Question

Comparing Bonds Issued at Par, at a Discount, and at a Premium (AP10-2) On January 1 of this year, Barnett Corporation sold bonds with a face value of $500,000 and a coupon rate of 7 percent. The bonds mature in 10 years and pay interest annually on December 31. Barnett uses the effective interest amortization method. Ignore any tax effects. Each case is independent of the other cases
Required: Complete the following table. The interest rates provided are the annual market rate of interest on the date the bonds were issued. Case A (7%) Case B (8%) Case C (6%)

a. Cash received at issuance
b. Interest expense recorded in Year 1
c. Cash paid for interest in Year 1 4. Cash paid at maturity for bond principal

Answer 1

Answer:

a) 500,000   //  466,450  //  536,800  //

b)   35,000   //      37,316  //    32,208

c)    35,000  //    35,000  //     35,000

d) 500,000  //  500,000  //   500,000

Explanation:

We should discount the bond coupon payment and maturity for the given discount rates of 6% 7% and 8%

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 35,000.00

time 10

rate 0.06

$35000 \times \frac{1-(1+0.06)^{-10} }{0.06} = PV$

PV $257,603.0468

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   500,000.00

time   10.00

rate  0.06

$\frac{500000}{(1 + 0.06)^{10} } = PV$  

PV   279,197.39

PV c $257,603.0468

PV m  $279,197.3885

Total $536,800.4353

interest expense:

536,800 x 0.06 = 32,208

When coupon and market rate are the same 7% face value and issuance is the same.

When market rate is 8%

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 35,000.00

time 10

rate 0.08

$35000 \times \frac{1-(1+0.08)^{-10} }{0.08} = PV$

PV $234,852.8490

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   500,000.00

time   10.00

rate  0.08

$\frac{500000}{(1 + 0.08)^{10} } = PV$  

PV   231,596.74

PV c $234,852.8490

PV m  $231,596.7440

Total $466,449.5930

interest expense:

466,450 x 0.08 = 37.316‬

The cash payment are indifirent to the maket rate what the market rate does is change the perception of the market. ower rate increase the price while higher rate decrease the price.