Question

Preform a benefit/cost analysis on the following project:

Expected costs: $5,000 today, $5,000 a year from today, and $5,000 two years from today

Expected revenue: $6,000 five years from today, $7,000 seven years from today, and $8,000 ten years from today.

Assume a 6% discount rate

The Net Present Value (NPV) of the project

The benefit/cost ratio

Is the project worth undertaking?

Answer 1

(1) NPV

PV of expected revenue ($) = 6,000 x P/F(6%, 5) + 7,000 x P/F(6%, 7) + 8,000 x P/F(6%, 10)

= 6,000 x 0.7473** + 7,000 x 0.6651* + 8,000 x 0.5584** = 4,484 + 4,656 + 4,467

= 13,607

PV of expected cost ($) = 5,000 + 5,000 x P/F(6%, 1) + 5,000 x P/F(6%, 2)

= 5,000 + 5,000 x 0.9434** + 5,000 x 0.8900* = 5,000 + 4,717 + 4,450

= 14,167

NPV ($) = PV of expected revenue - PV of expected cost = 13,607 - 14,167 = - 560

(2) Benefit/Cost ratio (BCR) = PV of expected revenue / PV of expected Cost

= $13,607 / $14,167 = 0.96

(3) Since NPV is negative and BCR is less than 1, project is not worth undertaking.