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. Please provide detail explanation ( not in handwriting form which I may not recognize it )

Find out at what interest rate this bridge would be worth building.

The answer should be, “The bridge is worth building if the interest rate is NO MORE THAN ________.”

Answer 1

hurdle rate / required interest rate = r

Equating present value of all cash flows to zero:

800/(1 + r) + 1200/(1 + r)² = (300 - 100)/(1 + r)³ + 200/(1 + r)⁴ + .....

800/(1 + r) + 1200/(1 + r)² = 200/(1 + r)³ x 1/(1 - (1/(1 + r))

800/(1 + r) + 1200/(1 + r)² = 200/(1 + r)² x 1/r

800 x (1 + r) + 1200 = 200/r

r = 9.63%