Question

Text needs to be at least 350 words

Give your own definition of the term present value, and as part of your answer, explain why present values are dependent on interest rates. Would the present value amount be more or less if you compounded more frequently than once a year? Explain in detail why?

Answer 1

Present value of any cash flow in the future is the equivalent worth of present money which should be obtained to give up the future cash flow and still remain in a situation of no profit or no loss. Thus it is the equivalent worth of a future cash flow translated into the current day.

Present value is dependent on interest rates because in order to give up on future cash flow we must receive a cash flow today which when compounded at the interest rate would amount to the same value we are giving up in the future.

Suppose that in 10 years time, we are to receive a cash flow of $ 1000. And we give up the future cash flow in order to receive $ 100 today. Then the implied interest rate is:

• 100*(1+i)^10 = 1000
• (1+i) = 10^(1/10)
• i=1.258 – 1 = 0.258
• Thus the implied interest rate i = 0.258

The present value would be less if we compounded more frequently.

This is because the relationship between PV & FV is :

PV = FV/(1+i)^n

So if FV =100 & i= 10% & n= 2 compounded annually

Then PV = 100/(1+10%)^2 = 82.64

Also if FV =100 & i= 10% & n= 2 compounded semi-annually

Then PV = 100/(1+10%/2)^4 = 82.27

Clearly PV is less for more frequent compounding.