Investment Appraisal Techniques

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Invest­ment Apprais­al Tech­niques

Net Cash Receipt: Dif­fer­ence between money com­ing in and going out.

A) Types of Tech­niques

These fall into two broad cat­egor­ies:

Tra­di­tion­al tech­niques, includ­ing the Account­ing Rate of Return (ARR) and Pay­back

Dis­coun­ted Cash Flow (DCF) tech­niques, includ­ing Net Present Value (NPV) and Intern­al Rate of Return (IRR)

1. The Account­ing (Aver­age) Rate of Return (ARR)

Prof­it­ab­il­ity is here expressed as an annu­al return on invest­ment.


Two altern­at­ive pro­jects for cap­it­al invest­ment, Pro­ject A and Pro­ject B, both involving the pur­chase of a new machine, are being con­sidered.

Pro­ject A requires an ini­tial invest­ment of Lm6,000. It will pro­duce net cash receipts (net cash flow) of Lm3,000 in Year 1, Lm4,000 in Year 2; and Lm8,000 in Year 3. It will have a scrap value of Lm1,200.

Pro­ject B will cost Lm12,000. It will pro­duce a net cash flow of Lm7,000 in Year 1; Lm8,000 in Year 2; and Lm9,000 in Year 3. It will then have a scrap value of Lm2,000.

Which pro­ject should be chosen?


Step 1: We will first add up the net cash receipts of the two pro­jects dur­ing their life, and divide the res­ult by the num­ber of years each pro­ject will last.

Pro­ject A: (Lm3,000 + Lm4,000 + Lm8,000) / 3 = Lm5,000

Pro­ject B: (Lm7,000 + Lm8,000 + Lm9,000) / 3 = Lm8,000

Step 2: We work out the Aver­age Invest­ment. This is found by adding up the open­ing and clos­ing val­ues and divid­ing by 2. (Note: Some account­ants and fin­an­cial man­agers do not work on â€˜Average Invest­ment’ but on â€˜Initial Invest­ment’ and would there­fore miss this step. Per­son­ally I do not agree with this meth­od) Pro­ject A: (Lm6,000 + Lm1,200) / 2 = Lm3,600

Pro­ject B: (Lm12,000 + Lm2,000) / 2 = Lm7,000 Step 3: We now cal­cu­late the depre­ci­ation to be suffered by the two pro­jects dur­ing their lives. Remem­ber that this is an â€œAccounting” rate of return, or profit, and account­ants take depre­ci­ation into con­sid­er­a­tion when cal­cu­lat­ing profits. Depre­ci­ation is a â€˜non-cash’ expense and would there­fore not have been included in

the cash flow fig­ures given to us.

Pro­ject A: (Lm6,000 – Lm1,200) = Lm4,800

Pro­ject B: (Lm12,000 – Lm2,000) = Lm10,000 Step 4: Cal­cu­late the depre­ci­ation on an annu­al basis:

Pro­ject A: Lm4,800 / 3 = Lm1,600

Pro­ject B: Lm10,000 / 3 = Lm3,333

We can now work out the ARR on the for­mu­la ARR = Aver­age Annu­al Profit Aver­age Invest­ment

To arrive at the â€˜annual profit’ we deduct depre­ci­ation from the cash flow. The ARR for the 2 pro­jects will there­fore be as fol­lows:

Pro­ject A: Lm5,000 – Lm1,600 = 94.4% Lm3,600

Pro­ject B: Lm8,000 – Lm3,333 = 66.7% Lm7,000

Note how ARR is expressed in per­cent­age terms.

2. Pay­back

The pay­back peri­od is the time it takes for the ori­gin­al amount inves­ted to be recovered. In cal­cu­lat­ing the pay­back peri­od, we must con­sider cash inflows (money in) and out­flows (money out) and not account­ing profit. Non-cash items, such as depre­ci­ation and trans­fers to reserves, are there­fore excluded.

