# How do you know when to switch to BGN mode?

I am finding TVM okay but always struggle when it comes to questions were you have to switch to BGN mode.

Can someone help expain this to me?

In the regular END mode the calculator assumes that payments are done at the end of each period. This implies that every payment starting with the payment in the first year is discounted to the present.

However, when you have payments that are made at the beginning of a period you must switch your calculator to BGN mode. By doing so you ensure that you do not discount the first payment and start discounting with the second payment at the beginning of the second period.

Hence, the PV in BGN mode will be higher than in END mode. Just draw a timeline to visualize and it should become clear.

An alternative way to calculate the PV when having payments at the beginning at the period is to calculate the PV in END mode and then multiplicate the result with (1+i). Best,

Oscar

Many candidates struggle with this. Fortunately, it’s an easy problem to overcome.

First and foremost, when you’re starting out learning to work TVM problems, draw a time line. If you get into the habit of drawing a time line, you’ll soon discover that you have to work harder to get the wrong answer than to get the right one.

Write down when the payments occur, and the time as of which you want the value of those payments. For example, suppose that you’re told that you’re investing \$10,000 per year for 10 years at 5% per year and you want to know that present value. If the payments start today, then you’ll write \$10k at times 0, 1, 2, . . ., 9; if the payments start one year from today, then you’ll write \$10k at times 1, 2, 3, . . ., 10; if the payments start 5 years from today, then you’ll write \$10k at times 5, 6, 7, . . ., 14; and so on. In any case, you want the value as of time 0: today.

Now for the understnding of BGN mode versus END mode:

• In BGN mode, the PV will be as of the time of the first payment, and the FV will be as of the time of the last payment, plus 1.
• In END mode, the PV will be as of the time of the first payment, minus 1, and the FV will be as of the time of the last payment.

So, if your payments were at times 0, 1, 2, . . ., 9, PV in BGN mode will give you value as of time 0, while PV in END mode will give you the value as of time −1. In this case, clearly BGN mode is more efficient: in END mode you would have to multiply the answer by (1 + r) to bring it forward one period from t = −1 to t = 0.

If your payments were at times 1, 2, 3, . . ., 10, PV in BGN mode will give you value as of time 1, while PV in END mode will give you the value as of time 0. In this case, clearly END mode is more efficient: in BGN mode you would have to divide the answer by (1 + r) to bring it back one period from t = 1 to t = 0.

If your payments were at times 5, 6, 7, . . ., 14, PV in BGN mode will give you value as of time 5, while PV in END mode will give you the value as of time 4. In this case, neither mode is superior: you will have to discount the answer in either case – 4 periods in END mode or 5 periods in BGN mode – to get the value at time t = 0.

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thank you both!!!

My pleasure.

If your payments were at times 5, 6, 7, . . ., 14, PV in BGN mode will give you value as of time 5, while PV in END mode will give you the value as of time 4. In this case, neither mode is superior: you will have to discount the answer in either case – 4 periods in END mode or 5 periods in BGN mode – to get the value at time t = 0.

I am facing trouble understanding this part. For eg: If the question is saying payment will begin from year five.

Then in that case END mode i.e. Usually used for Ordinary annuity should calculate the payment for the end of year 5. Why preceding year, i.e. 4th year Payment is starting from the year 5. Ordinary annuity takes payment at the end of year. If it calculates for year 4 it means payment is made for year 4 ending but payment is starting from year 5.

It would be great if you can share your thoughts on this. Would really appreciate it. Thanks