Pgs 59, 64, 66, 68, 70, 72, 76 - Tuckman PQ set

[Dr. Jayanthi Sankaran]

Hi David:

For the problem below:

316.3. Sarah won a lottery that gives her a choice between two payouts. Neglecting any liquidity or counterparty risk, she simply wants to select the option with the higher present value. Her choices are between an annuity and a perpetuity:

I. The annuity will pay her $1,000 every six months, six months from today, over the next ten years; i.e., equivalent to a 2.0% semiannual coupon on $100,000 notional.

II. A perpetuity will pay her $500 every six months but forever

The yield curve happens to be conveniently flat at 8.0% at all maturities. The annuity does not pay anything beyond the final $1,000 "coupon" which is why we might refer to a "notional" rather than a "principal." Which of the following is correct?

a) The annuity has a higher present value regardless of the yield
b) The annuity has a higher present value at the current 8.0% yield but not necessarily at any yield
c) The perpetuity has a higher present value regardless of the yield
d) The perpetuity has a higher present value at the current 8.0% yield but not necessarily at any yield

Your answer appears to be:

316.3. B. The annuity has a higher present value at this 8.0% yield but not necessarily at any yield. The perpetuity PV = $1,000/08= $12,500; or, equivalently, $500/0.04 = $12,500. The annuity factor, A(T) = (1 - 1/1.04^20)/008 = 6.795163 such that PV = $2,000*6.795163 = $13,590.33.

At 8.0% yield, the annuity has a higher PV, however, as the yield decreases the perpetuity gains in relative value. For example, the annuity has an upper bound of $2,000 * 10 years = $20,000 as the yield (discount rate) approaches zero but the perpetuity has no such limit.

My answer using Tuckman's formula

Annuity(T) = (1/(y/2))*[1 - 1/(1 + y/2)*2T = (1/.04)*[1 - 1/(1.04)^20 = 13.59
Present value of Annuity (T) = $1,000*13.59 = $13,590.325 which is exactly what you get above

However, in the case of the perpetuity:
Present value of perpetuity = C/y = $1000/0.04 = $25,000. This is because since C = $1,000 = 1%*$100,000. And, y = 8%/2 = 4% (semiannual compounding).

So my answer turns out to be c) The perpetuity has a higher present value regardless of the yield..

Could you please explain why PV of the perpetuity is higher than the annuity at the 8% semi-annual yield?

Thanks
Jayanthi

 

[Deepak Chitnis]

Hi @Jayanthi Sankaran, just want to correct you the perpetuity which is paid semi annually is $500 as I can see you have calculated perpetuity with $1000, read the question and try again solving. Hope that helps.
Thank you

 

[Dr. Jayanthi Sankaran]

Hi Deepak,

Yes you are right - I did not read the question carefully - it is indeed $500 which works out to a Perpetuity = $500/4% = $12,500. I just naturally assumed it was the semiannual coupon = $1,000.

Thanks!
Jayanthi

 

[Nicole Seaman]

Hello @Jayanthi Sankaran

Please remember to post in the original forum threads when asking questions about the Practice Question Sets. This helps to keep our forum organized, reduces duplicate questions and also helps others who may have the same questions The threads are listed in the PQ set on the answer pages. Here is the thread to this specific question set: https://forum.bionicturtle.com/threads/p1-t4-316-tuckmans-yield-to-maturity-ytm.6926/.

I am awarding you one star because your question actually pointed out that there were some forum links that did not work in that document, including this specific question. Although the forum link was incorrect in the PQ set, I found the correct forum thread by clicking on P1.T4.Valuation in the Practice Questions section of the forum and searching for 316.3. The document has been corrected and uploaded to the study planner.

Thank you,

Nicole

 

[Dr. Jayanthi Sankaran]

Thanks for the star Nicole - appreciate it

Jayanthi

 

[Dr. Jayanthi Sankaran]

Hi Nicole,

Sorry about this - It so happens that there are a lot of student forum links not available in the original Tuckman's PQ set. Thanks for posting the above thread I had no option...

Jayanthi

 

[Nicole Seaman]

Hi Nicole,

Sorry about this - It so happens that there are a lot of student forum links not available in the original Tuckman's PQ set. Thanks for posting the above thread I had no option...

Jayanthi

Hi Jayanthi,

No problem! I went through and fixed every link that was not working, and added any links that were missing so this should not be an issue with this document again. If you happen to find these issues again in any of our PQ sets, please let me know so I can fix them and I can direct you to the correct thread where you can post your question.

Nicole

 

[Dr. Jayanthi Sankaran]

Hi Nicole,

The link for the student forum on page 57 (old page number), page 55 (new page number) in the PQ set for Tuckman Chapter 4: One Factor Risk-Metrics and Hedges is missing. Would be grateful if you would fix it

Thanks!
Jayanthi

 

[Dr. Jayanthi Sankaran]

Hi Nicole,

The links on Pages 59, 64, 66, 68, 70, 72, 76 of Tuckman's PQ set are not working. Would be grateful if you would fix it

Thanks!
Jayanthi

 

[Nicole Seaman]

Hello Jayanthi,

I will look into this as soon as I get a chance If it is the same Tuckman document that I fixed last week, all of the links were working when I published it so I will have to go back and look into the issue.

Thank you,

Nicole

 

[Nicole Seaman]

Hello @Jayanthi Sankaran

I have checked all of the links in that practice question set and they are all working. There was one spreadsheet link that I found that needed to be fixed, but other than that none of the other links were broken.

Thank you,

Nicole