Question

In: Finance

Suppose your company needs to raise $35.4 million and you want to issue 24-year bonds for...

Suppose your company needs to raise $35.4 million and you want to issue 24-year bonds for this purpose. Assume the required return on your bond issue will be 7.9 percent, and you’re evaluating two issue alternatives: a 7.9 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent. Both bonds would have a face value of $1,000.
  
a. How many of the coupon bonds would you need to issue to raise the $35.4 million? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Number of coupon bonds            

How many of the zeroes would you need to issue? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Number of zero coupon bonds            

b. In 24 years, what will your company’s repayment be if you issue the coupon bonds? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Coupon bonds repayment            $

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

Zero coupon bonds repayment            $

c. 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. (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. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Coupon bond cash flow $
Zero coupon bond cash flow $

Solutions

Expert Solution

Given,

Raising capacity of company= $ 3,54,00,000

Bond Duration (n) = 24 years

Required rate of return on bond = 7.9%

Face value of bond = $ 1,000

Coupon rate of interest = 7.9% semi annually

a) Calculation number of coupon bonds and zero coupon bonds to raise $ 3,54,00,000:

To calculate the numbers, first we need to calculate the value of bond.

Value of bond is present value of interest of bond till maturity plus present value of bond on maturity.

As interest payment is semi annual,

n=24*2=48 years

After tax coupon rate=7.9%/2 = 3.95% - 35% = 2.5675%

After tax Rate of return = 3.95% - 35% = %2.5675%

Calculation of value of bond:

Year

Discounting factor ( D.F.)

( n=48 years and R=2.5675%)

Value Present value of bond
1-48 D.F. for 48 years = 27.4133 Interest @ 2.5675%= $1,000*2.5675%=$25.675 D.F.*Value=27.4133*$25.675=$703.84
48 D.F. for year 48= 0.296163 Value at the end of maturity= $1,000 D.F.*Value=0.296163*$1,000=$296.16
Total value of bond = $1,000

As coupon rate and rate of return is same as 7.9%, therefore current price of bond will be equal to face value of bond as $1,000.

Number of coupon bonds= Amount required to raise  

Value of bond

= $3,54,00,000/ $1,000

Therefore, Number of coupon bonds = 35,400 coupon bonds.

calculation of number of zero coupon bonds:

Zero coupon bond is a type of bond which doesn't pay any type of interest i.e. it is zero coupon interest bond. But, it is redeemed at huge discount at the time of maturity.

Value of zero coupon bond= Face value

(1+R)n

Where, Face value = $1,000

R= 3.95% (As zero coupon bonds are tax exempt)

n= 48 years

= $1,000  

(1+0.0395)48

   = $1.000

(1.0395)48

= $1,000

6.417935

Value of zero coupon bond= $155.81

Therefore number of zero coupon bonds= $3,54,00,000/ $155.81

number of zero coupon bonds = 2,27,199.79 Bonds.

b) Repayment of coupon bonds & zero coupon bonds:

1) If company issues coupon bond, company will have to pay interest to bondholders semi annually i.e. company will pay interest half yearly for 24 years which is 48 payments. And at the end of maturity period company will pay value of bond over the life of bond.

Therefore, if company issues coupon interest rate bonds, it will pay $703.84 per bond interest over the life of bond.i.e in total company will pay $703.84*35400 bonds = $2,49,15,936 interest payment

And at the end of maturity, company will pay $ 296.16*35400= $ 1,04,84,064 maturity value.

2) If company issues zero coupon rate bonds, company will have to pay zero interest to bond holders but at the end of maturity it will pay $155.81 per bond maturity value.

c)

After tax cash out flows for the first year :

In coupon interest bond, company will pay interest %25.675 per bond

Year Particulars Discounting Factor Discounted amount
0 Issue of bonds = $3,54,00,000 1 1*3,54,00,000=$3,54,00,000
1 Payment of interest= $25.675 half yearly i.e $25.675*2=$51.35 yearly *35400 bonds = 1817790 0.9750 0.9750*1817790= (-)$17,72,345.25
Net cash flow for first year $3,36,27,654.75

After tax cash outflows in case of zero coupon bonds:

In case of zero coupon bonds, company doesn't pay any interest hence no outflow in first year.

Therefore cash inflow in first year will be same as $3,54,00,000.

Coupon rate cash outflow - $ 17,72,345.25
Zero coupon rate cash outflow Zero

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