Question

In: Economics

Fresh Foods is considering the purchase of a new packaging system. The system costs $180623. The...

Fresh Foods is considering the purchase of a new packaging system. The system costs $180623. The company plans to borrow three-quarters (3/4) of the purchase price from a bank at 8% per year compounded annually. The loan will be repaid using equal, annualpayments over a 7-year period. The payments will be made at the end of each year for the life of the loan, with the first payment occurring at the end of year 1. The system is expected to last 19 years and have a salvage value of $24822 at the end of its life.

Over the 19-year period, the company expects to pay $601 per year for maintenance. In addition, the system will require an overhaul at the end of year 7 which will cost $13715. The system will save $2425 per year because of efficiencies. The company uses a MARR of 2% to evaluate investments. What is the equivalent uniform annual worth (EUAW) of this system?

Enter your answer as follows: 1234

Round your answer. Do not use a dollar sign ("$"), any commas (",") or a decimal point (".").

Hints: The loan interest is at a different interest rate than our MARR. How will this impact the problem?

The remainder of the purchase price (the amount we do not take out in the form of a loan) would be considered our initial cost, at year 0

Solutions

Expert Solution

We need to find net cash flow for each year and then find annual worth

Initial investment = 0.25*180623 = 45155.75

Loan value = 0.75*180623 = 135467.25

Loan interest rate = 0.08

Loan time period = 7 yrs

Overhaul in 7th year = 13715

salvage value = 24822

Total time of system = 19 yrs

MARR = 2%

Annual saving = 2425

Annual O&M Cost = 601

using excel

Year Invesetment & Overhaul Loan Paid Maintenance Savings Salvage value Net Cash Flow Discount Factor present value
0 -45155.75 -45155.75 1 -45155.75
1 -26019.52 -601.00 2425.00 -24195.52 0.980392 -23721.10
2 -26019.52 -601.00 2425.00 -24195.52 0.961169 -23255.98
3 -26019.52 -601.00 2425.00 -24195.52 0.942322 -22799.98
4 -26019.52 -601.00 2425.00 -24195.52 0.923845 -22352.92
5 -26019.52 -601.00 2425.00 -24195.52 0.905731 -21914.63
6 -26019.52 -601.00 2425.00 -24195.52 0.887971 -21484.93
7 -13715.00 -26019.52 -601.00 2425.00 -37910.52 0.870560 -33003.39
8 -601.00 2425.00 1824.00 0.853490 1556.77
9 -601.00 2425.00 1824.00 0.836755 1526.24
10 -601.00 2425.00 1824.00 0.820348 1496.32
11 -601.00 2425.00 1824.00 0.804263 1466.98
12 -601.00 2425.00 1824.00 0.788493 1438.21
13 -601.00 2425.00 1824.00 0.773033 1410.01
14 -601.00 2425.00 1824.00 0.757875 1382.36
15 -601.00 2425.00 1824.00 0.743015 1355.26
16 -601.00 2425.00 1824.00 0.728446 1328.69
17 -601.00 2425.00 1824.00 0.714163 1302.63
18 -601.00 2425.00 1824.00 0.700159 1277.09
19 -601.00 2425.00 24822.00 26646.00 0.686431 18290.63
-179857.49

Annual Worth = Present worth *(A/P, 2%, 19)

= -179857.49* 0.0637817

= -11471.63

Showing formula in excel

Year Invesetment & Overhaul Loan Paid Maintenance Savings Salvage value Net Cash Flow Discount Factor present value
0 =-180623*0.25 =B3+C3+D3+E3+F3 =1/(1+0.02)^A3 =H3*G3
1 =-PMT(8%,7,-0.75*180623) -601 2425 =B4+C4+D4+E4+F4 =1/(1+0.02)^A4 =H4*G4
2 =-PMT(8%,7,-0.75*180623) -601 2425 =B5+C5+D5+E5+F5 =1/(1+0.02)^A5 =H5*G5
3 =-PMT(8%,7,-0.75*180623) -601 2425 =B6+C6+D6+E6+F6 =1/(1+0.02)^A6 =H6*G6
4 =-PMT(8%,7,-0.75*180623) -601 2425 =B7+C7+D7+E7+F7 =1/(1+0.02)^A7 =H7*G7
5 =-PMT(8%,7,-0.75*180623) -601 2425 =B8+C8+D8+E8+F8 =1/(1+0.02)^A8 =H8*G8
6 =-PMT(8%,7,-0.75*180623) -601 2425 =B9+C9+D9+E9+F9 =1/(1+0.02)^A9 =H9*G9
7 -13715 =-PMT(8%,7,-0.75*180623) -601 2425 =B10+C10+D10+E10+F10 =1/(1+0.02)^A10 =H10*G10
8 -601 2425 =B11+C11+D11+E11+F11 =1/(1+0.02)^A11 =H11*G11
9 -601 2425 =B12+C12+D12+E12+F12 =1/(1+0.02)^A12 =H12*G12
10 -601 2425 =B13+C13+D13+E13+F13 =1/(1+0.02)^A13 =H13*G13
11 -601 2425 =B14+C14+D14+E14+F14 =1/(1+0.02)^A14 =H14*G14
12 -601 2425 =B15+C15+D15+E15+F15 =1/(1+0.02)^A15 =H15*G15
13 -601 2425 =B16+C16+D16+E16+F16 =1/(1+0.02)^A16 =H16*G16
14 -601 2425 =B17+C17+D17+E17+F17 =1/(1+0.02)^A17 =H17*G17
15 -601 2425 =B18+C18+D18+E18+F18 =1/(1+0.02)^A18 =H18*G18
16 -601 2425 =B19+C19+D19+E19+F19 =1/(1+0.02)^A19 =H19*G19
17 -601 2425 =B20+C20+D20+E20+F20 =1/(1+0.02)^A20 =H20*G20
18 -601 2425 =B21+C21+D21+E21+F21 =1/(1+0.02)^A21 =H21*G21
19 -601 2425 24822 =B22+C22+D22+E22+F22 =1/(1+0.02)^A22 =H22*G22
=SUM(I3:I22)

Rahul Sunny answered 2 years ago
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