Corporation Finance PV Problem-Car Lease You are considering buying a new car. T
ID: 2818545 • Letter: C
Question
Corporation Finance PV Problem-Car Lease You are considering buying a new car. The car costs $35,000. You can either lease it or purchase it with a three year loan. The lease arrangement requires that you pay $1 today and $450 per month for the next three years. You can also purchase the car with a three year loan at 8%. The loan would require monthly payments. Input the key facts into an excel spreadsheet. Then, use Excel to calculate the following information: a. What is the cash price of the car today? What is the PV of the loan arrangement? Is it equal to the cash price today? b. What is the PV of the lease arrangement? Why is it less than the cash price of buying the car? c. Note that the timeline must be modified when the customer purchases the car because he/she retains the value of the car at the end of the life of the loan. That benefit changes the "net" present value of the cost of buying the car. Suppose you believe you will sell the car for $23,000 at the end of the third year. What the new "net" present value of the car loan/purchase alternative? Is leasing still the less expensive alternative? d. What is the value of the car (in three years) that would make you indifferent between buying and leasing today? e. 23,Explanation / Answer
Current Price of Car /Loan Borrowed $35,000 Interest Rate of Loan per Year 8% Interest Rate of Loan per Month 0.006666667 Period 36 Month Beginning Pmt Interest Principal Ending Balance PV of PMT Amount per Month Lease Agreement PV of Lease Agreement Amount 1 $35,000.00 $1,096.77 $233.33 $863.44 $34,136.56 1089.509395 $ (450.00) $ (447.02) 2 $34,136.56 $1,096.77 $227.58 $869.20 $33,267.36 1082.294101 $ (450.00) $ (444.06) 3 $33,267.36 $1,096.77 $221.78 $874.99 $32,392.37 1075.126591 $ (450.00) $ (441.12) 4 $32,392.37 $1,096.77 $215.95 $880.82 $31,511.55 1068.006547 $ (450.00) $ (438.20) 5 $31,511.55 $1,096.77 $210.08 $886.70 $30,624.86 1060.933656 $ (450.00) $ (435.30) 6 $30,624.86 $1,096.77 $204.17 $892.61 $29,732.25 1053.907605 $ (450.00) $ (432.41) 7 $29,732.25 $1,096.77 $198.21 $898.56 $28,833.69 1046.928085 $ (450.00) $ (429.55) 8 $28,833.69 $1,096.77 $192.22 $904.55 $27,929.14 1039.994786 $ (450.00) $ (426.70) 9 $27,929.14 $1,096.77 $186.19 $910.58 $27,018.56 1033.107403 $ (450.00) $ (423.88) 10 $27,018.56 $1,096.77 $180.12 $916.65 $26,101.91 1026.265632 $ (450.00) $ (421.07) 11 $26,101.91 $1,096.77 $174.01 $922.76 $25,179.15 1019.469171 $ (450.00) $ (418.28) 12 $25,179.15 $1,096.77 $167.86 $928.91 $24,250.24 1012.71772 $ (450.00) $ (415.51) 13 $24,250.24 $1,096.77 $161.67 $935.10 $23,315.14 1006.01098 $ (450.00) $ (412.76) 14 $23,315.14 $1,096.77 $155.43 $941.34 $22,373.80 999.3486556 $ (450.00) $ (410.03) 15 $22,373.80 $1,096.77 $149.16 $947.61 $21,426.19 992.7304526 $ (450.00) $ (407.31) 16 $21,426.19 $1,096.77 $142.84 $953.93 $20,472.25 986.1560788 $ (450.00) $ (404.61) 17 $20,472.25 $1,096.77 $136.48 $960.29 $19,511.96 979.6252438 $ (450.00) $ (401.93) 18 $19,511.96 $1,096.77 $130.08 $966.69 $18,545.27 973.1376594 $ (450.00) $ (399.27) 19 $18,545.27 $1,096.77 $123.64 $973.14 $17,572.13 966.6930391 $ (450.00) $ (396.63) 20 $17,572.13 $1,096.77 $117.15 $979.63 $16,592.51 960.2910985 $ (450.00) $ (394.00) 21 $16,592.51 $1,096.77 $110.62 $986.16 $15,606.35 953.9315548 $ (450.00) $ (391.39) 22 $15,606.35 $1,096.77 $104.04 $992.73 $14,613.62 947.6141273 $ (450.00) $ (388.80) 23 $14,613.62 $1,096.77 $97.42 $999.35 $13,614.27 941.338537 $ (450.00) $ (386.23) 24 $13,614.27 $1,096.77 $90.76 $1,006.01 $12,608.26 935.104507 $ (450.00) $ (383.67) 25 $12,608.26 $1,096.77 $84.06 $1,012.72 $11,595.54 928.9117619 $ (450.00) $ (381.13) 26 $11,595.54 $1,096.77 $77.30 $1,019.47 $10,576.07 922.7600284 $ (450.00) $ (378.60) 27 $10,576.07 $1,096.77 $70.51 $1,026.27 $9,549.81 916.6490348 $ (450.00) $ (376.10) 28 $9,549.81 $1,096.77 $63.67 $1,033.11 $8,516.70 910.5785114 $ (450.00) $ (373.61) 29 $8,516.70 $1,096.77 $56.78 $1,039.99 $7,476.71 904.5481901 $ (450.00) $ (371.13) 30 $7,476.71 $1,096.77 $49.84 $1,046.93 $6,429.78 898.5578048 $ (450.00) $ (368.67) 31 $6,429.78 $1,096.77 $42.87 $1,053.91 $5,375.87 892.6070908 $ (450.00) $ (366.23) 32 $5,375.87 $1,096.77 $35.84 $1,060.93 $4,314.94 886.6957856 $ (450.00) $ (363.81) 33 $4,314.94 $1,096.77 $28.77 $1,068.01 $3,246.93 880.8236281 $ (450.00) $ (361.40) 34 $3,246.93 $1,096.77 $21.65 $1,075.13 $2,171.80 874.990359 $ (450.00) $ (359.00) 35 $2,171.80 $1,096.77 $14.48 $1,082.29 $1,089.51 869.1957209 $ (450.00) $ (356.63) 36 $1,089.51 $1,096.77 $7.26 $1,089.51 ($0.00) 863.4394578 $ (450.00) $ (354.26) Cash Price of Car Today $35,000.00 $ (16,200.00) $ (14,360.31) Total Amount Paid after taking Loan for 3 years(Entire PMT value in 3 years) $39,483.82 PV of Loan arrangement $35,000.00 (Equal to Cash Price of Car today) Total Lease Amount including $1(Entire lease amount in 3 years $ (16,199.00) PV of Lease Amount including $1 where Opportunity Cost of Capital is 8% $ (14,359.31) The lease amount is less because in this case the leasee is not owning the car.In the case of loan the loanee is the owner of the car Sale Value of Car after 3 years $ 23,000.00 PV of Sale value after 3 years(Discount Factor 8%) $ 18,258.14 NPV after purchasing/taking loan(Cost of Car-PV of Sale value after 3 years) $ (16,741.86) Difference between Leasing and Purchasing/Loan(PV of Lease Amount-NPV after purchasing/Taking Loan) $2,382.55 Leasing is still the least expensive option Value of Car that would make Leasing and Purchasing alternative the same(Sale Value of Car after 3 years+Difference between leasing and Purchasing/Loan amount in 3 years) 26001.32176