How to calculate initial carrying value – amortizing bond premiums/discounts

Question

This is part of a review question about bond premium amortization from a study material provider.

A six-year USD 1,000,000 bond was issued with an annual coupon rate of 5% when the market rate was 3%.

The answer says that the initial carrying value is USD1,108,343.83. However, there is no explanation for how to work this out solely from the information in the question.

Any help on how to do this would be much appreciated.

Thanks in advance.

mikey · Answer

I think of the question conceptually in my head as:
What is the value, at the start, of a financial instrument that will pay you USD50,000 (USD1,000,000 * 5%) every year for 6 years then repay you USD1,000,000 at the end?
So the initial carrying value can be calculated with your BA II Plus using NPV.

With your BA II Plus, enter:

NPV entry
BA II Plus keystrokes
Question parameter

N = 6
[6] [N]
6 year bond = 6 payment periods

I/Y = 3
[3] [I/Y]
3% market rate

PMT = 50,000
[50000] [PMT]
USD50,000 payment per year (5% of USD1M)

FV = 1,000,000
[1000000] [FV]
USD1,000,000 future value (at end of term)

Compute PV
[CPT] [PV]
Given all other parameters, compute PV

The calculator should show -1,108,343.83.

The result is negative because the cashflow is opposite to the payments you entered. In my example I set PMT and FV as positive (cashflow to me) so PV will be negative (cashflow from me to pay for the bond).

Which provider is this? They really should be providing an explanation with keystrokes.

stuck · Answer

Thanks for the help. There was another example question later on, which spelled it out. I'm using Bloomberg. It does tend to jump around a bit - throwing you straight into an advanced example and then later on going back to explain the basics. I assume it's the AI gauging my knowledge, but it can be a bit confusing.

Anyway, thanks again for your reply.