ch.10 P.16 redemption time

[iamminime]

Hi,
In ch.10 P.16, there is an example at the bottom where the worst scenario is latest redemption date since there is capital gain
However, when you defer capital gain, you also get 5 more years coupon

So, I try to redo this example with earliest redemption date:
P = 0.75*8*a(2):<10> + 100v^10 @7%
= 6* [1-1.07^(-10)]/[2*(1.07^0.5 - 1)] + 100 * 1.07^(-10)
= 6 * 7.144415392 + 100 * 1.07^(-10)
= 93.70142156

This is higher than the price in the example (91.83). So I think the worst scenario should be 10 years? Did I miss anything? Thanks a lot!

 

[Aman Sehra]

Thanks for your question. It is important to note that the capital gains test only tells us if there is a capital gain or not. This is then used to help us determine optimum optional redemption date, and thus the price. In the example you've mentioned, we have already determined there is a capital gain. The investor would want this as soon as possible, and so the minimum yield would be at the latest possible redemption date.

In order to think about this in terms of actual cashflows, I suggest you putting together an Excel spreadsheet based on the question mentioned above, showing columns: Time (0.5, 1, 1.5,and so on), Cashflows including a redemption payment (100?), the PV of these cashflows, and then a sum of all cashflows.

By setting the PV the same for both (say 110 for example) and keeping the interest rate variable, by using goalseek on the interest rate, you will see that all else being equal, if we had a 10 year term, or a 15 year term, the 15 year term would lead to a lower interest rate (ie the minimum yield).

I hope that helps

Aman
ActEd Tutor