Question

Following are the independent situations.

1. Calculate the selling price for 8% bonds with a par value of $567,000 due in 10 years, paying interest on January 1 and July 1 each year, issued at par.

2. Calculate the selling price for bonds with face value of $1,766,000, due in 15 years, paying 7% interest semi-annually, issued at par.

3. Calculate the selling price for bonds with a face value of $781,000 and face rate of 5%, issued to yield 7%, due in 10 years, paying interest semi-annually.

4. Calculate the selling price for 10% bonds with a par value of $5,220,000 and maturity date in 12 years’ time, paying interest on January 1 and July 1 each year, issued to yield 8%.

Answer 1

Answer 1.

Par Value = $567,000

Bond is issued at par

Selling Price = $567,000

Answer 2.

Par Value = $1,766,000

Bond is issued at par

Selling Price = $1,766,000

Answer 3.

Face Value = $781,000

Annual Coupon Rate = 5%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50%*$781,000
Semiannual Coupon = $19,525

Annual Yield = 7%
Semiannual Yield = 3.50%

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Selling Price = $19,525 * PVIFA(3.50%, 20) + $781,000 * PVIF(3.50%, 20)
Selling Price = $19,525 * (1 - (1/1.035)^20) / 0.035 + $781,000 / 1.035^20
Selling Price = $670,001.13

Answer 4.

Face Value = $5,220,000

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00%*$5,220,000
Semiannual Coupon = $261,000

Annual Yield = 8%
Semiannual Yield = 4.00%

Time to Maturity = 12 years
Semiannual Period to Maturity = 24

Selling Price = $261,000 * PVIFA(4.00%, 24) + $5,220,000 * PVIF(4.00%, 24)
Selling Price = $261,000 * (1 - (1/1.04)^24) / 0.04 + $5,220,000 / 1.04^24
Selling Price = $6,015,891.48