Question

Building a bridge costs $2,000,000,000. and takes 2 years, of this cost, $800 million would be spent in year 1, and $1.2 billion in year 2. The bridge yields no benefits during its construction. but starting in year 3, It generates $300 million in benefits a year and costs $100 million a year to maintain. The bridge will last forever. The discount rate is r=0.05. Is this bridge worth building? Please provide detail explanation ( not in handwriting form which I may not recognize it )

Specifically, I want to know why is it that 4,000 million should be divided by (1.05)^2? not (1.05)^3 since the question says that revenue started to generate from the third year.

Answer 1

I = 0.05

cost in year 1 = 800 million

cost in year 2 = 1200 million

revenue per year = 300 m

Cost per year = 100 m

Net revenue per year from 3rd year onwards = 300 m - 100m = 200m

Present value of Perpetual annuity = A/i

Present value of benefit starting from EOY3 at EOY 2 = 200m/0.05 = 4000 m

Here present value calculated is at EOY 2, as benefits are starting from EOY3

Present value is always calculated 1 period prior to start of cash flow

P = F/(1+i)^t

Net present value = - 800m / 1.05 - 1200m/1.05² + 4000m/1.05²

= 1777.78 m

As NPV is positive, Bridge is worth building