For illus­tra­tion we shall take the pre­vi­ous example:


Pro­ject A (Lm)

Pro­ject B (Lm)

Y0 out­flow



Y1 inflow



Y2 inflow



Y3 inflow



Y3 inflow (scrap)



The solu­tion will be as fol­lows:
Pro­ject A: There is an out­flow of Lm6,000 in Y0. Lm3,000 of this will be recovered
in Y1, leav­ing a bal­ance of Lm3,000 to be recovered in Y2.
In Y2 we get inflows for the whole year of Lm4,000 which is more than the bal­ance
of Lm3,000 which still needs to be recovered, Assum­ing con­stant inflows dur­ing the
year, we will recov­er those Lm3,000 in Y2 after 9 months.
The total pay­back peri­od for the pro­ject is there­fore 1 year 9 months.
Pro­ject B: When you work it out in the same way you get a pay­back peri­od of 1 year
7.5 months.

Con­clu­sion: All things being equal, you would choose Pro­ject B since it has the short­er pay­back peri­od.

3. Net Present Value (Import­ant)

Before we learn how to com­pute this, we must under­stand the con­cept of the Time Value of Money.

Invest­ment means spend­ing money now in the expect­a­tion of get­ting future returns. To know wheth­er the returns are large enough to pro­duce a profit or sur­plus, we need a way to com­pare money returns in the future with money out­flows (i.e. invest­ment now).

A given amount of money now is worth more than the same amount in the future for the fol­low­ing reas­ons:

Abil­ity to spend it: money held now can be spent imme­di­ately to sat­is­fy your wants.
Reduc­tion of Risk: until the money is actu­ally received, there is a risk that you will
not receive it.
Abil­ity to invest: even if the money is not required now, it could be inves­ted and earn
interest, and so accu­mu­late to a lar­ger sum in the future.
Let us sup­pose that money today can be inves­ted at 10% interest, Then, Lm100
inves­ted today will accu­mu­late (com­pound­ing annu­ally) to the fol­low­ing amounts:
after 1 year (Lm1001.10) = Lm110.00 after 2 years (Lm1101.10) = Lm121.00 after 3 years (Lm1211.10) = Lm133.10

Thus, using an interest rate of 10% a year, the future value in 3 years’ time of Lm100 now will be Lm133.10. We can say the same thing the oth­er way round: the present value of Lm133.10 to be received in 3 years’ time is Lm100.

In com­put­ing present val­ues we can either use a sim­ple for­mu­la or ready-made dis­count­ing factor tables, like the ones attached to this handout. If we look at these tables, we find that the dis­count­ing factor (D.F.) at 10% for 3 years is 0.751. We will mul­tiply the Lm133.10 we get in 3 years’ time by this factor to get the Present Value (P.V.):

P.V. = Lm133.100.751 = Lm99.96 i.e. Lm100 *

(if we use 5-fig­ure tables the D.F. will be 0.75131, and the P.V. would be Lm99.999)

Hav­ing under­stood the prin­ciple of the Time Value of Money, we can pro­ceed to under­stand the Net Present Value (NPV) meth­od of Invest­ment Apprais­al.

The NPV meth­od cal­cu­lates a project’s ‘profit’ by com­par­ing cash pay­ments (or out­flows) with cash receipts (or inflows) at the same point in time. It does this by dis­count­ing future cash flows back to the present (Y-); and then com­par­ing the total present value of the net future cash receipts with the present value of the cash pay­ments related to the cap­it­al inves­ted in the pro­ject.


Alpha Ltd. is con­sid­er­ing the pur­chase of a new machine. This requires an invest­ment of Lm8,000 now, and will last for 5 years, dur­ing which it will pro­duce goods which would be sold for Lm20,000 per year. The expec­ted costs include wages of Lm5,000 per annum and mater­i­als of Lm11,000 per annum. The com­pany dis­counts its cap­it­al pro­jects at 10%.

Using the NPV meth­od of invest­ment apprais­al, would you advise the com­pany to pur­chase the machine?


Y0 Y1 Y2 Y3 Y4 Y5

Invest­ment -8,000


Receipts 20,000 20000 20000 20000 20000

Wages -5,000 -5000 -5000 -5000 -5000

Mater­i­als -11,000 -11000 -11000 -11000 -11000

Net Cash
Flow -8,000 4,000 4,000 4,000 4,000 4,000
D.F. @ 10% 1 0,909 0,826 0,751 0,683 0,621

Value -8,000 3,636 3,304 3,004 2,732 2,484
If we add up the net cash flows from Y1 to Y5, and sub­tract the ini­tial out­flow in Y0, the Net Present value is found to be Lm7,160.