Question

Imagination Dragons Corporation needs to raise funds to finance a plant expansion, and it has decided to issue 25-year zero coupon bonds with a par value of $1,000 each to raise the money. The required return on the bonds will be 8 percent. Assume semiannual compounding periods.

a.	What will these bonds sell for at issuance? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	Using the IRS amortization rule, what interest deduction can the company take on these bonds in the first year? In the last year? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c.	Repeat part (b) using the straight-line method for the interest deduction. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer (a)

Par value = $1,000

Semiannual interest = 8% / 2 = 4%

Number of semiannual periods = 25 * 2 = 50

PV = FV /(1 + Periodic Interest rate) ^{Number of periods}

= 1000 / (1 + 4%) ⁵⁰

=140.7126

These value the bonds will sell for at issuance = $140.71

Answer (b):

As per IRS amortization rules interest deduction the company can take on these bonds in the first year is the amount equal to change in bond's value in the year.

Bond's value at the beginning of year 1 = $140.71

Bonds value at the end of the year 1:

PV = FV /(1 + Periodic Interest rate) ^{Number of periods}

= 1000 / (1 + 4%) ⁴⁸

= 152.1947

Bonds value at the end of the year 1 = $152.19

Hence:

Interest deduction in the year 1 = 152.19 - 140.71 = $11.48

Value of at the beginning of last year =

= 1000 / (1 + 4%) ²

= 924.56

Value of at the end of last year = $1,000

Interest deduction in the last year = 1000 - 924.56 = $75.44

Hence:

Interest deduction in the year 1 = $11.48

Interest deduction in the last year = $75.44

Answer (c):

Total interest over 25 years = Par value - Initial sales value = 1000 - 140.71 = $859.29

Hence:

Using the straight-line method for the interest deduction per year = 859.29 / 25 = $34.37

Hence:

Interest deduction in the year 1 = $34.37

Interest deduction in the last year = $34.37