A-. Taxes on zero coupon bond Answer: e Diff: M N

1457A-. Taxes on zero coupon bond Answer: e Diff: M N

Step 1: Determine the price of the bond today:

N = 15; I = 7; PMT = 0; FV = 1000; and then solve for PV =

-$362.446. V_B = $362.446.
Step 2: Determine the price of the bond one year from now:

N = 14; I = 7; PMT = 0; FV = 1000; and then solve for PV =

-$387.817. V_B1 = $387.817.
Step 3: Determine the capital gain on the bond:

Capital gain = $387.817 – $362.446 = $25.371.

Step 4: Calculate the first year’s taxes:

Taxes due = $25.371  0.25 = $6.34.

1467A-. Accrued value and interest expense Answer: a Diff: M

Financial calculator solution:

Inputs: N = 8; I = 9; PV = -178.43; PMT = 0. Output: FV = $355.53 = V₈.

Inputs: N = 7; I = 9; PV = -178.43; PMT = 0. Output: FV = $326.18 = V₇.

Difference: $355.53 - $326.18 = $29.35.

Solution check: $29.35/$326.18 = 9.0%.

1477A-. Zeros and expectations theory Answer: d Diff: T

First find the yields on one-year and two-year zero-coupon bonds, so you can find the implied rate on a one-year bond, one year from now. Then use this implied rate to find its price.

1-Year:

N = 1; PV = -938.9671; PMT = 0; FV = 1000; and then solve for I = 6.5%.

2-Year:

N = 2; PV = -873.4387; PMT = 0; FV = 1000; and then solve for I = 7.0%.

Therefore, if the implied rate = X


Now find the price of a 1-year zero, 1 year from now:

N = 1; I = 7.5; PMT = 0; FV = 1000; and then solve for PV = -$930.23.

V_B1 = $930.23.

1487A-. Zeros and expectations theory Answer: a Diff: T

Step 1: Calculate the YTM for the 3-year zero:

N = 3; PV = -827.8491; PMT = 0; FV = 1000; then solve for I = 6.5%.

Step 2: Calculate the YTM for the 4-year zero:

N = 4; PV = -762.8952; PMT = 0; FV = 1000; then solve for I = 7%.

Step 3: Calculate the interest rate on a 1-year zero, 3 years from now:

7% =

X = 8.5%.
Step 4: Calculate the price of a 1-year zero 3 years from now:

N = 1; I = 8.5; PMT = 0; FV = 1000; and then solve for PV =

-$921.66. V_B = $921.66.

1497A-. Zero coupon bond Answer: d Diff: T

Step 1: Calculate PV of zero coupon bond at Time 0:

N = 50; I = 4; PMT = 0; FV = 1000; and then solve for PV =
-$140.71. V_B = $140.71.
Step 2: Calculate accrued value at Year 5:

$140.71(1.04)²⁽⁵⁾ = $208.29.

Step 3: Call value at Year 5:

$208.29(1.04) = $216.62.

Step 4: Calculate EAR as follows:

N = 10; PV = -140.71; PMT = 0; FV = 216.62; and then solve for I = 4.41%; however, this is a semiannual rate.

EAR = (1.0441)² - 1 = 9.01%.

1507A-. Zero coupon bond Answer: e Diff: T
Financial calculator solution:

Step 1: Determine EAR for discounting. Using interest rate conversion feature:

Inputs: P/YR = 2; NOM% = 10%. Output: EFF% = 10.25%.

Formula method: EAR = - 1 = (1.05)² - 1 = 0.1025.

Step 2: Determine price of bond when issued.

Inputs: N = 25; I = 10.25; PMT = 0; FV = 1000. Output: PV = -$87.20. V_B = $87.20.

Step 3: Determine accrued value of bond today, and calculate call price.

Inputs: N = 5; I = 10.25; PV = -87.20; PMT = 0.

Output: FV = $142.04. Premium is 10% over accrued value. Call price = $142.04  1.10 = $156.24.
Step 4: Determine the periodic rate (semiannual compounding).

Inputs: N = 10; PV = -87.20; PMT = 0; FV = 156.24.

Output: I = 6.005%.

Nominal annual rate = 2  6.005% = 12.01%.

Step 5: Determine effective annual rate earned on bond using interest rate conversion feature:

Inputs: P/YR = 2; NOM% = 12.01. Output: EFF% = 12.37%.

1517A-. Taxes on zero coupon bond Answer: a Diff: T

Since zero coupon bonds do not make annual interest payments, the tax deduction is determined by the accumulated (but unpaid) interest on the bond over the year. To determine this we will calculate the value of the bond at t = 1 and at t = 2.

t = 1: N = 9; I/YR = 9.5; PMT = 0; FV = 1000; PV = -$441.85. V_B1 = $441.85.
t = 2: N = 8; I/YR = 9.5; PMT = 0; FV = 1000; PV = -$483.82. V_B2 = $483.82.
So the accumulated interest is: $483.82 - $441.85 = $41.97.

Tax savings = 30%($41.97) = $12.59.

1527A-. Zero coupon interest tax shield Answer: b Diff: T

Financial calculator solution:

Inputs: N = 3; PV = 727.25; PMT = 0; FV = -1000. Output: I = 11.20%.

0 1 2 3

1) Accrued value 727.25 808.70 899.28 1,000.00

2) Interest expense 81.45 90.58 100.72

3) Tax savings (line 2  0.40) 32.58 36.23 40.29

+40.29

-1,000.00

4) Cash flows +727.25 +32.58 +36.23 -959.71

1537A-. After-tax cost of debt Answer: c Diff: M

Financial calculator solution:

Solve for the YTM using the information from the previous question

Inputs: N = 3; PV = 727.25; PMT = 0; FV = -1000.

Output: I = 11.20. Before-tax cost debt of this issue = 11.20%.

k_d(After-tax) = 11.20%(1 - T) = 11.2%(0.6) = 6.72%.

Alternate solution using cash flows:

Inputs: CF₀ = 727.25; CF₁ = 32.58; CF₂ = 36.23; CF₃ = -959.71.

Output: IRR% = 6.72%.

154
WEB APPENDIX 7B SOLUTIONS


7B-. Liquidation procedures Answer: e Diff: M

1557B-. Bankruptcy law Answer: d Diff: M

1567B-. Bankruptcy issues Answer: e Diff: M

1577B-. Priority of claims Answer: c Diff: T

Chapter 7 - Page