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 $ 548 per month per​ cab, or you can purchase the cabs outright for $ 30 comma 800​, 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 $ 101 per month for the life of each cab. Each cab will generate revenues of $ 1 comma 068 per month. Assume the cost of capital is fixed at 12.2 %. ​(​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 200 or $ 15 comma 700​, with equal​ likelihood; will have maintenance costs of $ 490 per​ month; and will last three more years. Which option should you​ take?

Answer 1

given cost of capital = 12.2%

we have to calculate monthly rate

monthly rate = (1+r)^1/12 - 1

= (1+12.2%)^1/12 - 1

= 0.9639%

NPV lease:

monthly revenue = 1068

monthly lease payments = 548

net revenue = 1068 - 548 = 520

we have to calulate present value of $520 monthly revenues of 60 months(5 years)

present value of annuity = P[1 - (1+r)^-n / r ]

= 520[ 1 - (1.009639)^-60 / 0.009639 ]

NPV of lease = $23608.36

NPV of Buying:

here net revenue = 1068 - 101(maintenance)

= $967

so NPV = present value of future cash flows - initial cash outflow

present value of annuity = 967[1 - (1.009639)^-96 / 0.009639]

= 60378.28

NPV = 60378.28 - 30800

= $29,578.28

b)

in case of leasing Equivalent annual benefit = net revenue = $520

in case of buying option:

EAB = NPV / [1 - (1+r)^-n / r ]

= 29,578.28 / [1 - (1.009639)^-96 / 0.009639 ]

=$473.72

c)

here net benefit = 1068 - 490 = 578

useful life = 3 years = 36 months

cost will be either 10,200 or 15,700

so lets calculate NPV under both costs

when cost is 10,200

NPV = -10,200 + 578[1 - (1+ 0.009639)^-36 / 0.009639 ]

= 7311.05

when cost is 15700:

NPV = -15700 + 578[1 - (1+ 0.009639)^-36 / 0.009639 ]

= 1811.05

it is given equal probability

so NPV = 0.5*7311.05 + 0.5*1811.05

= 4561.05

present value = 4561.05 / (1.009639)^60

= 2565.08

so total NPV under lease option = 23608.36(calculated above) + 2365.08

= 25973.44

NPV of buying = 29,578.28 (it will not change)

since NPV of buying is higher BUYING is better option