Question

The NSW Government is building a new airport in Western Sydney. The airport will take 6 years to build and require $1.5 billion in outlays at the end of each of those 6 years. The airport is expected to produce revenue of $2 billion in years 7 and 8 and then $3.5 billion per annum in perpetuity from year 9 onwards. What is the value of this investment now to the NSW Government if the cost of capital is 11% p.a. compounded annually?

Answer 1

Given cost capital = 11% per annum.

Capital outflow each year = $1.5 billion at the end of each year for 6 years.

Accordingly , let us calculate the present value of investment with the help of table below.

	Capital investment( In Million $)	Discount Factor	Present Value
	1,500.00	0.90	1,351.35
	1,500.00	0.81	1,217.43
	1,500.00	0.73	1,096.79
	1,500.00	0.66	988.10
	1,500.00	0.59	890.18
	1,500.00	0.53	801.96
Present Value of investment	6345.807

Let us also caculate the NPV of the project.

Present value of cash inflows.

Year	Cash Inflows	Discount factor	Present Value( $ in million)
7	2,000	0.4817	963.3168
8	2,000	0.4339	867.8530

Present value of perpetuity = 3500/0.11 = $31818.18( A/i)

A = Annual Cash inflow

i = Annual Interest rate.

This value is at the end of year-8, Now we will calculate the present value = 31818.18*0.4339 = 13805.91

Total present value of cash inflows is $13805.91+867.853+963.3168 = $15637.08

NPV = 15637.08 - 6345.807 = $9291.273

Note - All amounts are calculated in Million $