Question

Suppose New York wants to build a new facility to replace Madison Square Garden. Assume that the cost of building a new arena in midtown Manhattan is $2.5 billion and that all the costs occur right away. Also assume that New York will receive annual benefits of $110 million for the next 25 years, after which the new arena becomes worthless. Does it make financial sense to build the new facility if interest rates are 6 percent? At what interest rate will we be indifferent between accepting and rejecting this project? Make sure to show your work.

Answer 1

Solution

In this question

Initial investment= 2.5 billion

Annual inflow= 110 million= .11 billion

NPV = Sum of present values of all inflows- Initial investment

Sum of present values of inflows can be calculated by considering this as an annuity of .11 billion for 25 years

PV of annuity= Annuity amount*[(1-(1/(1+r)^n)/r]

Here Annuity amount = .11 billion

r=6%

PV = .11*((1-(1/(1.06)^25)/.06)

Solving we get PV= 1.40617

Therefore NPV = 1.40617- 2.5=-1.09383

Since NPV is <0 therefore financially it does not make sense to go ahead with project

Now Interest rate at which we will be indifferent at accepting or rejecting the project where NPV will be 0

Therefore

NPV = Sum of present values of all inflows- Initial investment

Putting NPV= 0

Sum of present values of all inflows= Initial investment

PV of annuity= Initial investment

Annuity amount*[(1-(1/(1+r)^n)/r]=2.5

We have to find r

.11*[1-(1/(1+r)^25))/r=2.5

[1-(1/(1+r)^25))/r=22.727

Solving we get r= .0075

Rate at which we will be indifferent = .75%