A company has invested $10 million to construct a food irradiation plant with technology to destroy...

A company has invested $10 million to construct a food irradiation plant with technology to destroy organisms that cause spoilage and disease, thus extending the shelf life of the fresh produce and distances over which they can be shipped. The expected operating and maintenance costs (after taxes) would be $4 million at year 1 and increase by 2% each year. The plant is expected to have a useful life of 20 years. If the company's annual benefits (after taxes) are estimated to be $6 million after year 1 and increase by $100,000 each year, find the discounted payback period. The company's interest rate is 12%. (Provide excel spreadsheets for all problems)

Payback Period (Round to an integer):_______

Sketch of cash flow diagram:

Expert Solution

Annual net benefit (NAB) = Annual benefit - Annual O&M costs

In year 0, NAB = - $10 million

Year	Benefit ($)	Cost ($)	NAB ($)	PV Factor @12%	Discounted NAB ($)	Cumulative discounted NAB ($)
0		-100,00,000	-100,00,000	1.0000	-100,00,000	-100,00,000
1	60,00,000	40,00,000	20,00,000	0.8929	17,85,714	-82,14,286
2	61,00,000	40,80,000	20,20,000	0.7972	16,10,332	-66,03,954
3	62,00,000	41,61,600	20,38,400	0.7118	14,50,893	-51,53,061
4	63,00,000	42,44,832	20,55,168	0.6355	13,06,096	-38,46,965
5	64,00,000	43,29,729	20,70,271	0.5674	11,74,728	-26,72,237
6	65,00,000	44,16,323	20,83,677	0.5066	10,55,656	-16,16,582
7	66,00,000	45,04,650	20,95,350	0.4523	9,47,830	-6,68,752
8	67,00,000	45,94,743	21,05,257	0.4039	8,50,278	1,81,526
9	68,00,000	46,86,638	21,13,362	0.3606	7,62,100	9,43,626
10	69,00,000	47,80,370	21,19,630	0.3220	6,82,464	16,26,090
11	70,00,000	48,75,978	21,24,022	0.2875	6,10,606	22,36,696
12	71,00,000	49,73,497	21,26,503	0.2567	5,45,820	27,82,516
13	72,00,000	50,72,967	21,27,033	0.2292	4,87,461	32,69,977
14	73,00,000	51,74,427	21,25,573	0.2046	4,34,934	37,04,912
15	74,00,000	52,77,915	21,22,085	0.1827	3,87,697	40,92,609
16	75,00,000	53,83,473	21,16,527	0.1631	3,45,251	44,37,860
17	76,00,000	54,91,143	21,08,857	0.1456	3,07,143	47,45,003
18	77,00,000	56,00,966	20,99,034	0.1300	2,72,958	50,17,961
19	78,00,000	57,12,985	20,87,015	0.1161	2,42,317	52,60,277
20	79,00,000	58,27,245	20,72,755	0.1037	2,14,876	54,75,153

Discounted payback period (DPBP) is the time by when cumulative discounted NAB is zero.

DPBP lies between years 7 and 8. Therefore

DPBP = 7 + (Absolute value of cumulative discounted NAB in year 7 / Discounted NAB in year 8)

= 7 + (668,752/ 850,278) = 7 + 0.79 = 7.79 years

DPBP = 8 years

Cash flow diagram as follows (Values in $Million).

Rahul Sunny answered 2 years ago

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