Question

8. 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?

Answer 1

1)

To make that decision we need to calculate the net present value of the project

NPV = Present value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

NPV = 110,000,000 * [1 - 1 / (1 + 0.06)²⁵] / 0.06 - 2,500,000,000

NPV = 110,000,000 * [1 - 0.232999] / 0.06 - 2,500,000,000

NPV = 110,000,000 * 12.783356 - 2,500,000,000

NPV = -1,093,830,823

It does NOT make sense to build the new facility as it has a negative NPV

2)

IRR is the interest rate that makes it indifferent in accepting or rejecting the project

IRR is the rate that makes NPV equal to 0

NPV = 110,000,000 * [1 - 1 / (1 + R)²⁵] / R - 2,500,000,000

Using trial and error method, i.e., after trying various values for R, lets try R as 0.75%

NPV = 110,000,000 * [1 - 1 / (1 + 0.0075)²⁵] / 0.0075 - 2,500,000,000

NPV = 110,000,000 * [1 - 0.829609] / 0.0075 - 2,500,000,000

NPV = 110,000,000 * 22.718755 - 2,500,000,000

NPV = 0

Therefore, IRR is 0.75%