Fundamentals of Business

Investment analysis

There are two main approaches, Net Present Value (NPV) and Internal Rate of Return (IRR)
Key financial formulae
The following is the most important financial formulae.
It provides the key to almost all money problems.
Identify which variables are known and which one is to be calculated and choose the appropriate formula.

Where

PV = Present Value
FV = Future Value
R = Stream of income per conversion period
n = number of conversions period in total
r = rate of interest per conversion period as a proportion
k = number of convesion period per year
if k < 1, then r = i/k where i is the annual compound interest
Single payment
PV = FV ÷ (1 + r)n
FV = PV ÷ (1 + r)-n
Infinite streams of payments
PV = R ÷ r
Finite streams of payments
PV = [R1 X (1 + r)-1] + [R2 X (1 + r)-2] + ...+ [Rn x (1 + r)-n]
PV = R X [{1 - (1 + r)-n} ÷ r]
Formulae linking FV, PV, R, r and n
FV = [ Rn-1 x(1 + r)n-1] + [Rn-2 x (1 + r)n-2 + ...+ [R0 x (1 + r)0
FV = R x [{(1 + r)-n - 1} ÷ r]

Net Present Value = PV - Outlay (the amount spent to buy a capital asset)

Example
A machine is expected to produce output valued at £1250 next year, £950 in year 2, £700 in year 3 and £400 in year 4.
What present value of this stream of income, assuming an interest of 10% per annum?
Solution This involves a finite stream of income where the known facts are the rate of interest (r)
the number of periods (n) and the stream of income (R1, R2, ..., Rn)

The Present Value is to be found
Formula
Finite streams of payments
PV = [R1 X (1 + r)-1] + [R2 X (1 + r)-2] + ...+ [Rn x (1 + r)-n]
PV = [1250 X 1.10-1] + [950 X 1.10-2] + [700 x 1.10-3] + [400 X 1.10-4]
Therefore PV = £2720
The present value of the machine's output is £2720
If the machine cost £1500 its Net Present Value is
Net Present Value = PV - Outlay (the amount spent to buy a capital asset)
NPV = 2720 -1500 = £1220

Conclusion
A positive net present value indicates a project earns more than the chosen interest rate, hence, worth investing.
A zero net present value indicates the project will only Break even, hence, look for a lower interest rate.
A negative net present value indicates a project earns less than chosen interest, that is loss,
hence, not worth investing, discard it.