Question

Your company is considering adding a new production line in order to meet increasing product demand. The investment will be financed at an interest rate of 8% compounded annually. The new line will cost $650,000 in procurement and installation. An additional $21,000 will be incurred as annual operating and maintenance (O & M) cost. Additional annual revenue by using the new line is estimated to be $112,000. If the company wants to “break-even” by investing in the extra production line in 10 years. What advice will you give the company with this investment? What could be altered to make the investment more attractive?

Answer 1

We need to calculate the NPV of the investment:

• Annual CF = Additional revenue-O&M costs
  • Annual CF = 112000-21000 = 91000
• To break even the NPV should = 0:

Year	CF	Discount Factor		Discounted CF
0	$ -6,50,000.00	1/(1+0.08)^0=	1	1*-650000=	-6,50,000.00
1	$       91,000.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*91000=	84,259.26
2	$       91,000.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*91000=	78,017.83
3	$       91,000.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*91000=	72,238.73
4	$       91,000.00	1/(1+0.08)^4=	0.735029853	0.735029852796453*91000=	66,887.72
5	$       91,000.00	1/(1+0.08)^5=	0.680583197	0.680583197033753*91000=	61,933.07
6	$       91,000.00	1/(1+0.08)^6=	0.630169627	0.630169626883105*91000=	57,345.44
7	$       91,000.00	1/(1+0.08)^7=	0.583490395	0.583490395262134*91000=	53,097.63
8	$       91,000.00	1/(1+0.08)^8=	0.540268885	0.540268884501976*91000=	49,164.47
9	$       91,000.00	1/(1+0.08)^9=	0.500248967	0.500248967131459*91000=	45,522.66
10	$       91,000.00	1/(1+0.08)^10=	0.463193488	0.463193488084684*91000=	42,150.61
				NPV = Sum of all Discounted CF	-39,382.59

NPV is negative so this investment is not worth investing at 8%

If the interest rate is lower than 8%, the Negative NPV will improve. We need to find the rate at which NPV = 0, which is the IRR of the company. IRR can be calculated using either a financial calculator or excel or through hit and trial. Using Excel we get the IRR = 6.64% rounded to two decimal places

Year	CF	Discount Factor		Discounted CF
0	$ -6,50,000.00	1/(1+0.0663732594891085)^0=	1	1*-650000=	-6,50,000.00
1	$       91,000.00	1/(1+0.0663732594891085)^1=	0.937757948	0.937757948355806*91000=	85,335.97
2	$       91,000.00	1/(1+0.0663732594891085)^2=	0.87938997	0.879389969704491*91000=	80,024.49
3	$       91,000.00	1/(1+0.0663732594891085)^3=	0.824654934	0.824654933794758*91000=	75,043.60
4	$       91,000.00	1/(1+0.0663732594891085)^4=	0.773326719	0.773326718816865*91000=	70,372.73
5	$       91,000.00	1/(1+0.0663732594891085)^5=	0.725193277	0.725193277246431*91000=	65,992.59
6	$       91,000.00	1/(1+0.0663732594891085)^6=	0.68005576	0.680055759832036*91000=	61,885.07
7	$       91,000.00	1/(1+0.0663732594891085)^7=	0.637727694	0.637727694107639*91000=	58,033.22
8	$       91,000.00	1/(1+0.0663732594891085)^8=	0.598034214	0.598034214036059*91000=	54,421.11
9	$       91,000.00	1/(1+0.0663732594891085)^9=	0.560811338	0.560811337601031*91000=	51,033.83
10	$       91,000.00	1/(1+0.0663732594891085)^10=	0.525905289	0.525905289363419*91000=	47,857.38
				NPV = Sum of all Discounted CF	0.00