LOS e, (Part 2): Compute the value of a bond using spot rates.

Q1. An investor gathers the following information about a 2-year, annual-pay bond:

• Par value of $1,000
• Coupon of 4%
• 1-year spot interest rate is 2%
• 2-year spot interest rate is 5%

Using the above spot rates, the current price of the bond is closest to:

A)   $983.

B)   $1,000.

C)   $1,010.

Q2. Given the following spot rate curve:

Spot Rate
1-yr zero = 9.50%
2-yr zero = 8.25%
3-yr zero = 8.00%
4-yr zero = 7.75%
5-yr zero = 7.75%

What will be the market price of a five-year, 9% annual coupon rate bond?

A)   $1,067.78.

B)   $1,047.68.

C)   $1,000.00.

Q3. Using the following spot rates, what is the price of a three-year bond with annual coupon payments of 5%?

• One-year rate: 4.78%
• Two-year rate: 5.56%
• Three-year rate: 5.98%

A)   $97.47.

B)   $98.87.

C)   $93.27.

Q4. Assume that a callable bond's call period starts two years from now with a call price of $102.50. Also assume that the bond pays an annual coupon of 6% and the term structure is flat at 5.5%. Which of the following is the price of the bond assuming that it is called on the first call date?

A)   $100.00.

B)   $102.50.

C)   $103.17.

Q5. Can spot interest rates be used to value a callable bond?

A)   Yes.

B)   No.

C)   It depends on the slope of the term structure.

LOS e, (Part 2): Compute the value of a bond using spot rates.fficeffice" />

Q1. An investor gathers the following information about a 2-year, annual-pay bond:

• Par value of $1,000
• Coupon of 4%
• 1-year spot interest rate is 2%
• 2-year spot interest rate is 5%

Using the above spot rates, the current price of the bond is closest to:

A)   $983.

B)   $1,000.

C)   $1,010.

Correct answer is A)

The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $40 (0.04 × 1,000). The bond price = 40/(1.02) + 1,040/(1.05)² = $982.53.

Q2. Given the following spot rate curve:

Spot Rate
1-yr zero = 9.50%
2-yr zero = 8.25%
3-yr zero = 8.00%
4-yr zero = 7.75%
5-yr zero = 7.75%

What will be the market price of a five-year, 9% annual coupon rate bond?

A)   $1,067.78.

B)   $1,047.68.

C)   $1,000.00.

Correct answer is B)

90 / (1 + 0.095) + 90 / (1 + 0.0825)² + 90 / (1 + 0.08)³ + 90 / (1 + 0.0775)⁴ + 1,090 / (1 + 0.0775)⁵ = $1,047.68.

Q3. Using the following spot rates, what is the price of a three-year bond with annual coupon payments of 5%?

• One-year rate: 4.78%
• Two-year rate: 5.56%
• Three-year rate: 5.98%

A)   $97.47.

B)   $98.87.

C)   $93.27.

Correct answer is A)

The bond price is computed as follows:

Bond price = (5 / 1.0478) + (5 / 1.0556²) + (105 / 1.0598³) = $97.47

Q4. Assume that a callable bond's call period starts two years from now with a call price of $102.50. Also assume that the bond pays an annual coupon of 6% and the term structure is flat at 5.5%. Which of the following is the price of the bond assuming that it is called on the first call date?

A)   $100.00.

B)   $102.50.

C)   $103.17.

Correct answer is C)

The bond price is computed as follows:

Bond price = 6/1.055 + (102.50 + 6)/1.055² = $103.17

Q5. Can spot interest rates be used to value a callable bond?

A)   Yes.

B)   No.

C)   It depends on the slope of the term structure.

Correct answer is A)

Any complex debt instruments (like callable bonds, putable bonds, and mortgage-backed securities) can be viewed as the sum of the present value of its individual cash flows where each of those cash flows are discounted at the appropriate zero-coupon bond spot rate. It should be noted that while the appropriate spot interest rate can be used to discount each cash flow, determining the actual pattern of cash flows is uncertain due to the possibility of the bond being called away.

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