Bond Amortization

[michaelgrogan]

[original post removed]

[Ernest_Seow]

@michaelgrogan

_A company issued $1 million face value of five-year bonds on January 1st 2013 with a 5% coupon when the market interest rate was 4 percent. What is the amount of the amortization of the bond’s premium at the end of the first year?_a) $8,219 b) $8,472__c) $8,904 To arrive at the answer of $8,219, we are calculating the bond’s present value of $1,044,518. This is then being multiplied by .04 to arrive at $41,780.73, which taken away from $50k is $8,219. I have two questions. 1. How are we getting a present value of $1,044,518?

The bond issued is a premium bond as we see that:

Bond’s YTM < Bond’s Coupon

The proceeds received from issuing bond will be the price of the bond. To calculate the price of the bond we will consider the cashflows (" CFs") that will be generated throughout the tenure of the bond:

Yr 0:

Yr 1: 50k

Yr 2: 50k

Yr 3: 50k

Yr 4: 50k

Yr 5: 50k and face value of 1mio

If you present value back the CFs using the interest rate of 4%, you will be able to get $1,044,518; which is the price of the premium bond. This amount will be the initial bond liability value to be reported during the inception of the bond.

@michaelgrogan

2. To solve this question, what I did was calculated the present value of $50,000 using a 4% discount rate to get $48,076. Subtracting this from $50,000 clearly gives us the wrong answer. Can somebody please explain why doing it this way is incorrect?

The reason why they subtract the coupon payment of 50,000 by the interest exppense ($XXX amount) is to compute the amortization premium.

Under the effective interest rate method , each period interest expenses is caculated using the below:

’ Opening value of bond liability’ X ’ Bond’s YTM’ = Interest expense

Hence it follows that we compute interest expense for Year 1 by mutiplying 4% to $1,044,518 to get $41,781.

Then we will be able to obtain the amortization premium amount:

Amortization premium = Coupon Payment - Interest Expenses

= 50,000 - 41,781

= 8,219

[S2000magician]

@michaelgrogan

A company issued $1 million face value of five-year bonds on January 1st 2013 with a 5% coupon when the market interest rate was 4 percent. What is the amount of the amortization of the bond’s premium at the end of the first year?

a) $8,219

b) $8,472

c) $8,904

To arrive at the answer of $8,219, we are calculating the bond’s present value of $1,044,518. This is then being multiplied by .04 to arrive at $41,780.73, which taken away from $50k is $8,219. I have two questions.

1. How are we getting a present value of $1,044,518?

This problem assumes that the coupon payments are annual. They should have been clear on that. To get the present value, use your calculator:

• n = 5
• i = 4%
• FV = 1,000,000
• PMT = 50,000 (= 5% × 1,000,000)
• Solve for PV = -1,044,518

@michaelgrogan

2. To solve this question, what I did was calculated the present value of $50,000 using a 4% discount rate to get $48,076. Subtracting this from $50,000 clearly gives us the wrong answer. Can somebody please explain why doing it this way is incorrect?

The 4% discount rate applies to all of the cash flows, not just to the coupon payments. The proper way to work this problem is to compute the interest based on the present value, then subtract that from the $50,000 payment; the difference is the amortization of the principle. Thus:

Interest = 4% × $1,044,518 = $41,781

Principle = $50,000 – $41,781 = $8,219

If you haven’t practiced making an amortization table in Excel for a bond premium or discount, you should. After doing it a couple of times you’ll be skilled in doing the calculations above.

[michaelgrogan]

Many thanks once again for all your help.

[S2000magician]

My pleasure.