AIM 1: Compute the accrued interest and invoice price on a coupon bond.

1、Suppose a bond’s quoted price is 105 7/32 and the accrued interest is $23.54. If the bond has a par value of $1,000, what is the bond’s flat price?

A) $1,000.00.
 
B) $1,023.54.
 
C) $1,075.73.
 
D) $1,052.19.
 

The correct answer is D

The flat price is the bond price without the accrued interest, so it is equal to the quoted price of 105 7/32 = $1,052.19.

A) Zero-coupon bonds have only one cash inflow at maturity.
 
B) Accrual bonds have only one cash inflow at maturity.
 
C) Accrual bonds, like zero-coupon bonds, always sell at a discount to face value.
 
D) Step-up notes have coupon rates that increase over time at a pre-specified rate.

The correct answer is C

Accrual bonds, unlike zero-coupon bonds, do not always sell at a discount to face value. The interest accrues forward and thus the bonds are likely to sell for more than face value.

3、Assume a bond's quoted price is 105.22 and the accrued interest is $3.54. The bond has a par value of $100. What is the bond's clean price?

A) $100.00.
 
B) $103.54.
 
C) $105.22.
 
D) $108.76.

The correct answer is C

The clean price is the bond price without the accrued interest so it is equal to the quoted price.

4、 5% coupon bond with semi-annual coupon payments on a coupon payment date when the coupon has not been paid yet and the bond has a $1,000 par value. What is the accrued interest of the bond and what is the bond's full price?

Accrued Interest  Full Price
A)$25                            $1,000
B)$50                            $1,050
C)$25                            $1,025
D)$50                            $1,000

The correct answer is C 

 Accrued interest is found by simply dividing the coupon rate by two and then multiplying the result by $1,000. The full price or dirty price of the bond is the price of the bond plus accrued interest, if any.

5、If the issuer of a bond is in default, the bond will be trading:

A) registered.
 
B) flat.
 
C) on accrual.
 
D) off the market.

The correct answer is B

If an issuer of a bond is in default (i.e., it has not been making periodic contractual coupon payments), the bond is traded without accrued interest and is said to trade flat.
A registered bond is a bond whose owner's name is recorded as a book entry on the books of the issuer or its transfer agent.

6、In the context of bonds, accrued interest:

A) applies only to bonds with semi-annual or quarterly coupon payments.
 
 
B) equals interest earned from the previous coupon to the sale date.
 
 
C) is discounted along with other cash flows to arrive at the dirty, or full price.
 
 
D) covers the part of the next coupon payment not earned by seller.

 The correct answer is B

This is a correct definition of accrued interest on bonds. The other choices are false. Accrued interest can occur on all bonds with periodic coupon payments, not just bonds with payment frequencies greater than one year. Accrued interest is not discounted when calculating the price of the bond. The statement, "covers the part of the next coupon payment not earned by seller," should read, "…not earned by buyer."

7、The dirty, or full, price of a bond:

A) applies if an issuer has defaulted.
 
 
B) is paid when a security trades ex-coupon.
 
 
C) equals the present value of all cash flows, plus accrued interest.
 
 
D) is usually less than the clean price.

 The correct answer is C

The dirty price of a bond equals the quoted price plus accrued interest. If an issuer has defaulted, the bond trades without interest and is said to trade flat. When a security trades ex-coupon, the buyer pays the clean price, which is the quoted price without accrued interest. The dirty price of a bond is greater than the clean price by the amount of the accrued interest. (If the bond trades on a coupon date, the dirty price will equal the clean price.)

8、Peter Stone is considering buying a $100 face value, semi-annual coupon bond with a quoted price of 105.19. His colleague points out that the bond is trading ex-coupon. Which of the following choices best represents what Stone will pay for the bond?

A) $105.19 plus accrued interest.
 
 
B) $105.19.
 
 
C) $105.19 minus accrued interest.
 
 
D) $105.19 minus the coupon payment.

 The correct answer is B

Since the bond is trading ex-coupon, the buyer will pay the seller the clean price, or the price without accrued interest. So, Stone will pay the quoted price. The choice $105.19 plus accrued interest represents the dirty price (also known as full price). This bond would be said to trade cum-coupon.

9、Austin Traynor is considering buying a $1,000 face value, semi-annual coupon bond with a quoted price of 104.75 and accrued interest since the last coupon of $33.50. If Traynor pays the dirty price, how much will the seller receive at the settlement date?

A) $1,081.00.
 
B) $1,047.50.
 
