Calculator END/BGN mode

CFA Level I
#1

I have just read :

Only use BGN mode if the problem says “Starting today” or “Starting immediately” or ”Starting at the beginning of this…”

When it says starting today or immediately, then you know these are annuity due type of question, that is payment is due today or immediately.

When the problem says “Beginning next ……” or “Starting at the end of this….” this implies that the payment is not due immediately so you use your END mode as usual.

Is the above correct?

Thanks in advance

#2

correct

#3

Thanks

So I guess

* Annuity due: BGN (beginning of the year)

* Ordinary annuity: END (end of the year)

Thanks for your reply

#4

Alternatively, you don’t need to use BGN mode if you don’t want to. You can always first value the cash flows as an ordinary annuity and then multiply by the factor (1+ r), where r is the periodic interest rate, to get the value of an equivalent annuity due.

e.g.: If discount rate is 10%, what is the value of a security that pays $100 per annum for three years starting today?

if you prefer not to use BGN mode:

* You already know one $100 cash flow is at t=0. Just use you calculator to value an ordinary annuity with N=2, and add the $100 cash flow at t=0 to the PV of this 2yr ordinary annuity -> $100 + $173.55 = $273.55 OR

* Calculate the PV of a N= 3 ordinary annuity => 248.685; then multiply by (1+r) => 248.685 x (1.10) = 273.55

When you get problems like " A security pays $100 per annum for three years beginning in 2-years. If the discount rate is 10%, what is the price today ?"

if you do not use BGN mode : value as a N=3 ordinary annuity at t=1, and then discount back one period to t=0

if you prefer BGN mode : value as a N=3 annuity due at t=2, and then discount back two periods.

Whether you choose to use BGN or not, a quick timeline will always help keep things straight.

#5

A couple other things to keep in mind:

In an Ordinary Annuity (END mode):

  • The Present Value is “as of” one period before the first payment
  • The Future Value is calculated at the same time as the last payment

In an Annuity Due (BGN mode):

  • The Present Value is as of the same time as the first payment
  • The Future Value is calculated as of one period after the last payment

These distinctions become important when solving some two-part problems (like with a deferred annuity, or when you make a number of payments and then let the balance grow without further payments for a number of additional periods)