TM 661 Chapter 6 Solutions 1

The manager of a canned-food processing plant is trying to decide between two labeling machines. Their respective costs are as follows:

Machine A Machine BInitial Cost $15,000 $25,000Annual Operating Cost 1,600 400Salvage Value 3,000 6,000Life (in years) 7 10

The minimum attractive rate of return (MARR) is 10%.

Soln: Since a planning horizon is not specified, I will use LCM and the easiest method for LCM is to use Equivalent Uniform Annual Worth.

Alternative AEUAW =-15,000(A/P,10,7) - 1,600 + 3,000(A/F,10,7) = -15,000(.2054) - 1,600 + 3,000(.1054) = - 4,365

Alternative BEUAW = -25,000(A/P,10,10) - 400 + 6,000(A/F,10,10) = -25,000(.1627) - 400 + 6,000(.0627) = -4,091

EUAWB < EUAWA Choose B

TM 661 Chapter 6 Solutions 2

A $250,000 piece of machinery is installed and is to be depreciated over 5 years. You may assume that the salvage value at the end of 5 years is $ 0. The method of depreciation is to be 200% declining balance with conversion to straight line using the half-year convention (you may only deduct 1/2 year of depreciation in year 1). Establish a table showing the depreciation and the end of year book value for each year.

Soln:DDB for year 1 = 250,000 x 0.4 = 100,000 x 1/2

= 50,000DSl for year 1 = 250,000/5 = 50,000 x 1/2

= 25,000DSL for year 2 = 200,000/4.5 = 44,444

t D200 DSL Bt

0 250,0001 50,000 25,000 200,0002 80,000 44,444 120,0003 48,000 34,286 72,0004 28,800 28,800 43,2005 28,840 14,4006 14,400 0

TM 661 Chapter 6 Solutions 3

A company is thinking of investing in a new filter for a smokestack. The project will cost $750,000 which will be capitalized by investing $500,000 internally and borrowing the remaining $250,000. The loan is to be repaid over a 3 year period at 10% interest. Annual returns are expected to be $200,000 per year with a $100,000 salvage value at the end of year 5. The table below shows the project cash flow and loan repayment schedule. Complete the partial table below. MACRS deductions are based on a 3 year property class life. If the MARR is 20%, compute the Net Present Worth on an after tax cash flow basis.

Year Principle Interest Total Pmt. Loan Bal.Amt. Financed $250,000 0 $250,000Interest 10% 1 75,529 25,000 100,529 $174,471Period of Loan 3 2 83,082 17,447 100,529 $91,390Payment -100,529 3 91,390 9,139 100,529 $0Tax rate 34%MARR 20%

Project Loan Loan Before Tax MACRS MACRS Taxable Tax After Taxt Cash Flow Principle Interest Cash Flow % deduct Income 34% Cash Flow

0 (750,000) 250,000 (500,000) (500,000)1 200,000 75,529 25,000 99,471 33.3% 249,975 (74,975) (25,492) 124,9632 200,000 83,082 17,447 99,471 44.5% 333,375 (150,822) (51,280) 150,7513 200,000 91,390 9,139 99,471 14.8% 111,075 79,786 27,127 72,3444 200,000 200,000 7.4% 55,575 144,425 49,105 150,8965 200,000 200,000 200,000 68,000 132,0006 200,000 200,000 200,000 68,000 132,0007 300,000 300,000 300,000 102,000 198,000

NPW = $475,972