Question

You own a cab company and are evaluating two options to replace your fleet. Either you can take out a​ five-year lease on the replacement cabs for $ 500 $500 per month per​ cab, or you can purchase the cabs outright for $ 30 comma 000 $30,000​, in which case the cabs will last eight years. You must return the cabs to the leasing company at the end of the lease. The leasing company is responsible for all maintenance​ costs, but if you purchase the​ cabs, you will buy a maintenance contract that will cost $ 100 $100 per month for the life of each cab. Each cab will generate revenues of $ 1 comma 000 $1,000 per month. Assume the cost of capital is fixed at 12.0 % 12.0%. ​(​Hint: Make sure to round all intermediate calculations to at least four decimal places.​) ​ a. Calculate the NPV per cab of both​ possibilities: purchasing the cabs or leasing them. b. Calculate the equivalent monthly benefit of both opportunities. c. If you are leasing a​ cab, you have the opportunity to buy the used cab after five years. Assume that in five years a​ five-year-old cab will cost either $ 10 comma 000 $10,000 or $ 16 comma 000 $16,000​, with equal​ likelihood; will have maintenance costs of $ 500 $500 per​ month; and will last three more years. Which option should you​ take? a. Calculate the NPV per cab of both​ possibilities: purchasing the cabs or leasing them. The NPV of leasing the cabs is ​$ nothing per cab.  ​(Round to the nearest​ dollar.)

Answer 1

A)Converting the cost of capital to a monthly discount rate gives:

(1 + 0.12)1/12− 1 = 0.00949, so the monthly discount rate is 0.949%

????????=5000.00949(1 −1(1.00949)60) = $22,794

??????= −30,000 +9000.00949(1 −1(1.00949)96) = $26,541

B)

Calculate the equivalent monthly annual benefit of both opportunities. Timeline:

Calculate the EAB of leasing:

????????=22,794×0.009491−1/1.0094960= $500

Calculate the EAB of leasing:

??????=26,541×0.009491−1/1.0094996= $422

C)

If you are leasing a cab, you have the opportunity to buy the used cab after five years. Assume that in five years a five-year-old cab will cost either $10,000 or $16,000 with equal likelihood, will have maintenance costs of $500 per month, and will last three more years. Which option should you take

In month 60, the NPV of buying a cab is either

??? = −10,000 +5000.00949(1 −1(1.00949)36) = $5,188

Or

??? = −16,000 +5000.00949(1 −1(1.00949)36) = −$813

The expected value of replacing the cabs in year 5 is:

?(?) = 0.5 × 5,188 + 0.5 × (−813) = $2,187.5

The value today of this:

?? =2,187.51.0094960= $1,241.16

Adding this to the NPV of leasing from part a gives:

????????= 1,241.16 + 22,794 = $24,035

Since the NPV of buying as not changed

??????= $26,541

So you should buythe cab.