Question

Great company is going to issue new coupon bonds. The bond issue is going to have the following characteristics: bonds mature in 8 years from now and carry 4% coupon rate paid out quarterly. The par value of a bond is $5000 and the prevailing market interest rate for bonds with similar and maturity is 6%. Altogether 12000 bonds will be issued.

a) Find the value of a single bond issue by Great company

b) How much capital is company Inc. going to raise through the issue of bonds , If the issue costs amount to 0.45% of the par value of each bond.

Answer 1

a) Value of single Bond: $8,190.94 [See Calculation below]
Value of the bond is the present value of all future cash flows. For the present value we need to use 6% as discount rate because it is the prevailing market interest rate for bonds with similar maturity.

Coupon payment is 4% x $5000 = $200 per quarter for 8 years, that is 32 instalments of $200.

• PV annuity factor of (6%/4) for 32 periods [that is 1.5% for 32 periods] is 25.2672 (rounded to 4 decimals). It can be obtained from Excel function: =ROUNDUP(PV(6%/4,32,-1),4).
  So, the present value of all coupon payments = 25.2672 x $200 = $5,053.44
  
• PV of $5000 received at the end of 8 years is 0.6275 x $5,000 = $3,137.50. This can be calculated from Excel formula: =5000*ROUNDUP((1/(1.06)^8),4)
  
• Value of Bond = $5053.44 + $3137.50 = $8,190.94

b) Capital Raised = $98,021,280 [See calculation below]

• Value of all bonds = $8,190.94 x 12000 = $98,291,280
• Issue cost of 0.45% of par value = 0.45% x $5000 x 12000 = $270,000
• Capital raised = $98291280 - $270000 = $98,021,280

Hope this helps.
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