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ID: 2809539 • Letter: E
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edback s.. cengage Dashboard G Gram marly 1 Gramm 3 search rights, hot Jotapcom-Best- 0 med 0 deat uestion 2 20 pts You can lease a car for 5 years by paying $5,000 today and then making lease payments of $350 per month (starting next month) for 5 years. Or you can buy the car now for $30.000 and then in 5 years sell the car for $18,000 Either way you have use of the car for 5 years. If your investments earn 5.00% APR (compounded monthly) which alternative is cheaper and by how much in present value terms? D Buying is cheaper in PV terms by $7.572 Leasing is cheaper in PV terms by $7,572 Buying is cheaper in PV terms by $7.209 Leasing is cheaper in PV terms by $2 572 O Leasing is cheaper in PV terms by $7209 Buying is cheaper in PV terms by $2. 572 10 ptsExplanation / Answer
PV of lease = $ 5,000 + PV of lease payments
We can use formula for PV of annuity to compute present value of monthly lease payments as:
Formula for PV of annuity is:
PV = P x [1-(1+r)-n/r]
P = Periodic cash flow = $ 350
r = Rate per period = 5 % or 0.05/12 = 0.004166667 p.m.
n = Numbers of periods = 5 x 12 = 60
PV = $ 350 x [1-(1 + 0.004166667)-60/ 0.004166667]
= $ 350 x [1-(1.004166667)-60/ 0.004166667]
= $ 350 x [(1-0.77920539)/ 0.004166667]
= $ 350 x (0.22079461/ 0.004166667)
= $ 350 x 52.9907063
= $ 18,546.75
PV of lease = $ 5,000 + $ 18,546.75 = $ 23,546.75
Computation of PV of purchasing the car:
PV of purchasing = Initial price - PV of sales price at the end of 5th year
Initial price = $ 30,000
PV of sales price can be computed using formula for PV of a single sum as:
PV = FV/ (1+r)n
= $ 18,000/ (1+0.004166667)60
= $ 18,000/ (1.004166667)60
= $ 18,000/ 1.283358679
= $ 14,025.70
PV of purchasing = $ 30,000 - $ 14,025.70 = $ 15,974.30
Advantage of purchasing = $ 23,546.75 - $ 15,974.30 = $ 7,572.44
Hence option 1st “Buying is cheaper in PV of terms by $ 7,572” is correct answer.
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