You are considering whether to buy or lease a car. If you lease, you have to pay
ID: 2725716 • Letter: Y
Question
You are considering whether to buy or lease a car.
If you lease, you have to pay a refundable security deposit of $6 hundred, and a monthly lease payment of $424 for 3 years, with payments due at the beginning of the month.
If you buy, you will pay a downpayment of $25 hundred, and a monthly loan payment of $512, over the same period of time, with payments due at the end of the month. The car is estimated to have a residual value of $8 thousand at the end of this time.
If the appropriate discount rate is 6 percent, what is the relative benefit of buying as opposed to leasing?
Hint: find the present value of all the buy cash flows, and subtract the present value of all the lease cash flows. Pay attention to the signs!
Explanation / Answer
Details Discount rate =6% pa Discount rate =6%/12= 0.5% per month Discounting starts from month 2 as the payment is at the beginning of Month PV of Lease Month PV factor @0.5% Security Deposit Lease rental Net Costs PV of costs Month 1 1 600 424 1,024 1,024 Month 2 0.9950 424 424 422 Month 3 0.9901 424 424 420 Month 4 0.9851 424 424 418 Month 5 0.9802 424 424 416 Month 6 0.9754 424 424 414 Month 7 0.9705 424 424 411 Month 8 0.9657 424 424 409 Month 9 0.9609 424 424 407 Month 10 0.9561 424 424 405 Month 11 0.9513 424 424 403 Month 12 0.9466 424 424 401 Month 13 0.9419 424 424 399 Month 14 0.9372 424 424 397 Month 15 0.9326 424 424 395 Month 16 0.9279 424 424 393 Month 17 0.9233 424 424 391 Month 18 0.9187 424 424 390 Month 19 0.9141 424 424 388 Month 20 0.9096 424 424 386 Month 21 0.9051 424 424 384 Month 22 0.9006 424 424 382 Month 23 0.8961 424 424 380 Month 24 0.8916 424 424 378 Month 25 0.8872 424 424 376 Month 26 0.8828 424 424 374 Month 27 0.8784 424 424 372 Month 28 0.8740 424 424 371 Month 29 0.8697 424 424 369 Month 30 0.8653 424 424 367 Month 31 0.8610 424 424 365 Month 32 0.8567 424 424 363 Month 33 0.8525 424 424 361 Month 34 0.8482 424 424 360 Month 35 0.8440 424 424 358 Month 36 0.8398 (600) 424 (176) (148) Total $ 14,103.10 So PV of Lease Rentals = $ 14,103.10 PV of Buying costs Discount starts from fisrt month as payment made at the end of month Month PV factor @0.5% Down payment Lease rental Residual value Net Costs PV of costs Now 1 2,500 2,500 2,500.00 Month 1 0.9950 512 512 509.45 Month 2 0.9901 512 512 506.92 Month 3 0.9851 512 512 504.40 Month 4 0.9802 512 512 501.89 Month 5 0.9754 512 512 499.39 Month 6 0.9705 512 512 496.91 Month 7 0.9657 512 512 494.43 Month 8 0.9609 512 512 491.97 Month 9 0.9561 512 512 489.53 Month 10 0.9513 512 512 487.09 Month 11 0.9466 512 512 484.67 Month 12 0.9419 512 512 482.26 Month 13 0.9372 512 512 479.86 Month 14 0.9326 512 512 477.47 Month 15 0.9279 512 512 475.09 Month 16 0.9233 512 512 472.73 Month 17 0.9187 512 512 470.38 Month 18 0.9141 512 512 468.04 Month 19 0.9096 512 512 465.71 Month 20 0.9051 512 512 463.39 Month 21 0.9006 512 512 461.09 Month 22 0.8961 512 512 458.79 Month 23 0.8916 512 512 456.51 Month 24 0.8872 512 512 454.24 Month 25 0.8828 512 512 451.98 Month 26 0.8784 512 512 449.73 Month 27 0.8740 512 512 447.49 Month 28 0.8697 512 512 445.27 Month 29 0.8653 512 512 443.05 Month 30 0.8610 512 512 440.85 Month 31 0.8567 512 512 438.65 Month 32 0.8525 512 512 436.47 Month 33 0.8482 512 512 434.30 Month 34 0.8440 512 512 432.14 Month 35 0.8398 512 512 429.99 Month 36 0.8356 512 (8,000) (7,488) (6,257.31) Total 12,644.80 So PV of Buying = $ 12,644.80 So PV of Lease Rentals = $ 14,103.10 So net benefit of Buying = $ 1,458.30
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