First guess for interest rates

When asked to find the interest rate i for Index linked securities, i believe we use the coupon rate as a first guess - is this correct?

Can we also use the coupon rate as a first guess for Fixed interest securities?

And in which cases do we use the first order binomial approximation (1+i)^n≈(1+ni) ? Is this only applicable when trying to find a first guess for the internal rate of return?

Any clarifications would be really helpful.

Thank you

 

Please disregard the title of this thread being "Chapter 13 - Example page 14". I don't know how to remove it...

 

Hi sir, thank you for your comment.

I didn't quite understand what you mean by "the annualised capital gain".

Lets say I have a 5-year FI bond, the price is 990 and the redemption 1100. Coupons are £80 per annum (payable half-yearly in arrears). Income tax 25% and Capital Gains tax 30%.

From what you said, I understand that to get the first guess I should do:

([Net annual coupon income] + [Net capital gain])^1/n ?

i.e. ([0.75*80]+[0.3*(1100-990)])^1/5 which is approx. 2.5%

But if I follow the method you demonstrated:

i.e. (Redemption/Purchase Price)^1/n = (1100/990)^1/5=1.11.. so first guess would be (1.11-1)*100=11%

I am not quite sure which of the 2 methods above I should follow..

 

I can understand the net annual coupon payment bit.

For the net annual capital gain: we do [0.7*(1100/990)]^1/5=0.951 and if I subtract 1 from this I get -0.049=-4.9%

I don't understand how your calculations get 2%. Am I missing something else?

Also, would you be able to give us an example for finding the first guess for IRR? How does the "average time and average payment" method you mentioned works?

Thank you very much for all the help.

 

For the net annual coupon payment, think about it this way: Redemption is 1100, but we have to pay CGT. Hence, after tax, the gain is equal to:

(1100-990)*0.7 = £77

Meaning that in fact our redemption payment is worth £1067 (i.e. 990+77). Now, the annualised return based on this redemption payment is:

(1067/990)^(1/5) = 1.01509 ..

Meaning that the return is approximately 1.5%. At least this is what is intuitive to me.

Personally, for first guesses I usually just use the calculator to write the RHS of the value equation using ANS in place of (1+i), then simply type a starting point that looks in the right ball park (say 1.05), press UP and = so that it replaces ANS with my guess. Personally, this has been much faster for me that either trying to find the sensible right guess by hand or using the TABLES function on a calculator (which tends to take time to calculate, especially if you have a wide range of possible values).

IMO with IRR questions knowing how to use your calculator and memory functions etc. well really helps whittle down the time it takes to find first guesses and to interpolate etc.

Good luck.

BTW: you feeling confident for the exam? I'm kind of ready now I think ... make mistakes still in questions but usually calculation errors. Wordy questions still need some work I think.