**Valuation**
**Concepts- value and return.**

Most financial decisions affect the firm’s cash flows in different time periods.

The recognitions of the time value of money and risk is extremely vital in financial decision making.

**Time Preference for Money.**

Time preference for money is an individual’s preference for possession, of a given amount of money now, rather than the same amount at some future time.

There for reasons attributed for it,
- Risk
- Preference for consumption
Investment opportunities

**Required rate of return **

Time preference of money is generally expressed by an interested rate.

**Required rate of return = risk free rate + risk premium**

Interest rate will be positive even in the absence of any risk it called risk free rate.

An investor will be exposed to some degree of risk there fore he would require a rate of return, called risk premium

The risk free rate compensates for time while risk premium compensates for risk. The required rate of return may also be called the opportunity cost of capital of comparable risk.

**Future value**

**For a single cash flow**

Fn = P (1+i) nFn = Future Sum

P = Principal

I = Interest rate

n = Number of years

**Future value of a lump Sum**

Fn = P X CVFn,iFn = Future Sum

P = Principal

CVF = Compound value factor for n periods at I rate of interest

**Future value of an annuity**

Annuity is fixed payment or receipt each year for a specified number of years.

**Fn = A X CVFAn,i**Fn = Future sum

CVFAn,I = Compound value factor for annuity = ((1+i)n-1)/i)

**Sinking Fund**Sinking fund is a fund which is created out of fixed payments each period to accumulate to a future sum after a specified period.

**A = Fn X SFFn,i**

SFFn,I = ((i)/(1+i)-1)

**Present Value**

Present value of a future cash flow is the amount of current cash that is of equivalent value to the decision maker.

For a single cash flow.

**P = Fn (1/(1+i)n)**

Present value of a lump sum.

**PV = Fn X PVAn,i**

Present value of an annuity.

**PV = A X PVFAn,i**

A = Annuity

PVFAn,i= Present value annuity factor

Present value of perpetuity.

Perpetuity is an annuity that occurs indefinites.

**P = A/ i**

Present value of an uneven cash flow.

**P = (A1 X PVF1) + (A2 X PVF2) +………………………+ (An X PVAFn)**

**Net Present Value**Net present value of a financial decision is the difference between the present value of cash inflows and the present value of cash outflows.

That the financial objective should be monetize the shareholders wealth. Wealth is defined as net present value.