ABC Co issues 500000 10 10 year bonds when the prevailing ma

ABC Co. issues $500,000, 10%, 10 year bonds when the prevailing market rate of interest is 9%. The bonds pay interest annually. Compute the issue price of the bonds.

I tried 106,418 and 532,205 are wrong answers.

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.

470,450 and 470,124 are wrong answers.

Solution

Solution:

Problem 1 --- Issue Price of the bond – Market Interest Rate is 9%

We need to calculate the issue price of the bonds by using Market Interest Rate 9%. It is the market rate that an investor expects from the company.

Annual Coupon Interest = Face value of the bonds x Coupon Rate= $500,000*10% = $50,000

Market Interest Rate (R) = 9%

Period to maturity (n) = 10

Issue Price of the bonds = Coupon Interest x PVIFA (9%, 10) + Face value x PVIF (9%, 10)

= (50,000*6.41766) + (500,000*0.42241)

= $532,088

Calculation of Discounting factors rounded to 5 decimal places (In case question is provided rounded of 3 decimal places, the answer will be changed accordingly)

Present value interest factor for ordinary annuity PVIFA (R%, n) = (1 – 1/(1+R)ⁿ) / R

PVIFA (9%, 10) = ((1 – 1/(1+0.09)¹⁰)/0.09 = 6.41766

Present value interest factor PVIF (R%, n) = 1/(1+R)ⁿ

PVIF (9%, 10) = 1/(1+0.09)¹⁰ = 0.42241

Problem 2 --- Issue Price of the bond – Market Interest Rate is 11%

Annual Coupon Interest = Face value of the bonds x Coupon Rate= $500,000*10% = $50,000

Market Interest Rate (R) = 11%

Period to maturity (n) = 10

Issue Price of the bonds = Coupon Interest x PVIFA (11%, 10) + Face value x PVIF (11%, 10)

= (50,000*5.88923) + (500,000*0.35218)

= $294,462 + 176,090

= $470,552

Calculation of Discounting factors rounded to 5 decimal places (In case question is provided rounded of 3 decimal places, the answer will be changed accordingly)

Present value interest factor for ordinary annuity PVIFA (R%, n) = (1 – 1/(1+R)ⁿ) / R

PVIFA (11%, 10) = ((1 – 1/(1+0.11)¹⁰)/0.11 = 5.88923

Present value interest factor PVIF (R%, n) = 1/(1+R)ⁿ

PVIF (11%, 10) = 1/(1+0.11)¹⁰ = 0.35218