Question

Your company is buying a new piece of equipment to reduce emissions in your factory. It will cost $8,000 to run next year (Year 1), and that operating cost will increase by 6% every year until Year 20, at which point you will discard it (after paying the operating cost- there is a cash flow in Year 20). You will also have to pay to maintain the equipment, which you estimate will cost $6.400 next year (Year 1) and increase by 7% per year until Year 20. Assume an interest rate of 5%. a. What is the equivalent present value in Year 0 of the total costs of the equipment? b. What is the equivalent future value in Year 20 of the total costs of the equipment? a. What is the equivalent present value in Year 0 of the total costs of the equipment? $ (Round to the nearest dollar) b. What is the equivalent future value in Year 20 of the total costs of the equipment? $ (Round to the nearest dollar)

Answer 1

a opereting Cost. first, celuuleting the present velue of uring the following fomunles Pu- Px ($1 (1+g) x (1+1) where P = leniedic payment = $8000 i i periodi interest rate 0.05. 9- grew rete a = 0.06 no no. of perieds - 20- 5 8000 C1-(4+0.00) (1+0.05)) 0.05-0.06 - 8000 / 1 (3.207135) * 0.376881]] = $ 458 89 per 872 88 = $ 166987.12 Now, Celculeting present Velief meinteince uring abou formule & information except Meintoinco Cost - Cost by growth rate & PU- 6400 x (1 - 114007) x (1 +0.05 Lo 0.05-0.0Z = 640 x 1 -((3.869684) (2768872 -0.02 $ 146.701,23 So, Prevent Value d hotel Cost - $ 159872888 & 168987.12 + $ 14670 1.23. $ 313688

Page No. Date 6 Operating Cost first Calculating the future Value of using the following formules future Value - Px (itish (149)". where, P = Periodic annuities = $ 8000 i periodi interest rate = 0.05 - ge growth rate - 0.06. nog periods = 20 f = 8000 litoos) - (1+0.06) 0.05-0.ob - Scoo (2.653298- 3.207135 Yuzo 69.6. Now uring abou & Celuuleting the futur vel & Mointedince formule a information encept growth Maintainence Cost: Cost rate. fu- 6400 (C1toost - (1 +0.07 ] 0.05-0.07 6400 (2-683298 - 3.869 864 L -0.02 $ 389301.12 - So Erriveent future leke & to tel Cost is - $ bere 443069.6 + 389301.12 - $ 1832371

a). Equivalent Present value in Year 0 of the total cost of equipment is $ 313688

b). Equivalent Future value in Year 20 of the total cost of equipment is $ 832371

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