C) $1,014.00.
 
D) $1,033.50.

 The correct answer is A

The dirty price is equal to the agreed upon, or quoted price, plus interest accrued from the last coupon date. Here, the quoted price is 1,000 × 104.75%, or 1,000 × 1.0475 = 1,047.50. Thus, the dirty price = 1,047.50 + 33.50 = 1,081.00.

10、Scott Malooly recently paid 109.05 for a $1,000 face value, semi-annual coupon bond with a quoted price of 105.19. Assuming that transaction costs are zero, which of the following statements is most accurate?

A) The price Malooly paid covers the amount of the next coupon payment not earned by the seller.
 
B) The bond was trading ex-coupon. 
 
C) Malooly purchased the bond between coupon dates.
 
D) The price Malooly paid includes the discounted amount of accrued interest due to seller.

The correct answer is C

When a bond trades between two consecutive coupon dates, the seller is entitled to receive interest earned from the previous coupon date until the date of the sale. The price paid includes accrued interest and is referred to as the “dirty price.”

The other statements are false. The price Malooly paid includes the amount of the next coupon payment that he, the buyer, has not earned. When a security trades ex-coupon, the buyer pays the clean price, which is the quoted price without accrued interest. Accrued interest is not discounted when calculating the dirty price of a bond.

11、Which of the following statements regarding accrued interest is most accurate?

A) The accrued interest is paid by the seller of the bond to the buyer (new owner) of the bond. 
 
B) The bond is trading flat if the bond issuer is in default and the bond is trading without accrued interest. 
 
C) If the seller must pay the buyer accrued interest, the bond is said to be trading cum-par. 
 
D) If the buyer must pay the seller the accrued interest, the bond is said to be trading ex-coupon. 
 

 The correct answer is B

The accrued interest is paid by the new owner of the bond to the seller of the bond. If the buyer must pay the seller accrued interest, the bond is said to be trading cum-coupon. Otherwise, it is trading ex-coupon.

AIM 2: Distinguish among simple, semiannual, monthly, daily, and continuously compounded rates and compute simple, semiannual, monthly, daily, and continuously compounded rates given a discount factor or market interest rate for a specified period.

1、A Treasury bill, with 45 days until maturity, has an effective annual yield of 12.50%. The bill's holding period yield is closest to:

A) 1.57%.
 
 
B) 12.50%.
 
 
C) 1.46%.
 
 
D) 1.54%.

 The correct answer is C

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t ? 1. HPY = (EAY + 1)t/365 ? 1 = (1.125)45/365 ? 1 = 1.46%.

2、Use a stated rate of 9% compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.

The semi-annual effective rate is:

A) 9.00%.
 
B) 9.20%.
 
C) 10.25%.
 
D) 9.31%.

The correct answer is B

First, we need to calculate the periodic rate, or 0.09 / 2 = 0.045.
Then, the effective semi-annual rate = (1 + 0.045)2 ? 1 = 0.09203, or 9.20%.

 The correct answer is A

First, we need to calculate the periodic rate, or 0.09 / 4 = 0.0225.
Then, the effective annual rate = (1 + 0.0225)4 ? 1 = 0.09308, or 9.31%.

The correct answer is A

The continuously compounded rate = er ? 1 = e0.09 ? 1 = 0.09417, or 9.42%.
Calculator Keystrokes for et: Using the TI BA, enter [0.09] [2nd] [ex] (this is the key with LN on the face of the button). On the HP, enter [0.09] [g] [ex] (this key is located in blue on the key with 1/x in white print).

3、The effective annual yield (EAY) of a loan with a quoted rate of 8%, compounded quarterly is equivalent to the EAY of a loan with a continuously compounded quoted rate of:

A) 8.16%.
 
B) 8.08%.
 
C) 7.92%.
 
D) 8.24%.

The correct answer is C

For the quarterly compounded loan, EAY = (1 + (0.08 / 4))4 ? 1 = 0.824. For the continuously compounded loan, we want to find the value of r that solves 1.0824 = er(1). r = ln(1.0824) = 0.0792.

AIM 4: Explain and apply the linear yield interpolation and piecewise cubic methods for estimating complete discount functions.

1、A method for interpolating discount rates between known instruments that smoothes curves and avoids discontinuities is known as:

A) cubic linear approximation. 
 
B) cubic spline approximation. 
 
C) convexity approximation.
 
D) concavity approximation.

The correct answer is B

Piecewise cubic spline functions are used to interpolate discount rate curves between existing securities.