Question

Odense Counsel has received a proposal to build a new multipurpose outdoor sports stadium. The expected life of the stadium is 20 years and there will be no cost or no value after this. It will be financed with a 20-year loan (8 percent interest rate annually/cost of capital). The stadium's primary tenant will be Odense's football team (OB). In the project proposal, it is anticipated that the site will also be used for rock concerts and college and high school sports. Odense Counsel does not pay any taxes. The costs and estimated revenues are presented next: Cash inflows OB's Lease payment Concerts Rent from local schools 6,500,000 DDK per year 3,500,000 DKK per year 500,000 DDK per year Cash Outflows Construction costs 90,000,000 DKK General maintenance (including labor) 2,400,000 DDK per year Anticipate that maintenance will increase with 2 percent annually Required: 1. Should Odense Counsel build the stadium (assume all payments are made at the end of the year)? 2. OB have threatened to move out of Odense in case the proposal of building the new stadium will not be realized! The Odense Counsel financial controller estimates, that an OB move like this will cost Odense Counsel 2,000,000 DDK per year for the first 10 years (from year 0 to 10) in lost taxes, parking and other fees. Taken this additional information into consideration: Should Odense Counsel build the stadium? State your reasoning.

Answer 1

Solution 1:
To determine if the stadium should be built or not, we need to determine the Net Present Value (NPV) of the stadium. If the NPV is positive, the stadium should be built, else the proposal should be rejected.
NPV is determined by = (Present Value of Cash inflows - Present Value of Cash outflows)

Given, cost of capital = 8%

Present Value of Cash inflows:
Total Annual Cash inflow -

Particulars	Amount in DDK
OB's Lease payments	6,500,000
Concerts	3,50,0000
Rent from schools	500,000
Total	10,500,000

PV Annuity Factor @ 8%, 20 years = 9.8181

Therefore, PV of Cash inflows = 10,500,000 * 9.8181 = 103,090,050 ................ (I)

Present Value of Cash outflows:
Total construction cost = 90,000,000 (incurred at year 0)
General maintenance = 2,400,000 (increases @2% per year for 20 years)
Interest expense (8% of construction cost) = 7,200,000 (per year for 20 years)

PV of construction cost = 90,000,000 .......(a)
PV of General maintenance cost:

Year	Maintenance Cost	PV Factor @ 8%	PV of Maintenance Cost
1	2400000	0.9259	2222222.22
2	2448000	0.8573	2098765.43
3	2496960	0.7938	1982167.35
4	2546899	0.7350	1872046.94
5	2597837	0.6806	1768044.34
6	2649794	0.6302	1669819.65
7	2702790	0.5835	1577051.89
8	2756846	0.5403	1489437.90
9	2811983	0.5002	1406691.35
10	2868222	0.4632	1328541.83
11	2925587	0.4289	1254733.95
12	2984098	0.3971	1185026.51
13	3043780	0.3677	1119191.70
14	3104656	0.3405	1057014.39
15	3166749	0.3152	998291.36
16	3230084	0.2919	942830.73
17	3294686	0.2703	890451.25
18	3360579	0.2502	840981.73
19	3427791	0.2317	794260.53
20	3496347	0.2145	750134.94
		Total	27247706.00 .............(b)

PV of Interest expense = (Interest expense * PV Annuity Factor @ 8%, 20 years)
= 7,200,000 * 9.8181
= 70,690,320 .....................(c)

Therefore, total PV of cash outflows = (a)+(b)+(c)
= 187,938,026 .....................(II)

Therefore, NPV = (I) - (II)
= 103,090,050 - 187,938,026
= (84,847,976)
As the NPV is negative, i.e the PV of cash outflows exceed the PV of cash inflows, the Stadium should not be built.

Solution 2:
In case the Stadium is not built and OB quits, the estimated cost will be 2,000,000 per year for 10 years.
Therefore, PV of the cost will be = 2,000,000 * PV factor @8% for 10 years
= 2,000,000 * 6.7101
= 13,420,200

As the PV of the costs of OB quiting Odense is still less that the NPV of the cost of building the stadium (i.e 13,420,000 < 84,847,976), Odense should not change their decision, and therefore the stadium should not be built.