# Reading 14, Example 26 errata confused

Hi,

Long time reader of these forums. I have not wrote level 2 in 10 years so really, really don’t remember bonds that much. I’m writing level 3 again but it’s been some time as well.

Answer in text for price appreciation on page 114 says [101.118 - 100.937/100.937]. Which I thought was correct. In errata it says it should be [101.118 - 100.937/100]. I don’t understand how 100 can be initial value. I just don’t understand.

I’m assuming this has something to do with par value but I don’t understand. Can somebody explain to me from fundamentals. Would 100.937 ever be denominator?

The change makes no sense to me; the original makes sense.

They are expressing the difference as % of par 100. So when you calculate the appreciation, you use total par value multiplies by price appreciation as a percentage of par.

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On carefully reading the example, the AUD 50 million is face (i.e., par) value, not market value. So it makes sense to divide by 100 (par value), not 100.937 (market value).

Note to self: read the examples carefully.

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Thanks for replies.

If was not \$50M face value and instead was market value, would we divide by 100.941?

Indeed, you would.

See? You understand this stuff!

I understand that we divide by 100 is because it’s par value but I don’t understand the logic. For this we have 101.118 and 100.937 as MV. I think this means 101.118% of par value and 100.937% of par value.

I don’t understand the math of how this relates to dividing by 100 if since we have 50M in face value. In my head, I still think it’s the old answer multiplied by 50M. I can memorize this but I wish this could stay in my head with logic. It’s been a long time since I wrote papers.

Because the original market price was 100.937, a par value of AUD 50 million will have an original market value of:

AUD\ 50\ million \times 100.937\% = AUD\ 50,468,500

The original price appreciation calculation was based on market value, not on par value. I’ll show you that they’re equivalent:

\left(\frac{101.118 - 100.937}{100.937}\right)AUD\ 50,468,500 = \left(101.118 - 100.937\right)\left(\frac{AUD\ 50,468,500}{100.937}\right)
= \left(101.118 - 100.937\right)\left(AUD\ 500,000\right)
= \left(101.118 - 100.937\right)\left(\frac{AUD\ 50,000,000}{100}\right)
= \left(\frac{101.118 - 100.937}{100}\right)AUD\ 50,000,000
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Thank you very much for this. I’m starting to remember. This is very kind of you.

My pleasure.

Only if its coupon rate equals its YTM, which usually isn’t the case.

I’m not sure what you mean by the market value of the underlying index. Please explain this further.