Chapter 12 - page 12

[The Warrior]

Can someone please help me to understand this.

For deferred income tax, the formula is given as
A = DNa_n^(2) + RNv^n - t1DNv^ka_n

here it is a_n at the last

but if we refer to the example given after this

it uses a_10^2 as the last term?

Thanks,
Warrior

 

[Edwin]

The payments in the example are made half yearly,

Consider that

a_n^2]i can be expresses as a_2n]i^(2)/2 and letting n' = 2n gives a_n']i(2)/2

 

[The Warrior]

nope Edwin...I am not able to understand it.

If you look at the formula, then the general formula comtains "...- t1DNv^ka_n"
and as I understood the DN is the amount obtained at the end of the year irrespective of the frequency of D payments.

So in the example also DN is used but for annuity, a_n^(2) is used?

 

[The Warrior]

Also, from page 25
1. why do we first calculate the nominal payments (i.e. cash actually received) and then payment in time 0 units?

2. what does this indicate?
ct*Q(t)/Q(0)

as I have seen that when we use the inflation index values to calculate the cashflow value at time t, it should be

ct
-----------
[Q(t)/Q(0)]

 

[Edwin]

QUOTE[Warrior]
nope Edwin...I am not able to understand it.
END QUOTE...

Working form first principles is usually easier for this type of questions:

PV = 6a_n^2 + 100v^10 - t1*3*v^(10/12) - t1*3*v^(16/12) - - - t1*3*v^(124/12)

= 6a_n^2 + 100v^10 - t1*3*v^(4/12)*[t1*v^(6/12) + t1*v^(12/12) + + + t1*v^(120/12)]

= 6a_n^2 + 100v^10 - t1*6*v^(4/12)*a_n^(2) @ 9%

HOW IS THAT WARRIOR??

 

[Edwin]

Also, from page 25

1. why do we first calculate the nominal payments (i.e. cash actually received) and then payment in time 0 units?

We want the real yield, if the question says for example that the payments are inflation adjusted we just calculate the actual payments by ct*Q(t)/Q(0), but if it asks us to find the real yield we have to express the payments themselves in real terms (today's money's terms).i.e time zero.

2. what does this indicate?

ct*Q(t)/Q(0)
[end QUOTE]

this is for non-lagged inflation, it is just the cash flows multiplied the inflation index.Without inflation at time t we get ct, but if we adjust to prevent inflation from corroding the value of our money we pay more i.e ct*Q(t)/Q(0)

as I have seen that when we use the inflation index values to calculate the cashflow value at time t, it should be

ct
-----------
[Q(t)/Q(0)]

------

 

[Mark Mitchell]

Chapter 12, page 12
The situation in Core Reading is that there is a single tax payment each year based on the total coupons paid in the previous year.

eg, in 2011 two coupons might be received in June and December, say, and the tax on both of the coupons is paid at the same time, say in April 2012.

For a bond with regular coupons, based on the above example, then there would be two coupons paid each year, needing a (2) annuity, but there would only be one tax payment each year (so no (2) on the annuity).

In the example following this part of Core Reading, the income tax is still deferred (ie paid after the coupons are), which is the topic of this section. But the situtation is different. The tax in this example is not paid in a single installment, but instead is paid four months after each coupon. So there will be two coupon payments each year, and two tax payments. Hence the (2) on the annuity for the tax payments.

The example is there to illustrate that you can get different situations described to you in the exam, and you have to read the question carefully to work out what to do.