Question

Q.10: A private investor will pay SR 55 million to build a new bridge that is expected to last
well over 100 years. Assuming zero maintenance and operational costs:
a) How much toll revenue is required each year to yield a return of 6.75%?
b) If there are 500,000 vehicles per year that pay SR 5.25 for each crossing, what
is the yield on this investment?

Answer 1

Suppose the annual toll revenue is X

We know that the NPV of Ct is Ct/(1+r)^t where r is the interest rate, t is the time period.

So, we have 55 = X/(1+r)+X/(1+r)^2+...+X/(1+r)^100

55 = (X/r)[1-(1/1+r)^100]

55= (X/0.0675)[1-(1/1.0675)^100]

55*0.0675/0.9985438315=X

X=3.71791390912

So, $3,717.913.91 toll revenue is required to get an yield of 6.75%

b> The total annual income is number of vehicles* toll charge = 500,000*5.25 = 2625000 =2.625 million

55 = X/(1+r)+X/(1+r)^2+...+X/(1+r)^100

55 = (2.625/r)[1-(1/1+r)^100]

We get r= 0.04725 = 4.725% (Ans)