Imagination Dragons Corporation needs to raise funds to finance a plant expansion, and it has decided to issue 15-year zero coupon bonds with a par value of $1,000 each to raise the money. The required return on the bonds will be 7 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.)

a) Zero coupon bond does not pay periodical interest and formula to compute the value of a zero-coupon bond:

Value = Face Value / (1 +Yield / 2) ** Years to Maturity * 2

b) Interest deduction

After 1 year bond value from the above equation is 437.08

437.08 - 411.99 = 25.09

In the 14th year bond value from the above equation is 942.60

1000 - 942.60 = 57.40

c) Straight Line Method

Total Interest Paid = 1000 - 411.99

= 588.01

For yearly calculation

588.01 / 15 = 39.21

Further computation is done in the image below.

A) 365.28

B) first year:

25.37593  

and during last year:

66.49

C) straight line will generate interest evenly throughout the life of the bond:

(1,000 - 365.28) / 15 = 42.32 interest expense per year

Explanation:

We solve for the present value of a lump sum as the zero-coupon is a bond with no interest payment only maturity.

Is important to notice the required return is compounding semiannually thus, there are two payment per year and the rate should be halved:

Maturity  $1,000.00

time  30.00 (15 years x 2 payment per year)

rate  0.03500 (7% annual compounding semiannually)

PV   356.2784

Now, we calculate the interest expense for the year

356.2784 x (1.035 x 1.035 -1 ) =  25.37593  

For the last year

Maturity  $1,000.00

time  2.00

rate  0.03500

PV   933.5107

1000 maturity - 933.51 value one year before = 66.49