Present Value Or Discounted Value

Present Value or Discounted Value                    

We know that a dollar today is worth than a dollar tomorrow.

An understanding of the present value concept should enable us to answer a question that which would you prefer?

1000 dollar today or 2000 dollars 5 years from now

The answer to this question is that

What is 2000 dollars received at the end of ten years worth to you today?

This is done by finding the opportunity cost of capital

Opportunity Cost Of Capital

What is lost by not taking the next best investment Alternative?

Discount Rate Or Capitalization Rate

Suppose you could borrow or lend at 8 percent per annum this 8 percent will be your opportunity cost of capital and this 8 percent will also become the discount rate or capitalization rate.

Present Value is simply the reverse of compounding

Now Future Value would be

FV= Po (1 + i) power n

Now Rearranging terms, we solve for present value

PVo= Po=FV/ (1+ i) power n

PVIF (Present Value Interest Factor)

This reciprocal [1/(1 + i) power n] has its own name- the present value interest factor at i% for n periods (PVIF)

Back to the question that what is 2000 dollars received at the end of ten years’ worth to you today?

Now we can easily calculate Present value of 2000 dollars discounted at 8 percent per anum

PVo= FV (PVIF8%, 10) = 2000[1/ (1 + 0.08)] power 10

PVo= $926

You can also calculate Present value or discounted value factor by just entering figures

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Now, if we compare this present value amount ($926) received after ten years we would prefer to take $1000 today because in present value terms we would be better off by $74($1000-$926).

We have learnt one important rule now that

“The greater the interest rate, the lower the present value”