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Wednesday, 16 October 2013

Suppose your company needs to raise $36.2 million and you want to issue 22-year bonds for this purpose. Assume the required return on your bond issue will be 8.7 percent, and you’re evaluating two issue alternatives: a 8.7 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent. Requirement 1: (a) How many of the coupon bonds would you need to issue to raise the $36.2 million? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567).) Number of coupon bonds (b) How many of the zeroes would you need to issue? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Number of zero coupon bonds Requirement 2: (a) In 22 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).) Coupon bonds repayment $ (b) What if you issue the zeroes? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to the nearest whole dollar amount (e.g., 32).) Zero coupon bonds repayment $ Requirement 3: Assume that the IRS amortization rules apply for the zero coupon bonds. Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Do not round intermediate calculations. Input a cash outflow as a negative value and a cash inflow as a positive value. Enter your answers in dollars, not millions of dollars (e.g., 1,234,567). Round your answers to 2 decimal places (e.g., 32.16).) Coupon bond cash flow $ Zero coupon bond cash flow $ Explanation: 1: (a) The coupon bonds have a 8.7 percent coupon which matches the 8.7 percent required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so: Number of coupon bonds to sell = $36,200,000 / $1,000 = 36,200 (b) The number of zero coupon bonds to sell would be: Price of zero coupon bonds = $1,000/1.043544 = $153.58 Number of zero coupon bonds to sell = $36,200,000 / $153.58 = 235,709.19 2: (a) The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So: Coupon bonds repayment = 36,200($1,000) + 36,200($1,000)(.087/2) = $37,774,700 (b) The repayment of the zero coupon bond will be the par value times the number of bonds issued, so: Zeroes repayment = 235,709.19($1,000) = $235,709,193 3: The total coupon payment for the coupon bonds will be the number bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments. To do this, we will multiply the total coupon payment times one minus the tax rate. So: Coupon bonds: (36,200)($87)(1 – .35) = $2,047,110 cash outflow Note that this is cash outflow since the company is making the interest payment. For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. The price of the zeroes in one year will be: P1 = $1,000/1.043542 = $167.23 The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so: Year 1 interest deduction per bond = $167.23 – 153.58 = $13.65 The total cash flow for the zeroes will be the interest deduction for the year times the number of zeroes sold, times the tax rate. The cash flow for the zeroes in year 1 will be: Cash flows for zeroes in Year 1 = (235,709.19)($13.65)(.35) = $1,126,264.81 Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow. During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. (a) The coupon bonds have a 8.7% coupon which matches the 8.7% required return, so they will sell at par. For the zeroes, the price is: Enter 22 × 2 8.7% / 2 ±$1,000 N I/Y PV PMT FV Solve for $153.58 (c) The price of the zeroes in one year will be: Enter 21 × 2 8.7% / 2 ±$1,000 N I/Y PV PMT FV Solve for $167.23

Suppose your company needs to raise $36.2 million and you want to issue 22-year bonds for this purpose. Assume the required return on your bond issue will be 8.7 percent, and you’re evaluating two issue alternatives: a 8.7 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent.

 
Requirement 1:
(a)
How many of the coupon bonds would you need to issue to raise the $36.2 million? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567).)

 
  Number of coupon bonds  

 
(b)
How many of the zeroes would you need to issue? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).)

 
  Number of zero coupon bonds  

 
Requirement 2:
(a)
In 22 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

 
  Coupon bonds repayment $  

 
(b)
What if you issue the zeroes? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to the nearest whole dollar amount (e.g., 32).)

 
  Zero coupon bonds repayment $  

 
Requirement 3:
Assume that the IRS amortization rules apply for the zero coupon bonds.
  
Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Do not round intermediate calculations. Input a cash outflow as a negative value and a cash inflow as a positive value. Enter your answers in dollars, not millions of dollars (e.g., 1,234,567). Round your answers to 2 decimal places (e.g., 32.16).)

