Question

The Ocean City water park is considering the purchase of a new log flume ride. The cost to

purchase the equipment is $5,000,000, and it will cost an additional $380,000 to have it installed. The equipment has an expected life of six years, and it will be depreciated using a MACRS 7-year class life. Management expects to run about 150 rides per day, with each ride averaging 25 riders. The season will last for 120 days per year. In the first year the ticket price per rider is expected to be $5.25, and it will be increased by 4% per year. The variable cost per rider will be $1.4, and total fixed costs will be $425,000 per year. After six years, the ride will be dismatled at a cost of $215,000 and the parts will be sold for $450,000. The cost of capital is 8.5%, and its marginal tax rate is 35%.

a. Calculate the initial outlay, annual after-tax cash flow for each year, and the terminal cash flow.

b. Calculate the NPV, IRR, and MIRR of the new equipment. Is the project acceptable?

c. Create a Data Table that shows the NPV, IRR, and MIRR for MACRS classes of 3, 5, 7, 10, 15 and 20 years. What do you conclude about the speed of depreciation and the profitability of an investment?

d. Using Goal Seek, calculate the minimum ticket price that must be charged in the first year in order to make the project acceptable.

Answer 1

Formula	Year (n)	0	1	2	3	4	5	6
(Purchase price+installation cost)	Initial outlay (IO)	(53,80,000)
	Number of rides/day (a)		150	150	150	150	150	150
	Number of riders/ride (b)		25	25	25	25	25	25
	Number of days/year ('c)		120	120	120	120	120	120
Increasing at 4% pa	Ticket price/rider (d)		5.25	5.46	5.68	5.91	6.14	6.39
	Variable cost/rider ('e)		1.40	1.40	1.40	1.40	1.40	1.40
(a*b*c*d)	Total sales (S)		23,62,500	24,57,000	25,55,280	26,57,491	27,63,791	28,74,342
(a*b*c*e)	Total variable cost (VC)		6,30,000	6,30,000	6,30,000	6,30,000	6,30,000	6,30,000
	Fixed cost (FC)		4,25,000	4,25,000	4,25,000	4,25,000	4,25,000	4,25,000
From the 7-year MACRS dep. Sch.	Depreciation (D)		7,68,802	13,17,562	9,40,962	6,71,962	4,80,434	4,79,896
	Cost of dismantling (CD)							2,15,000
(S-VC-FC-D-CD)	EBIT		5,38,698	84,438	5,59,318	9,30,529	12,28,357	11,24,446
35%*EBIT	Tax @35%		1,88,544	29,553	1,95,761	3,25,685	4,29,925	3,93,556
(EBIT-Tax)	Net Income (NI)		3,50,154	54,885	3,63,557	6,04,844	7,98,432	7,30,890
	Add: Depreciation (D)		7,68,802	13,17,562	9,40,962	6,71,962	4,80,434	4,79,896
(NI+D)	Operating Cash Flow (OCF)		11,18,956	13,72,447	13,04,519	12,76,806	12,78,866	12,10,786
	Salvage value (sv)							4,50,000
	Book value at the end of Year 6 (bv)							7,20,382
sv-(sv-bv)*tax	After-tax salvage value (ASV)							5,44,634
(IO+OCF+ASV)	FCF	(53,80,000)	11,18,956	13,72,447	13,04,519	12,76,806	12,78,866	17,55,420
1/(1+d)^n	Discount factor @ 8.5%	1.000	0.922	0.849	0.783	0.722	0.665	0.613
(FCF*Discount factor)	PV of FCF	(53,80,000.00)	10,31,295.58	11,65,832.11	10,21,318.25	9,21,310.36	8,50,503.95	10,75,976.02
Sum of all PVs	NPV	6,86,236.26
	IRR	12.42%

a).

Year (n)	0	1	2	3	4	5	6
FCF	(5,380,000)	1,118,956	1,372,447	1,304,519	1,276,806	1,278,866	1,755,420

7-year MACRS depreciation schedule:

Year	Dep. %	Dep. Exp.	Ending BV
0			53,80,000
1	14.29%	7,68,802	46,11,198
2	24.49%	13,17,562	32,93,636
3	17.49%	9,40,962	23,52,674
4	12.49%	6,71,962	16,80,712
5	8.93%	4,80,434	12,00,278
6	8.92%	4,79,896	7,20,382
7	8.93%	4,80,434	2,39,948
8	4.46%	2,39,948	-

b). NPV = 686,236.26

IRR = 12.42%; MIRR (using 8.5% cost of capital) = 10.69%

Since NPV is positive and IRR/MIRR are greater than the cost of capital, the project is acceptable.

c). Changing the depreciation schedule, the respective NPV, IRR and MIRR are as follows:

Depreciation schedule	3-year	5-year	7-year	10-year	15-year	20-year
NPV	858,080.03	758,904.14	686,236.26	620,806.14	525,103.36	497,375.04
IRR	13.94%	13.02%	12.42%	11.92%	11.26%	11.07%
MIRR	11.21%	10.91%	10.69%	10.49%	10.20%	10.11%

(Note: Due to the answer word limit, it is not possible to put in MACRS depreciation schedule and NPV table for all.)

d). Using goal-seek, the break-even NPV occurs at a ticket price of $4.78 per rider so this is the minimum ticket price that must be charged in the first year for the project to be acceptable.