Annualizing a 4 Month IRR & Simple Interest

CFA Level I Quant
#1

Hello,

I have CFs whereby:

Jan 1 - Apr 30: CF = 100 1 May - Aug 30: CF = 20 Sep 1 - Dec 30: CF = 0 31 - Dec: CF = -142.64

Solving for the 4 Month IRR, I get 6.28% Annualizing this IRR: (1+6.28%)(1/3)-1 => 20.05% However I am having trouble equating the annualized IRR because of the second CF, here’s what I mean:

4 Month IRR

100*(1+6.28%)3 + 20*(1+6.28%)2 => 142.64 (so this is correct as it equals the last CF)

Annualized IRR

100*(1+20.05%) + 20*(1+20.05%) => 144.05 (this is not equal to the last CF)

Can someone point out my mistake please?

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Also I would like to ask, if I have a T-bill with a face value (or par value) of $100,000 and 150 days until maturity is selling for $98,000.

  • The BDY is 4.8% and this is the “360-Day Annualized Rate of Return with simple interest” BDY = 2000/100000 x 360/150 So I decided to see if this equates: Simple Interest + Principal => Principal + [Principal * Simple Interest * # of times you get simple interest] 98000 + [98000 * 4.8% * 1 Year] ~ 102,704 With Compound Interest The EAY of the question is (100,000/98000)(365/150)-1 EAY => 5.04% 98000*(1+5.04%) => 102,938

Why is there a difference? Thank you

#2

It appears that the cash flows were:

  • +100 on 1/1
  • +20 on 5/1
  • −142.64 on 12/31

In that case, I get 6.2803% as the 4-month IRR.

To get the annual IRR:

1 + IRRannual = (1 + IRR4-month)3

= 1.0628033

= 1.200490

IRRannual = 0.200490 = 20.0490%

The problem with your last line is that it says that you’re investing 20 for the entire year. In fact, you’re investing 20 for only 8 months. Try:

100(1 + 20.0490%) + 20(1 + 20.0490%)8/12

#3

BDY is a discount yield, not an add-on yield. This means that it’s computed on 100,000, not on 98,000. But you’re trying to use it as an add-on yield (i.e., you’re multiplying 98,000 by the BDY, instead of multiplying 100,000 by the BDY).

Also, BDY is computed using a 360-day year, whereas EAY is computed using a 365-day year.

#4

Thank you so much Sir!

#5

My pleasure.

#6

Sir, may I ask you a follow up question within the context of the bond question concerning equivalence of yields:

  • When you have a HPY of 2% in 150 days, and you find its equivalent simple 360 day annual yield of 4.8% (say the BEY ), do you then conclude the following: I am indifferent between (1) Purchasing a bond that matures in 150 days for $98,000 and earning $100,000 and thus earning 2% Yield (2) Depositing 98,000 at the beginning of the year and earning 4.8% Interest at the end of the year [360 days]

Or do you conclude:

  • I am indifferent between (1) Depositing $98,000 in a bank account that earns 2% Simple Interest every 150 Days (2) Depositing $98,000 in a bank account that earns 4.8% Interest in 360 Days

Thank you this is the last bit of confusion I had after re thinking the question, I believe it is the latter.

#7

Error

#8

Calculate it.

(98000 x 2% x 360/150) - (98000 x 4.8% x 1)

=> 0

=> Indifference (so its the latter option)!