The B-C ratio is calculated by finding the present value of the annual net benefits of the bridge investment using the interest rate and comparing it to the initial investment. The bridge generates around 65.45 cents for every invested dollar over a 20-year period at an 8% discount rate, resulting in a B-C ratio of 0.6545.
To calculate the conventional benefit-cost (B-C) ratio of the bridge investment project, we can follow these steps:
- First, we need to establish the net benefit stream. Since the annual benefit is $3 million and the annual maintenance cost is $2 million, the net benefit each year is $1 million.
- Second, we discount the net benefit to present value using the interest rate of 8% over the 20-year study period. This is done using the present value of annuity formula.
- Lastly, we compare the present value of the total benefits to the initial $15 million investment to obtain the B-C ratio.
The present value of annuity formula is:
PV = Pmt × ((1 - (1 + r)^-n) / r)
Where:
- PV is the present value of annuity
- Pmt is the annual payment (net benefit)
- r is the interest rate (expressed as a decimal)
- n is the number of periods
For this case:
Pmt = $1 million
r = 0.08
n = 20
The present value of the net benefits would be:
PV = $1 million × ((1 - (1 + 0.08)^-20) / 0.08)
PV = $1 million ×9.8181
PV = $9.8181 million
The B-C ratio is then calculated by dividing the present value of the net benefits by the initial investment:
B-C ratio = $9.8181 million / $15 million
B-C ratio = 0.6545
This means that for every dollar invested, the project generates approximately 65.45 cents in present value terms over the 20-year period at an 8% discount rate, which is less than 1, indicating that the project may not be economically viable.