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 )

Answer 1

calculation of present value of cash outflows :

cost of construction =$2000millions

Outflows in year-1=$800millions

Outflows in year-2=$1200millions

Present value of outflows=outflows*pvf

=$800*0.952+$1200*0.907

=$761.6+$1088.4

Present value of cash outflows =$1850millions

calculation of present value of cash inflows :

we get cash inflows for infinity of years so we required to calculate present value of perpetuity.

Yearly cash inflows =$300millions

Yearly maintenance cost=$100millions

Yearly net cash inflows =$200millions

Present value of perpetuity =D/r

D=yearly inflows

r=discounting rate

Present value of perpetuity =$200millions/0.05

=$4000millions

Above calculated present value of perpetuity is from 3rd year so we want calculate the present value for this amount .

Present value of cash inflows =$4000millions*0.9070

=$3628millions

NPV=P.V OF CASH INFLOWS -P. V CASH OUTFLOWS

NPV=$3628millions - $1850millions

NPV=$1778millions.

Here NPV is positive i.e cash inflows is more than cash outflows. So it is better to invest in that project.