Question

On January 1, 2018, Frontier World issues $41 million of 9% bonds, due in 20 years, with interest payable semiannually on June 30 and December 31 each year. The proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride.

References

Required information

Required:

1-a. If the market rate is 8%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Enter your answers in dollars not in millions.)_12_2016_QC_CS-571

Required information

2-a. If the market rate is 9%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Enter your answers in dollars not in millions. Round "Market interest rate" to 1 decimal place.)
information

3-a. If the market rate is 10%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Enter your answers in dollars not in millions.)

Answer 1

1-a) Semi annual interest on bonds = Face Value*Interest rate*6 months/12 months

= $41,000,000*9%*6/12 = 1,845,000

Interest rate for discounting = Market rate*6/12 months

= 8%*6/12 = 4%

No. of semiannual Periods = 20 yrs*2 periods = 40 periods

Issue Price = PV of Interest payments+PV of Face Value

= [Interest amount*PVAF(40, 4%)]+[Face Value*PVF(40, 4%)]

= (1,845,000*19.792784)+(41,000,000*0.208289)

= $36,517,686+$8,539,849 = $45,057,535

2-a) Interest rate for discounting = Market rate*6/12 months

= 9%*6/12 = 4.5%

No. of semiannual Periods = 20 yrs*2 periods = 40 periods

Issue Price = PV of Interest payments+PV of Face Value

= [Interest amount*PVAF(40, 4.5%)]+[Face Value*PVF(40, 4.5%)]

= (1,845,000*18.401584)+(41,000,000*0.171929)

= $36,950,922+$7,049,089 = $44,000,011

3-a) Interest rate for discounting = Market rate*6/12 months

= 10%*6/12 = 5%

No. of semiannual Periods = 20 yrs*2 periods = 40 periods

Issue Price = PV of Interest payments+PV of Face Value

= [Interest amount*PVAF(40, 5%)]+[Face Value*PVF(40, 5%)]

= (1,845,000*17.159086)+(41,000,000*0.142046)

= $31,658,514+$5,823,886 = $37,482,400