Confusion in Pricing T-Bill one, methods, interest, discount, face

lxwarr30

Why can not we price the t-bill using the present value formula and get the same answer as by applying the discount on the face value and then subtracting it from the face value?

E.g. $100,000 tbill pays 5% in interest with one month remaining to maturity

Book's method:
Purchase price = $100,000 - [ .05 x (1/12) x ($100,000) ] = $995,833.33

Present value method:
Purchase Price = $100,000 / [ 1 + 0.05 x (1/12) ] ^ 1 = $99,585.06

Why both these methods are not giving the same answers?

jim8z3

Um, because they are different formulas...

The first one is just an approximation.

Note that the the second formula assumes monthly compounded returns.

Jolyn

T-bills are just like zero cupon bonds, aren't they? So I think they should be valued using the second formula. I hope I'm not missing any concept over here :S

JoeyDVivre

Correction in first post:

Book's method:
Purchase price = $100,000 - [ .05 x (1/12) x ($100,000) ] = $99,583.33

RobertA

It's because the T-Bill was invented before the calculator and it's a lot easier to compute the first method by hand.

kamara5

Hmm alrite thanks guys. I got it. First one is easy to calculate as it ignores the compounding of interest whereas Second one will give you the more accurate and meaningful answer.

dece2011

SpyAli Wrote:
-------------------------------------------------------
> Hmm alrite thanks guys. I got it. First one is
> easy to calculate as it ignores the compounding of
> interest whereas Second one will give you the more
> accurate and meaningful answer.


Yes, but do remember the "more accurate and meaningful answer" could give you the wrong price if the "easy" formula was the one used to calculate the discount rate from the market price.

There is one market price, and you have to know which "convention" was used to calculate if you wish to recover the market price from the discount rate.