Reading 44: introduction to fixed income valuation

Question 1

A 20-year, 10% annual-pay bond has a par value of $1,000. What is the price of the bond if it has a yield-to-maturity of 15%?
$685.14.
$687.03.
$828.39.

Answer 1

N = 20; I/Y = 15; FV = 1,000; PMT = 100; CPT → PV = –$687.03. (LOS 44.a)

Question 2

An analyst observes a 5-year, 10% semiannual-pay bond. The face amount is £1,000. The analyst believes that the yield-to-maturity on a semiannual bond basis should be 15%. Based on this yield estimate, the price of this bond would be:
£828.40.
£1,189.53.
£1,193.04.

Answer 2

N = 10; I/Y = 7.5; FV = 1,000; PMT = 50; CPT → PV = –$828.40. (LOS 44.a)

Question 3

An analyst observes a 20-year, 8% option-free bond with semiannual coupons. The required yield-to-maturity on a semiannual bond basis was 8%, but suddenly it decreased to 7.25%. As a result, the price of this bond:
increased.
decreased.
stayed the same.

Answer 3

The price-yield relationship is inverse. If the required yield decreases, the bond’s price will increase, and vice versa. (LOS 44.b)

Question 4

A $1,000, 5%, 20-year annual-pay bond has a YTM of 6.5%. If the YTM remains unchanged, how much will the bond value increase over the next three years?
$13.62.
$13.78.
$13.96.

Answer 4

With 20 years to maturity, the value of the bond with an annual-pay yield of 6.5% is N= 20, PMT = 50, FV = 1,000, I/Y = 6.5, CPT → PV =–834.72. With N = 17, CPT→ PV = –848.34, so the value will increase $13.62. (LOS 44.a, 44.b)

Question 5

If spot rates are 3.2% for one year, 3.4% for two years, and 3.5% for three years, the price of a $100,000 face value, 3-year, annual-pay bond with a coupon rate of 4% is closest to:
$101,420.
$101,790.
$108,230.

Answer 5

bond value= 4000/1.032+4000/(1.034)^2+104000/(1.035)^3= 101,416.28

Question 6

An investor paid a full price of $1,059.04 each for 100 bonds. The purchase was between coupon dates, and accrued interest was $23.54 per bond. What is each bond’s flat price?
$1,000.00.
$1,035.50.
$1,082.58.

Answer 6

The full price includes accrued interest, while the flat price does not. Therefore, the flat (or clean) price is 1,059.04 – 23.54 = $1,035.50.(LOS 44.d)

Question 7

Cathy Moran, CFA, is estimating a value for an infrequently traded bond with six years to maturity, an annual coupon of 7%, and a single-B credit rating. Moran obtains yields-to-maturity for more liquid bonds with the same credit rating:
5% coupon, eight years to maturity, yielding 7.20%.
6.5% coupon, five years to maturity, yielding 6.40%.
The infrequently traded bond is most likely trading at:

par value.
a discount to par value.
a premium to par value.

Answer 7

Using linear interpolation, the yield on a bond with six years to maturity should be 6.40% + (1 / 3)(7.20% – 6.40%) = 6.67%. A bond with a 7% coupon and a yield of 6.67% is at a premium to par value. (LOS 44.e)

Question 8

A market rate of discount for a single payment to be made in the future is:
a spot rate.
a simple yield.
a forward rate.

Answer 8

A spot rate is a discount rate for a single future payment. Simple yield is a measure of a bond’s yield that accounts for coupon interest and assumes straight-line amortization of a discount or premium. A forward rate is an interest rate for a future period, such as a 3-month rate six months from today. (LOS 44.g)

Question 9

Based on semiannual compounding, what would the YTM be on a 15-year, zero-coupon, $1,000 par value bond that’s currently trading at $331.40?
3.750%.
5.151%.
7.500%.

Answer 9

N=30; FV=1000; PMT=0; PV=-331.40; CPT-> I/Y=3.750 x 2= 7.5%

Question 10

An analyst observes a Widget & Co. 7.125%, 4-year, semiannual-pay bond trading at 102.347% of par (where par is $1,000). The bond is callable at 101 in two years. What is the bond’s yield-to-call?
3.167%.
5.664%.
6.334%.

Answer 10

N = 4; FV = 1,010; PMT = 35.625; PV = –1,023.47; CPT → I/Y = 3.167 × 2 =6.334%. (LOS 44.g)

Question 11

A floating-rate note has a quoted margin of +50 basis points and a required margin of +75 basis points. On its next reset date, the price of the note will be:
equal to par value.
less than par value.
greater than par value.

Answer 11

If the required margin is greater than the quoted margin, the credit quality of the issue has decreased and the price on the reset date will be less than par value. (LOS 44.g)

Question 12

Which of the following money market yields is a bond-equivalent yield?
Add-on yield based on a 365-day year.
Discount yield based on a 360-day year.
Discount yield based on a 365-day year.

Answer 12

An add-on yield based on a 365-day year is a bond-equivalent yield.
(LOS 44.h)

Question 13

Which of the following yield curves is least likely to consist of observed yields in the market?
Forward yield curve.
Par bond yield curve.
Coupon bond yield curve.

Answer 13

Par bond yield curves are based on the theoretical yields that would cause bonds at each maturity to be priced at par. Coupon bond yields and forward interest rates can be observed directly from market transactions. (Module 44.4, LOS 44.i)

Question 14

The 4-year spot rate is 9.45%, and the 3-year spot rate is 9.85%. What is the 1-year forward rate three years from today?
8.258%.
9.850%.
11.059%.

Answer 14

(1.0945)^4=(1.0985)^3 x (1+3y1y)

3y1y=[(1.0945)^4/(1.0985)^3]-1= 8.258%

approx forward rate: 4(9.45%)-3(9.85%)= 8.25%

Question 15

Given the following spot and forward rates:
Current 1-year spot rate is 5.5%.
One-year forward rate one year from today is 7.63%.
One-year forward rate two years from today is 12.18%.
One-year forward rate three years from today is 15.5%.
The value of a 4-year, 10% annual-pay, $1,000 par value bond is closest to:

$996.
$1,009.
$1,086.

Answer 15

bond value= 100/1.055+ 100/(1.055)(1.0763)+ 100/(1.055)(1.0763)(1.1218)+ 100/(1.055)(1.0763)(1.1218)(1.155)= 1009.03

Question 16

A corporate bond is quoted at a spread of +235 basis points over an interpolated 12-year U.S. Treasury bond yield. This spread is:
a G-spread.
an I-spread.
a Z-spread.

Answer 16

G-spreads are quoted relative to an actual or interpolated government bond yield. I-spreads are quoted relative to swap rates. Z-spreads are calculated based on the shape of the benchmark yield curve. (Module 44.5, LOS 44.k)