Question

Over the past six months, Six Flags conducted a marketing study on improving their park experience. The study cost $3.00 million and the results suggested that Six Flags add a kid's only roller coaster.

Suppose that Six Flags decides to build a new roller coaster for the upcoming operating season. The depreciable equipment for the roller coaster will cost $50.00 million and an additional $5.00 million to install. The equipment will be depreciated straight-line over 20 years.

The marketing team at Six Flags expects the coaster to increase attendance at the park by 5%. This translates to 107,097.00 more visitors at an average ticket price of $38.00. Expenses for these visitors are about 17.00% of sales.

There is no impact on working capital. The average visitor spends $22.00 on park merchandise and concessions. The after-tax operating margin on these side effects is 29.00%. The tax rate facing the firm is 34.00%, while the cost of capital is 10.00%.

What is the NPV of this coaster project if Six Flags will evaluate it over a 20-year period? (Six Flags expects the first year project cash flow to grow at 5% per year, going forward)
(Express answer in millions)

Answer 1

Keys:

• $3 million is irrelevant here.
• $55 million [installation cost is part of cost of asset] will be treated as cash outflow in year 0 and will be depreciated to 0 over 20 years, SLM. Depreciation per year will be $2.75 million. Tax savings on depreciation = $0.935 million per year.
• After tax cash flow in year 1 from ticket sales = 107097 x $38 x 83% x 66% = $2.23 million (rounded up)
• After tax cash flow in year 1 from merchandise = 107097 x $22 x 29% = $0.68 million.
• So, year 0 cash outflow = $55 million
• Year 1 cash inflow = ($2.23 + $0.68 + $0.935) million = $2.91 million. This will grow at 5% until year 20. Such cash flow will be added to the yearly tax savings on depreciation to find yearly cash flow.

Year	Cash Flow in millions	Discount Factor	DCF in millions
0	$ -55.0000	1	$ -55.0000
1	$     3.8450	0.909091	$      3.4955
2	$     3.9905	0.826446	$      3.2979
3	$     4.1433	0.751315	$      3.1129
4	$     4.3037	0.683013	$      2.9395
5	$     4.4721	0.620921	$      2.7768
6	$     4.6490	0.564474	$      2.6242
7	$     4.8347	0.513158	$      2.4810
8	$     5.0297	0.466507	$      2.3464
9	$     5.2344	0.424098	$      2.2199
10	$     5.4494	0.385543	$      2.1010
11	$     5.6751	0.350494	$      1.9891
12	$     5.9121	0.318631	$      1.8838
13	$     6.1609	0.289664	$      1.7846
14	$     6.4222	0.263331	$      1.6912
15	$     6.6966	0.239392	$      1.6031
16	$     6.9847	0.217629	$      1.5201
17	$     7.2872	0.197845	$      1.4417
18	$     7.6048	0.179859	$      1.3678
19	$     7.9383	0.163508	$      1.2980
20	$     8.2884	0.148644	$      1.2320
			$ -11.7937

NPV is -$11.7937 millions, which is negative. The project shall not be accepted.

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