Question
In: Finance
Sydney is deciding whether to buy or lease a vehicle for her personal use only. If...
Sydney is deciding whether to buy or lease a vehicle for her personal use only. If Sydney’s cost of funds is 8% per year, which of the following options should she select to acquire the new car?
She should buy the car with no down payment and $700 monthly payments for 5 years
She should buy the car with a $6,000 down payment and $600 monthly payments for 5 years
She should lease the car for $2,000 down, $500 monthly payments for 5 years, and a $10,000 payments at the end of the lease
She should lease the car for $4000 down, $550 monthly payments for 5 years, and a $5,000 payment at the end of the lease.
Solutions
Expert Solution
Hello Sir/ Mam
Evaluation Table of each of the options @ 8% cost of funds and calculation of Present Value :
| Option 1 | Option 2 | Option 3 | Option 4 | ||||||
| Time | Discounting Factor | Cash Flows | Present Value | Cash Flows | Present Value | Cash Flows | Present Value | Cash Flows | Present Value |
| 0 | 1.000 | $0.00 | $0.00 | $6,000.00 | $6,000.00 | $2,000.00 | $2,000.00 | $4,000.00 | $4,000.00 |
| 1 | 0.993 | $700.00 | $695.36 | $600.00 | $596.03 | $500.00 | $496.69 | $550.00 | $546.36 |
| 2 | 0.987 | $700.00 | $690.76 | $600.00 | $592.08 | $500.00 | $493.40 | $550.00 | $542.74 |
| 3 | 0.980 | $700.00 | $686.18 | $600.00 | $588.16 | $500.00 | $490.13 | $550.00 | $539.15 |
| 4 | 0.974 | $700.00 | $681.64 | $600.00 | $584.26 | $500.00 | $486.89 | $550.00 | $535.57 |
| 5 | 0.967 | $700.00 | $677.13 | $600.00 | $580.39 | $500.00 | $483.66 | $550.00 | $532.03 |
| 6 | 0.961 | $700.00 | $672.64 | $600.00 | $576.55 | $500.00 | $480.46 | $550.00 | $528.50 |
| 7 | 0.955 | $700.00 | $668.19 | $600.00 | $572.73 | $500.00 | $477.28 | $550.00 | $525.00 |
| 8 | 0.948 | $700.00 | $663.76 | $600.00 | $568.94 | $500.00 | $474.12 | $550.00 | $521.53 |
| 9 | 0.942 | $700.00 | $659.37 | $600.00 | $565.17 | $500.00 | $470.98 | $550.00 | $518.07 |
| 10 | 0.936 | $700.00 | $655.00 | $600.00 | $561.43 | $500.00 | $467.86 | $550.00 | $514.64 |
| 11 | 0.930 | $700.00 | $650.66 | $600.00 | $557.71 | $500.00 | $464.76 | $550.00 | $511.23 |
| 12 | 0.923 | $700.00 | $646.35 | $600.00 | $554.02 | $500.00 | $461.68 | $550.00 | $507.85 |
| 13 | 0.917 | $700.00 | $642.07 | $600.00 | $550.35 | $500.00 | $458.62 | $550.00 | $504.49 |
| 14 | 0.911 | $700.00 | $637.82 | $600.00 | $546.70 | $500.00 | $455.59 | $550.00 | $501.14 |
| 15 | 0.905 | $700.00 | $633.60 | $600.00 | $543.08 | $500.00 | $452.57 | $550.00 | $497.83 |
| 16 | 0.899 | $700.00 | $629.40 | $600.00 | $539.49 | $500.00 | $449.57 | $550.00 | $494.53 |
| 17 | 0.893 | $700.00 | $625.23 | $600.00 | $535.91 | $500.00 | $446.59 | $550.00 | $491.25 |
| 18 | 0.887 | $700.00 | $621.09 | $600.00 | $532.36 | $500.00 | $443.64 | $550.00 | $488.00 |
| 19 | 0.881 | $700.00 | $616.98 | $600.00 | $528.84 | $500.00 | $440.70 | $550.00 | $484.77 |
| 20 | 0.876 | $700.00 | $612.89 | $600.00 | $525.34 | $500.00 | $437.78 | $550.00 | $481.56 |
| 21 | 0.870 | $700.00 | $608.83 | $600.00 | $521.86 | $500.00 | $434.88 | $550.00 | $478.37 |
| 22 | 0.864 | $700.00 | $604.80 | $600.00 | $518.40 | $500.00 | $432.00 | $550.00 | $475.20 |
| 23 | 0.858 | $700.00 | $600.80 | $600.00 | $514.97 | $500.00 | $429.14 | $550.00 | $472.05 |
| 24 | 0.853 | $700.00 | $596.82 | $600.00 | $511.56 | $500.00 | $426.30 | $550.00 | $468.93 |
| 25 | 0.847 | $700.00 | $592.87 | $600.00 | $508.17 | $500.00 | $423.48 | $550.00 | $465.82 |
| 26 | 0.841 | $700.00 | $588.94 | $600.00 | $504.80 | $500.00 | $420.67 | $550.00 | $462.74 |
