3% decline in rates may not elevate the bond price by 16.33% if the bond’s call price
is violated and protection against a call has elapsed.
years 442.5
0475.1
7.5
(.095/2) 1
5.7
duration Modified ==
+
=