Question

Arlington, Texas wants to build a new recreation center. The estimated cost of construction cost us $14 million with annual staffing and maintenance costs of $520,000 per year over the twenty-year life of the center. At the end of the life of the center, Arlington expects to sell the land for $5 million, though that figure might be as low as $1 million and as high $ 9 million. City staff estimate first year benefits to be $2.1 million (accruing at the end of the first year). Staff expect annual benefits to grow in real terms at 4 percent, though this could be as low as 1 percent and as high as 6 percent. They assume that the real discount rate for use in Arlington should be 7 percent, thought it might be a percentage point higher or lower

a) What is the present value of net benefits for the recreation project using staff predictions?

b) What is the sensivity of the present value of net benefits to alternative predictions about land price, growth rate of annual benefits and the real discount rate.

Answer 1

A.

Information Provided	Units	Value
Construction Cost	$ mn	14
Staffing & Maintenance Cost	$ mn/year	0.52
Life of project	years	20
Land Value	$mn	5
First Year Benefit	$mn	2.1
Growth Rate	%	4%
Discount Rate	%	7%

Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Construction Cost	-14	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Staffing & Maintenance Cost	-	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52	-0.52
Benefits	-	2.1	2.2	2.3	2.4	2.5	2.6	2.7	2.8	2.9	3.0	3.1	3.2	3.4	3.5	3.6	3.8	3.9	4.1	4.3	4.4
Land Value	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	5
Cash Flow per Year	-14.0	1.6	1.7	1.8	1.8	1.9	2.0	2.1	2.2	2.4	2.5	2.6	2.7	2.8	3.0	3.1	3.3	3.4	3.6	3.7	8.9
Present Value per year	-14.0	1.5	1.5	1.4	1.4	1.4	1.4	1.3	1.3	1.3	1.3	1.2	1.2	1.2	1.2	1.1	1.1	1.1	1.1	1.0	2.3
Net Present Value	12.1

The above table can be duplicated in excel worksheet.

1. Construction Cost is outflow in 0th year

2. Staffing & Maintenance cost is outflow each year from operation of recreational center

3. Benefits is inflow from 1st year which is growing at 4%. From 2nd year onwards, use the formula:

Benefit of last year*(1+4%)

4. Land Value is inflow in last year (20th year)

5 Cash flow per year is summation of above four points

6 Present value per year is discount of cash flow per year using the formula:

Cash flow of nth year / (1+discount rate)^nth year

7 Net present value (NPV) is summation of all present value per year

B. By doing above and linking the formula in excel worksheet, you can easily change the inputs and see the sensitivity in different scenario.

1. Changing the land value from $5mn to $1mn and remaining inputs remain unchanged, the NPV will change from $12.1mn to $11.1mn

2. Changing the land value from $5mn to $9mn and remaining inputs remain unchanged, the NPV will change from $12.1mn to $13.2mn

3. Changing the growth rate from 4% to 1% and remaining inputs remain unchanged, the NPV will change from $12.1mn to $5.7mn

4. Changing the growth rate from 4% to 6% and remaining inputs remain unchanged, the NPV will change from $12.1mn to $17.7mn

5. Changing the discount rate from 7% to 6% and remaining inputs remain unchanged, the NPV will change from $12.1mn to $14.9mn

6. Changing the discount rate from 7% to 8% and remaining inputs remain unchanged, the NPV will change from $12.1mn to $9.8mn