Question

Splash Planet

is considering purchasing a water park in​ Atlanta, Georgia, for

$1,920,000.

The new facility will generate annual net cash inflows of $481,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses​ straight-line depreciation, and its stockholders demand an annual return of 12​% on investments of this nature.

Future Value of Ordinary Annuity of​ $1
Periods	​1%	​2%	​3%	​4%	​5%	​6%	​7%	​8%	​9%	​10%	​12%	​14%	​15%
1	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2	2.010	2.020	2.030	2.040	2.050	2.060	2.070	2.080	2.090	2.100	2.120	2.140	2.150
3	3.030	3.060	3.091	3.122	3.153	3.184	3.215	3.246	3.278	3.310	3.374	3.440	3.473
4	4.060	4.122	4.184	4.246	4.310	4.375	4.440	4.506	4.573	4.641	4.779	4.921	4.993
5	5.101	5.204	5.309	5.416	5.526	5.637	5.751	5.867	5.985	6.105	6.353	6.610	6.742
6	6.152	6.308	6.468	6.633	6.802	6.975	7.153	7.336	7.523	7.716	8.115	8.536	8.754
7	7.214	7.434	7.662	7.898	8.142	8.394	8.654	8.923	9.200	9.487	10.09	10.73	11.07
8	8.286	8.583	8.892	9.214	9.549	9.897	10.260	10.64	11.03	11.44	12.30	13.23	13.73
9	9.369	9.755	10.16	10.58	11.03	11.49	11.98	12.49	13.02	13.58	14.78	16.09	16.79
10	10.46	10.95	11.46	12.01	12.58	13.18	13.82	14.49	15.19	15.94	17.55	19.34	20.30
11	11.57	12.17	12.81	13.49	14.21	14.97	15.78	16.65	17.56	18.53	20.65	23.04	24.35
12	12.68	13.41	14.19	15.03	15.92	16.87	17.89	18.98	20.14	21.38	24.13	27.27	29.00
13	13.81	14.68	15.62	16.63	17.71	18.88	20.14	21.50	22.95	24.52	28.03	32.09	34.35
14	14.95	15.97	17.09	18.29	19.60	21.02	22.55	24.21	26.02	27.98	32.39	37.58	40.50
15	16.10	17.29	18.60	20.02	21.58	23.28	25.13	27.15	29.36	31.77	37.28	43.84	47.58
16	17.26	18.64	20.16	21.82	23.66	25.67	27.89	30.32	33.00	35.95	42.75	50.98	55.72
17	18.43	20.01	21.76	23.70	25.84	28.21	30.84	33.75	36.97	40.54	48.88	59.12	65.08
18	19.61	21.41	23.41	25.65	28.13	30.91	34.00	37.45	41.30	45.60	55.75	68.39	75.84
19	20.81	22.84	25.12	27.67	30.54	33.76	37.38	41.45	46.02	51.16	63.44	78.97	88.21
20	22.02	24.30	26.87	29.78	33.07	36.79	41.00	45.76	51.16	57.28	72.05	91.02	102.4
21	23.24	25.78	28.68	31.97	35.72	39.99	44.87	50.42	56.76	64.00	81.70	104.8	118.8
22	24.47	27.30	30.54	34.25	38.51	43.39	49.01	55.46	62.87	71.40	92.50	120.4	137.6
23	25.72	28.85	32.45	36.62	41.43	47.00	53.44	60.89	69.53	79.54	104.6	138.3	159.3
24	26.97	30.42	34.43	39.08	44.50	50.82	58.18	66.76	76.79	88.50	118.2	158.7	184.2
25	28.24	32.03	36.46	41.65	47.73	54.86	63.25	73.11	84.70	98.35	133.3	181.9	212.8
26	29.53	33.67	38.55	44.31	51.11	59.16	68.68	79.95	93.32	109.2	150.3	208.3	245.7
27	30.82	35.34	40.71	47.08	54.67	63.71	74.48	87.35	102.7	121.1	169.4	238.5	283.6
28	32.13	37.05	42.93	49.97	58.40	68.53	80.70	95.34	113.0	134.2	190.7	272.9	327.1
29	33.45	38.79	45.22	52.97	62.32	73.64	87.35	104.0	124.1	148.6	214.6	312.1	377.2
30	34.78	40.57	47.58	56.08	66.44	79.06	94.46	113.3	136.3	164.5	241.3	356.8	434.7
40	48.89	60.40	75.40	95.03	120.8	154.8	199.6	259.1	337.9	442.6	767.1	​1,342	​1,779
50	64.46	84.58	112.8	152.7	209.3	290.3	406.5	573.8	815.1	​1,164	​2,400	​4,995	​7,218

​Next, determine the formula and calculate the accounting rate of return​ (ARR). ​(Round the percentage to the nearest tenth​ percent, X.X%.)

Average annual operating income	/	Average amount invested	=	ARR
	/		=		%

Answer 1

ARR = Average Annual Profit / Average Investment

Average Annual Profit Calculation :-

Cash Inflows for egiht years = $481,000 * 8 = $3,848,000

Depreciation on investment in eight years = $1,920,000 (we use all the value of investment for depreciation because we are using straight line method and investment value become zero at the end of the eight years)

Profit in eight years = $3,848,000 - $1,920,000 = $1,928,000

Average Annual Profit = $1,928,000/8 Years = $241,000

Average Investment = $1,920,000

ARR = $241,000 / $1,920,000 = 12.55%