Book Value Versus Market Value for a Zero-Coupon Bond
Summary
The document uses a four-year zero-coupon bond to ask how book value differs from market value after two years. It distinguishes the bond’s market value, which reflects the yield used to discount its remaining cash flow, from its accounting book value, which depends on how the purchase cost and accrued return are recognized. The response illustrates one possible straight-line allocation of the bond’s discount over its life, producing an amortized book value partway through the term.
It then contrasts that treatment with a convention under which return is recognized only as a capital gain at maturity, leaving book value at purchase cost before maturity. The stated difference therefore cannot be inferred from bond yields and face value alone: the accounting convention matters. The answer explicitly presents its calculation as uncertain and asks for clarification; it should not be treated as authoritative accounting guidance. It gives no definitive market value for the bond at the intermediate date under a specified prevailing yield, and does not set out formal accounting standards or effective-interest amortization.
Key ideas
- Market value discounts the remaining bond payment using the relevant market yield.
- Book value depends on how purchase discount and investment return are recognized over time.
- Straight-line accretion and recognition only at maturity can produce different book values.
- The document’s illustrative treatment is tentative and does not specify a controlling accounting standard.
- A yield and face value alone do not determine the bond’s accounting book value.
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Full text
# What is the difference between a book value and a market value?
# What is the difference between a book value and a market value?
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I would like to understand the following problem.
> A 2yr zero-coupon bond has an annual yield rate of 11% per year. A 4yr zero-coupon bond has an annual yield rate of 19% per year. Find the difference between the book value and the market value of a par value 100 4yr zero-coupon bond in two years.
Which one represents the present (at time 2) value of the bond that can be calculated as 400(1.19)−2 ?
## Answer by Quantifeye (score 1)
https://quant.stackexchange.com/a/16715
I am only taking a stab at this so please do not consider what I have to say as authoritative.
If we buy a two year zero coupon bond at time zero (at the above mentioned rates assumed to be annual effective rates), we would pay $\frac{100}{1.11^2}=81.16224$ and $\frac{100}{1.19^4}=49.86688$ respectively. The book value of an instrument in this context, I suspect is cost price plus amortization/accretion. In other words, when is “profit” from the instrument recognised? If profit is allocated to each year linearly, we can say that $\frac{100-81.16224}{2}$ is realised in each year for the 2-year-zero. And that $\frac{100-49.86688}{4}$ Is realised each year on the 4-year-zero. So after two years (at maturity) the two year zero would have market value and book value of $100$. The 4-year-zero would have a book value of $49.86688+2\times12.53328=74.93344$. So the difference would be approximately $25$.
But this would depend on how profit/growth on the instrument is recognised. Is it seen as capital gains or income? If it is seen as income, what proportion of it is recognised in each period?
If all return are seen as capital gains and only realized at maturity. Then the book value of the two-year-zero would be $100$ at time $2$. and the book value of the four-year-zero would $49.86688$ (Purchase Price) at every date before maturity.
Would be great if other members could help me out on this one as well... As I am not particularly sure of myself on this one.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.