Highway Engineering

60 Highway Engineering

quickly for investment in other ventures. This is particularly the case in times of

recession when cash availability may be limited. Highway projects with a rela-

tively short payback period can be attractive to a prospective developer. The

short time frame is seen as lessening the risk associated with a venture, though

road projects are seen as relatively low-risk enterprises.

The following formula enables the payback period to be derived:

(3.1)

where

C 0 =the initial construction cost of the highway project

NAS =net annual savings

Equation 3.1 assumes that a zero discount value is being used. This is not always

the case. If it is assumed that the net cash flows will be identical from year to

year, and that these cash flows will be discounted to present values using a value

i π0, then the uniform series present worth factor (P/A) can be utilised within

the following equation:

(3.2)

Equation 3.2 is solved to obtain the correct value ofnp.

The method is, however, widely used in its simplified form, with the discount

rate,i, set equal to zero, even though its final value may lead to incorrect judge-

ments being made. If the discount rate,i, is set equal to zero in Equation 3.2,

the following relationship is obtained:

(3.3)

Equation 3.3 reduces to np=C 0 /NAS, exactly the same expression as given in

Equation 3.1.

(^00)
1

=+

=

=

C Â t

t

tnp

NAS

0 =+CPAin 0 NAS(), , p

Payback period ()nCp =∏() 0 NAS

Example 3.1 – Comparison of toll-bridge projects based on payback analysis

A developer is faced with a choice between two development alternatives for

a toll bridge project: one large-scale proposal with higher costs but enabling

more traffic to access it, and the other less costly but with a smaller traffic

capacity. Details of the costs and revenues associated with both are given in

Table 3.5.

Calculate the payback period and check this result against the net present

value for each.

Contd