# Economic assessment

Investment calculation — new plant

Present capitalised value method

The ventilation plant whole-life cost KL can be calculated as the sum of the investment cost K| and the capitalised operational costs KDcap- The operational costs must be paid annually and therefore be summated to a capitalised present value. This is carried out with the aid of a present capitalised value factor F.

The whole-life cost becomes:

Kl = K, + KDcap = K, + F — KD Equ 19.1

Where

KL = whole-life cost (currency)

K| = investment cost (currency)

KDcap = capitalised operational cost (currency)

F = present capitalised value factor

KD = annual operating costs (currency/annum)

The present capitalised value factor is calculated from the re­lationship:

^ 1 — (1 + r)-" c

F =—————- — Equ19.2

R

Where

F = present capitalised value factor

R = estimated annual profits (decimal)

N = number of years

Example:

Two alternative designs of ventilation plant have been pro­posed. Their cost review is as follows:

Investment I = Ј10000 annual operational costs = Ј1000

Investment II = Ј7500 annual operational costs = Ј1500

Which plant is more suitable from an economic point of view, if the estimated profits are 15% and the service life is 10 years?

If r = 15% and n = 10 years, the present capitalised value factor F = 5, from Figure 19.2.

Thus:

I KL = Ј10000 +5 x 1000 = Ј15000

II KL= Ј7500 +5 x 1500 = Ј15000

Both plants are similar in this particular instance. If it is probable that the service life will not exceed 10 years, then alternative II would normally be preferred since it requires a smaller initial capital investment.

 R * 5 % Figure 19.2 Present capitalised value factor

Annuity method

For the annuity method the annual plant costs are calculated and minimised. The annual costs consist of the sum of the an­nuity interest and repayments for a proposed loan which covers the investment cost and the annual operational costs.

K = A + KD = aF • K, + KD Equ 19.3

 Where K = annual cost (currency/annum) A = annuity (currency/annum) Kd = annual operating costs (currency/annum) AF = annuity factor (decimal) K, = investment (currency)

The annuity factor is identical to the reciprocal of the present capitalised value factor

AF = ~ Equ 19.4

And is determined by service life and estimated profit. Applying this method, for the two alternatives in the previous example:

10000

 I K = + 1000 = Ј3000

5

7500

+ 1500 = Ј3000

The two alternatives are equivalent, as before.

Posted in Fans Ventilation A Practical Guide