Question

1. ABC Co. issues $500,000, 10%, 10 year bonds when the prevailing market rate of interest is 11%. The bonds pay interest annually. Compute the issue price of the bonds.(I tried 470552, 470124, 470450 are wrong answers)

2. ABC Co. issues $500,000, 10%, 10 year bonds when the prevailing market rate of interest is 9%. The bonds pay interest semi-annually. Compute the issue price of the bonds.(WRONG 532498, 106504 532300)

Please give a correct answer. Thanks

Answer 1

Answer to Question 1:

Par Value = $500,000
Time to Maturity = 10 year
Annual YTM = 11%

Annual Coupon Rate = 10%
Annual Coupon = 10% * $500,000
Annual Coupon = $50,000

Price of Bond = $50,000 * PVIFA(11%, 10) + $500,000 * PVIF(11%, 10)
Price of Bond = $50,000 * (1 - (1/1.11)^10) / 0.11 + $500,000 / 1.11^10
Price of Bond = $470,554

So, Issue price of the bond is $470,554

Answer to Question 2:

Par Value = $500,000

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

Annual YTM = 9%
Semiannual YTM = 4.50%

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $500,000
Semiannual Coupon = $25,000

Price of Bond = $25,000 * PVIFA(4.50%, 20) + $500,000 * PVIF(4.50%, 20)
Price of Bond = $25,000 * (1 - (1/1.045)^20) / 0.045 + $500,000 / 1.045^20
Price of Bond = $532,520

So, Issue price of the bond is $532,520