| 27 | 0.836 | $700.00 | $585.04 | $600.00 | $501.46 | $500.00 | $417.88 | $550.00 | $459.67 |
| 28 | 0.830 | $700.00 | $581.16 | $600.00 | $498.14 | $500.00 | $415.12 | $550.00 | $456.63 |
| 29 | 0.825 | $700.00 | $577.32 | $600.00 | $494.84 | $500.00 | $412.37 | $550.00 | $453.60 |
| 30 | 0.819 | $700.00 | $573.49 | $600.00 | $491.56 | $500.00 | $409.64 | $550.00 | $450.60 |
| 31 | 0.814 | $700.00 | $569.69 | $600.00 | $488.31 | $500.00 | $406.92 | $550.00 | $447.62 |
| 32 | 0.808 | $700.00 | $565.92 | $600.00 | $485.08 | $500.00 | $404.23 | $550.00 | $444.65 |
| 33 | 0.803 | $700.00 | $562.17 | $600.00 | $481.86 | $500.00 | $401.55 | $550.00 | $441.71 |
| 34 | 0.798 | $700.00 | $558.45 | $600.00 | $478.67 | $500.00 | $398.89 | $550.00 | $438.78 |
| 35 | 0.793 | $700.00 | $554.75 | $600.00 | $475.50 | $500.00 | $396.25 | $550.00 | $435.88 |
| 36 | 0.787 | $700.00 | $551.08 | $600.00 | $472.35 | $500.00 | $393.63 | $550.00 | $432.99 |
| 37 | 0.782 | $700.00 | $547.43 | $600.00 | $469.22 | $500.00 | $391.02 | $550.00 | $430.12 |
| 38 | 0.777 | $700.00 | $543.80 | $600.00 | $466.12 | $500.00 | $388.43 | $550.00 | $427.27 |
| 39 | 0.772 | $700.00 | $540.20 | $600.00 | $463.03 | $500.00 | $385.86 | $550.00 | $424.44 |
| 40 | 0.767 | $700.00 | $536.62 | $600.00 | $459.96 | $500.00 | $383.30 | $550.00 | $421.63 |
| 41 | 0.762 | $700.00 | $533.07 | $600.00 | $456.92 | $500.00 | $380.76 | $550.00 | $418.84 |
| 42 | 0.756 | $700.00 | $529.54 | $600.00 | $453.89 | $500.00 | $378.24 | $550.00 | $416.07 |
| 43 | 0.751 | $700.00 | $526.03 | $600.00 | $450.89 | $500.00 | $375.74 | $550.00 | $413.31 |
| 44 | 0.746 | $700.00 | $522.55 | $600.00 | $447.90 | $500.00 | $373.25 | $550.00 | $410.57 |
| 45 | 0.742 | $700.00 | $519.09 | $600.00 | $444.93 | $500.00 | $370.78 | $550.00 | $407.86 |
| 46 | 0.737 | $700.00 | $515.65 | $600.00 | $441.99 | $500.00 | $368.32 | $550.00 | $405.15 |
| 47 | 0.732 | $700.00 | $512.24 | $600.00 | $439.06 | $500.00 | $365.88 | $550.00 | $402.47 |
| 48 | 0.727 | $700.00 | $508.84 | $600.00 | $436.15 | $500.00 | $363.46 | $550.00 | $399.81 |
| 49 | 0.722 | $700.00 | $505.47 | $600.00 | $433.26 | $500.00 | $361.05 | $550.00 | $397.16 |
| 50 | 0.717 | $700.00 | $502.13 | $600.00 | $430.39 | $500.00 | $358.66 | $550.00 | $394.53 |
| 51 | 0.713 | $700.00 | $498.80 | $600.00 | $427.54 | $500.00 | $356.29 | $550.00 | $391.92 |
| 52 | 0.708 | $700.00 | $495.50 | $600.00 | $424.71 | $500.00 | $353.93 | $550.00 | $389.32 |
| 53 | 0.703 | $700.00 | $492.22 | $600.00 | $421.90 | $500.00 | $351.58 | $550.00 | $386.74 |
| 54 | 0.699 | $700.00 | $488.96 | $600.00 | $419.11 | $500.00 | $349.26 | $550.00 | $384.18 |
| 55 | 0.694 | $700.00 | $485.72 | $600.00 | $416.33 | $500.00 | $346.94 | $550.00 | $381.64 |
| 56 | 0.689 | $700.00 | $482.50 | $600.00 | $413.57 | $500.00 | $344.64 | $550.00 | $379.11 |
| 57 | 0.685 | $700.00 | $479.31 | $600.00 | $410.83 | $500.00 | $342.36 | $550.00 | $376.60 |
| 58 | 0.680 | $700.00 | $476.13 | $600.00 | $408.11 | $500.00 | $340.09 | $550.00 | $374.10 |
| 59 | 0.676 | $700.00 | $472.98 | $600.00 | $405.41 | $500.00 | $337.84 | $550.00 | $371.63 |
| 60 | 0.671 | $700.00 | $469.85 | $600.00 | $402.73 | $10,500.00 | $7,047.71 | $5,550.00 | $3,725.22 |
| $34,522.90 | $35,591.06 | $33,371.32 | $34,481.19 | ||||||
As it is clearly evident from the table, OPTION C requires the least amount of time adjusted cashflow. Hence, OPTION C is better.
I hope this solves your doubt.
Do give a thumbs up if you find this helpful.
jeff jeffy answered 1 year agoRelated Solutions
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