Investment Appraisal

Posted on November 24th, 2021

An investment appraisal is used to assess the financial implications of a business case.

When documenting, always use a currency.

Time-Value

Time-value refers to the value of an item relative to a point in time. Currency is a prime example of this, as inflation dictates the value of $1 today will worth less in a year's time.

Applying this concept to a project means its projections need to account for the value of returns relative to the time.

From the perspective of the investors, this is referred to a return on investment, i.e., breaking even one year later is ultimately a loss.

Calculations

Present value $PV$ is an amount of money at-present.

Future value $FV$ is an amount of money in the future, corresponding to some prevent value.

Interest is the annual rate $R$ at which the present value changes; discount applies to future value retrospectively.

Lastly, the rates are applied across a number of annual periods $N$ . Since the rate for a given year is derived from the year previous, they are applied cumulatively.

FV = PV(1 + R)^{N} \\ PV = \frac{PV}{(1 + R)^{N}}

Present & Future Value Formulae

For example, 10% interest turns $1 into $1.10 across one year:

1(1 + 0.1)^1 = \$1.10

Methods of Appraisal

Payback

Payback is the most simple method, as it assumes the time-value of money remains the same.

Item	Year 1	Year 2	Year 3	Year 4	Year 5
Hardware Purchase	500	0	0	0	0
Hardware Maintenance	50	50	50	50	50
Software Purchase	180
Software Support	20	20	20	20	20
Cumulative Costs	750	820	890	960	1,030

Staff savings (per year)	220	220	220	220	220
Cumulative Savings	220	440	660	880	1,100

Cumulative Net Return(Difference)	-530	-380 (+150)	-230 (+150)	-80 (+150)	70 (+150)

Example of Payback calculations

Net Present Value

The Net Present Value (NPV) of the project applies a discount rate to the project's returns.

From the payback example, the initial (year 1) costs were $530. Each following year had a net return of $150, resulting in a $70 profit at year 5. However, this does not account for an changes in the value of currency.

By applying a discount rate of 0.2 (20%), the value of the project can be calculated relative to the present value; more importantly, the profits become relative to the initial costs:

Year	Net Profit (FV)	Rate	Net Profit (PV)
1	-530	$1\div{}(1.2)^0 = 1$	-530
2	+150	$1\div{}(1.2)^1 = 0.833$	125
3	+150	$1\div{}(1.2)^2 = 0.694$	104
4	+150	$1\div{}(1.2)^3 = 0.579$	87
5	+150	$1\div{}(1.2)^4 = 0.482$	72
			-141 👎

Example of NPV calculations

Internal Rate of Return

Internal Rate of Return (IRR) uses sensitivity analysis, which applies best case and worst case scenarios determine the elasticity of the costs. By providing a range of potential investment options, both the project management team and potential customers can understand the project's viability in different contexts.

IRR uses the same calculations as above, with changes to the input data, e.g., investment period, initial cost(s), net profit.