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) |
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