Bond Yeild in HP 12C

[Delo]

Hull.04.12:
04.12a. A 3-year bond provides a coupon of 8% semiannually and has a cash price of 104.
What is the bond’s yield?

Any idea how do I solve for this in HP 12C?

4e -0.5y + 4e -1.0y + 4e -1.5y + 4e -2.0y + 4e -2.5y + 104e -3.0y = 100
With yield = 7.588%

 

[joshsmith0221]

@ckat, I'm not as familiar with HP 12C, but if convention is similar I can walk you through based on inputs in BA II Plus.

PV=-104
FV=104
N=6 (6 is used because this is the # of periods, ex. 3 years compounded semi-annually)
PMT=4 (coupon is half for same reason, coupon per 6 months)
compute (CPT) I/Y = 3.774
*2 for to scale to annual yield = 7.548%

Slightly off due to compounding.

Note that in BA II Plus this also required the adjusting of P/Y and C/Y (example in link below). Payments per year defaults to 12 in the BA II Plus so I changed to 1 to reflect a single payment per period N. Additionally, per suggestion online I adjusted C/Y to 1mm to have a close reflection to continuous compounding.

http://www2.fiu.edu/~barberj/quick.pdf
https://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=84339

@David Harper CFA FRM CIPM, can you please answer a couple of questions, as I found this thread after encountering a few issues of my own attempting to work out this formula via BA II Plus a second time around w/ a calculator instead of paper & pen.

- In general, is it your impression that the answers for these questions typically will be spaced far enough apart that differences in compounding will not cause for significant pause when evaluating the correct answer? I believe I saw in a prior thread a statement by you regarding correspondence w/ GARP related to this matter, but just want to be sure.
- Are there any other caveats that should be considered when adjusting P/Y and C/Y on the BA II Plus? Or in general using TVM functions? I want to try and become as fluid as possible before the exam using my calculator to solve these problems.

Thanks in advance for your reply.

 

[JC5]

@ckat, I'm not as familiar with HP 12C, but if convention is similar I can walk you through based on inputs in BA II Plus.

PV=-104
FV=104
N=6 (6 is used because this is the # of periods, ex. 3 years compounded semi-annually)
PMT=4 (coupon is half for same reason, coupon per 6 months)
compute (CPT) I/Y = 3.774
*2 for to scale to annual yield = 7.548%

Slightly off due to compounding.

Note that in BA II Plus this also required the adjusting of P/Y and C/Y (example in link below). Payments per year defaults to 12 in the BA II Plus so I changed to 1 to reflect a single payment per period N. Additionally, per suggestion online I adjusted C/Y to 1mm to have a close reflection to continuous compounding.

http://www2.fiu.edu/~barberj/quick.pdf
https://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=84339

@David Harper CFA FRM CIPM, can you please answer a couple of questions, as I found this thread after encountering a few issues of my own attempting to work out this formula via BA II Plus a second time around w/ a calculator instead of paper & pen.

- In general, is it your impression that the answers for these questions typically will be spaced far enough apart that differences in compounding will not cause for significant pause when evaluating the correct answer? I believe I saw in a prior thread a statement by you regarding correspondence w/ GARP related to this matter, but just want to be sure.
- Are there any other caveats that should be considered when adjusting P/Y and C/Y on the BA II Plus? Or in general using TVM functions? I want to try and become as fluid as possible before the exam using my calculator to solve these problems.

Thanks in advance for your reply.

Would the PV be the cash price as you mentioned and the FV be the face value or par value of 100?

 

[joshsmith0221]

The PV would be the cash price. However, I believe I've misstated the FV input as $104 and not $100. David's example video on the subject of YTM calculation with BA II Plus considers FV as $100 and it wouldn't make sense to have the additional $4 included in the future value as we consider 6 payments of $4 (which would include the final coupon with the face). However, when I use these inputs in the BA II Plus for the current example (with 1 P/Y and 1mm C/Y), my answer does not match the expected result.

EDIT: This has admittedly kept me from sleeping. After some further research the only possible explanation I can find appears to be caused by the application of current bond yield, which cannot be calculated via TVM functions on BA II Plus according to the below link, and yield to maturity, which can be calculated by TVM functions. Apologies for the confusion I've undoubtedly created here, certainly not my intention. I'm frankly not sure if another solution exists, will try to look further.

http://tvmcalcs.com/calculators/apps/baiiplus_bond_yields

 

[heretolearn]

Hi all,
I am really confused by this question and David's suggested answer - for years I have calculated bond yield as shown above:

PV=-104
FV=100
N=6
PMT=4
--> Solve for I/Y = 3.2553 * 2 = 6.51%

Why does DH come up with 7.588? And Hull with 6.407%? This question seems so basic that I am a bit worried that what I thought was a really easy answer now seems wrong?

Would much appreciate if someone could help me out here.

Thank you!

 

[Deepak Chitnis]

Hi @heretolearn, when you calculate the yield using calculator it assume semi annual compounding but hull assume continuouse compounding frequency so you need to convert 6.51% semi annual compounding to continuouse like:LN(1+6.51%/2)*2=6.4-629% or 6.407%. Hope that helps.
Thank you

 

[heretolearn]

Thank you Deepak!!