Question

Consider the following investment opportunity: Initial cost $ 100,000 Additional cost at end of Year 1 150,000 Benefit at end of Year 1 0 Annual benefit per year at end of Years 2- 10 20,000 With interest at 5 %, what is the benefit-cost ratio for this project?

Answer 1

The benefit-cost ratio for this project is 0.766.

Step-by-step explanation:

The benefit-cost ratio is a way to measure the profitability of an investment opportunity.

To calculate the benefit-cost ratio, we need to divide the present value of the benefits by the present value of the costs.

In this case, the initial cost is $100,000, and the additional cost at the end of Year 1 is $150,000.

The benefit at the end of Year 1 is $0, and the annual benefit from Years 2 to 10 is $20,000.

To calculate the present value of the costs and benefits, we need to discount them using the interest rate of 5%.

Using the formula for present value, the present value of the costs is:

$100,000 + $150,000/(1 + 0.05)

= $242,424.24.

The present value of the benefits is:

$0 + $20,000/(1 + 0.05)² + $20,000/(1 + 0.05)³ + ... + $20,000/(1 + 0.05)¹⁰

= $185,739.95.

Therefore, the benefit-cost ratio is

$185,739.95 / $242,424.24

= 0.766.