 

 

 
  Coupon bond cash flow $  
  Zero coupon bond cash flow $  



Explanation:
1:
(a)
The coupon bonds have a 8.7 percent coupon which matches the 8.7 percent required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so:

 
Number of coupon bonds to sell = $36,200,000 / $1,000 = 36,200

 
(b)
The number of zero coupon bonds to sell would be:

 
Price of zero coupon bonds = $1,000/1.043544 = $153.58

 
Number of zero coupon bonds to sell = $36,200,000 / $153.58 = 235,709.19

 
2:
(a)
The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So:

 
Coupon bonds repayment = 36,200($1,000) + 36,200($1,000)(.087/2) = $37,774,700

 
(b)
The repayment of the zero coupon bond will be the par value times the number of bonds issued, so:

 
Zeroes repayment = 235,709.19($1,000) = $235,709,193

 
3:
The total coupon payment for the coupon bonds will be the number bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments. To do this, we will multiply the total coupon payment times one minus the tax rate. So:

 
Coupon bonds: (36,200)($87)(1 – .35) = $2,047,110 cash outflow

 
Note that this is cash outflow since the company is making the interest payment.

 
For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. The price of the zeroes in one year will be:

 
P1 = $1,000/1.043542 = $167.23

 
The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so:

 
Year 1 interest deduction per bond = $167.23 – 153.58 = $13.65

 
The total cash flow for the zeroes will be the interest deduction for the year times the number of zeroes sold, times the tax rate. The cash flow for the zeroes in year 1 will be:

 
Cash flows for zeroes in Year 1 = (235,709.19)($13.65)(.35) = $1,126,264.81

 
Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow.

 
During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes.

 
Calculator Solution:
  
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

 
(a) The coupon bonds have a 8.7% coupon which matches the 8.7% required return, so they will sell at par. For the zeroes, the price is:

 
Enter
22 × 2
8.7% / 2

 

 
±$1,000


 
N

 

 
I/Y

 

 
PV

 

 
PMT

 

 
FV

 
Solve for

 

 
$153.58

 

 

 
(c) The price of the zeroes in one year will be:

 
Enter
21 × 2
8.7% / 2

 

 
±$1,000


 
N

 

 
I/Y

 

 
PV

 

 
PMT

 

 
FV

 
Solve for

 

 
$167.23

 

 

Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 3.9 percent. Required: What was your real return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Real return % Explanation: The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) r = [(1 + .15) / (1 + .039)] – 1 r = .1068, or 10.68%

Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 3.9 percent.

Required:
What was your real return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

  Real return %   


Explanation:
The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is:
  
(1 + R) = (1 + r)(1 + h)
  
r = [(1 + .15) / (1 + .039)] – 1
r = .1068, or 10.68%

Volbeat Corporation has bonds on the market with 12.5 years to maturity, a YTM of 9.8 percent, and a current price of $949. The bonds make semiannual payments.

Volbeat Corporation has bonds on the market with 12.5 years to maturity, a YTM of 9.8 percent, and a current price of $949. The bonds make semiannual payments.

Required:
What must the coupon rate be on the bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

  Coupon rate %  


Explanation:
 

App Store Co. issued 17-year bonds one year ago at a coupon rate of 6.8 percent. The bonds make semiannual payments.

App Store Co. issued 17-year bonds one year ago at a coupon rate of 6.8 percent. The bonds make semiannual payments.

Required:
If the YTM on these bonds is 5.4 percent, what is the current bond price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

  Current bond price $  


Explanation:
To find the price of this bond, we need to realize that the maturity of the bond is 16 years. The bond was issued one year ago, with 17 years to maturity, so there are 16 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is:

P = $34.00(PVIFA2.70%,32) + $1,000(PVIF2.70%,32)
P = $1,148.73

Calculator Solution:
  
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter
16 × 2
5.4% / 2
±$68 / 2
±$1,000

N
I/Y
PV
PMT
FV
Solve for
$1,148.73