LOS c: Compute the value of a bond and the change in value that is attributable to a change in the discount rate.

Q1. What is the present value of a 7% semi-annual pay corporate bond with a $1,000 face value and 20 years to maturity if it is yielding 6.375%? If a municipal bond is yielding 4.16% and an investors marginal tax rate is 35%, would the investor prefer the corporate bond or the municipal bond?

          Value                                 Investor preference

A)  $1,070.09                              municipal bond

B)  $1,121.23                              municipal bond

C)  $1,070.09                              corporate bond

Q2. Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6%. How much does the bond price change if the term structure of interest rates shifts down by 1% instantaneously?

A)   2.67.

B)   -2.67.

C)   0.00.

Q3. What is the probable change in price of a 30-year semiannual 6.5% coupon, $1000 par value bond yielding 8% when the nominal risk-free rate changes from 5% to 4%?

A)   $98.83.

B)   $106.34.

C)   $107.31.

Q4. If a bond's coupon is greater than the prevailing market rate on new issues, the bond is called a:

A)   discount bond.

B)   term bond.

C)   premium bond.

Q5. Assuming the risk-free rate is 5% and the appropriate risk premium for a AAA-rated issuer is 4%, the appropriate discount rate for a 10-year Treasury note is:

A)   4%.

B)   9%.

C)   5%.

Q6. An investor has the following choices available:

• She can buy a 10% semi annual coupon, 10-year bond for $1,000.
• She can reinvest the coupons at 12%.
• She can sell the bond in three years at an estimated price of $1,050.

Based on this information, the average annual rate of return over the three years is:

A)   9.5%.

B)   11.5%.

C)   13.5%.

LOS c: Compute the value of a bond and the change in value that is attributable to a change in the discount rate.fficeffice" />

Q1. What is the present value of a 7% semi-annual pay corporate bond with a $1,000 face value and 20 years to maturity if it is yielding 6.375%? If a municipal bond is yielding 4.16% and an investors marginal tax rate is 35%, would the investor prefer the corporate bond or the municipal bond?

          Value                                 Investor preference

A)  $1,070.09                              municipal bond

B)  $1,121.23                              municipal bond

C)  $1,070.09                              corporate bond

Correct answer is A)

N = 20 × 2 = 40; I/Y = 6.375/2 = 3.1875; PMT = 70/2 = 35; FV = 1,000; CPT → PV = $1,070.09.

The taxable-equivalent yield on the municipal bond is: 4.16% / (1 ? 0.35) = 6.4%

The investor would prefer the municipal bond because the taxable-equivalent yield is greater than the yield on the corporate bond: 6.4% > 6.375%

Q2. Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6%. How much does the bond price change if the term structure of interest rates shifts down by 1% instantaneously?

A)   2.67.

B)   -2.67.

C)   0.00.

Correct answer is A)

This value is computed as follows:

Bond Price Change = New Price – Old Price = 100 – (5/1.06 + 5/1.06² + 105/1.06³) = 2.67.

-2.67 is the correct value but the wrong sign. The value 0.00 is incorrect because the bond price is not insensitive to interest rate changes.

Q3. What is the probable change in price of a 30-year semiannual 6.5% coupon, $1000 par value bond yielding 8% when the nominal risk-free rate changes from 5% to 4%?

A)   $98.83.

B)   $106.34.

C)   $107.31.

Correct answer is C)

Price at 8% is N = 60, FV = $1,000, I = 4%, PMT = $32.50, CPT PV = $830.32; price at 7% is N = 60, FV = $1,000, I = 3.5%, FV = $1,000, CPT PV = $937.64. Change in price is $107.31.

Q4. If a bond's coupon is greater than the prevailing market rate on new issues, the bond is called a:

A)   discount bond.

B)   term bond.

C)   premium bond.

Correct answer is C)

When the coupon rate on a bond is higher than the prevailing market rate the bond will be selling at a premium.  This occurs because the bonds price will be higher than the face value because as interest rate goes down price goes up.

Q5. Assuming the risk-free rate is 5% and the appropriate risk premium for a AAA-rated issuer is 4%, the appropriate discount rate for a 10-year Treasury note is:

A)   4%.

B)   9%.

C)   5%.

Correct answer is C)

For a 10-year treasury the relevant discount rate is the risk free rate.

Q6. An investor has the following choices available:

• She can buy a 10% semi annual coupon, 10-year bond for $1,000.
• She can reinvest the coupons at 12%.
• She can sell the bond in three years at an estimated price of $1,050.

Based on this information, the average annual rate of return over the three years is:

A)   9.5%.

B)   11.5%.

C)   13.5%.

Correct answer is B)

Step 1. Find the FV of the coupons and interest on interest:

N = 3(2) = 6; I = 12/2 = 6; PMT = 50; compute FV = 348.77

Step 2. Determine the value of the bond at the end of 3 years:

$348.77 + 1,050.00 = $1,398.77

Step 3. Equate FV (1,398.77) with PV (1,000) over 3 years (n = 6):

compute I = 5.75(2) = 11.5%.

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