Question

Thompson Corporation is planning to issue $250,000, five-year, 5 percent bonds. Interest is payable semi-annually each June 30 and December 31. All of the bonds will be sold on July 1, 2017; they mature on June 30, 2022. Use Table 9C.1, Table 9C.2

Required:
Compute the issue (sale) price on July 1, 2017, if the yield is: (Round time value factor to 4 decimal places. Round the final answers to the nearest dollar amount.)

a. 5%

b. 2%

c. 6%

Answer 1

(a) Face value = $ 250,000; Interest rate = 5% or 2.50% half yearly; Yield = 5% or 2.50% half yearly

Interest received half yearly = ($ 250,000 * 2.50%) i.e. $ 6,250. The same will be discounted at the rate of 2.50% for 10 periods (i.e. 5 years)

PVAF @2.50% for 10 periods = 8.7520

PVF @2.50% for the 10th period = 0.7812

Thus, issue price of the bond = (250,000 * 0.7812) + (6250 * 8.7520)

= $ 250,000

In the given case, as the coupon rate and the discounting rate, the bond will be issued at par.

(b) Face value = $ 250,000; Interest rate = 5% or 2.50% half yearly; Yield = 2% or 1% half yearly

Interest received half yearly = ($ 250,000 * 2.50%) i.e. $ 6,250. The same will be discounted at the rate of 1% for 10 periods (i.e. 5 years)

PVAF @1% for 10 periods = 9.4713

PVF @1% for the 10th period = 0.9053

Thus, issue price of the bond = (250,000 * 0.9053) + (6250 * 9.4713)

= $ 285,520

In the given case, as the coupon rate is greater than the discounting rate i.e. rate of return on the bond is greater than the cost of the bond, the bond will be issued at premium (> $ 250,000)

(c) Face value = $ 250,000; Interest rate = 5% or 2.50% half yearly; Yield = 6% or 3% half yearly

Interest received half yearly = ($ 250,000 * 2.50%) i.e. $ 6,250. The same will be discounted at the rate of 3% for 10 periods (i.e. 5 years)

PVAF @3% for 10 periods = 8.5302

PVF @3% for the 10th period = 0.7441

Thus, issue price of the bond = (250,000 * 0.7441) + (6250 * 8.5302)

= $ 239,339

In the given case, as the coupon rate is less than the discounting rate i.e. rate of return on the bond is lower than the cost of the bond, the bond will be issued at a discount (< $ 250,000)