Question

Explain what Present Value and Future Value are in you own words. What is the difference between the Present Value of $ and the Present Value of an Annuity? What is a perpetuity?

Answer 1

Present value is the current worth of the future money or the Cash that we are likey to obtain in future. The present value is calculated by using the discounting factors . The higher the discounting factor the lower the present value of future cash .

Future value is the vise versa of present value , this is determining the future rate of an investment( at a particular date ) or an asset by taking a constant growth rate into consideration .

Present value of dollar can be calculated by using the following formula

pv = Fv 1 ÷ (1+r)ⁿ

r = rate of return

n = number of Periods

Present value of annuity can be calculated by using

In PV of dollar there will be no additional inflows in the middle

In pv of annuity there will be amount added annually . So, both are different .

Perpetuty : Perpetuity refers to an infinite amount of time. In finance, perpetuity is a constant stream of identical cash flows with no end. The present value of a security with perpetual cash flows.

For example, if a company is projected to make $100,000 in year 10, and the company’s cost of capital is 8%, with a long-term growth rate of 3%, the value of the perpetuity is:

= [Cash FlowYear 10 x (1 + g)] / (r - g)

= ($100,000 x 1.03) / (0.08 - 0.03)

= $103,000 / 0.05

= $2.06 million

This means that $100,000 paid into a perpetuity, assuming a 3% rate of growth with an 8% cost of capital, is worth $2.06 million in 10 years. Now, a person must find the value of that $2.06 million today. To do this, analysts use another formula referred to as the present value of a perpetuity.