Fashion

Introduction to Finance

BUSFIN 1030

Professor Schlingemann

Problem Set 3

SOLUTIONS

Problem 1:

You are deciding among three cars to use as a company car. The garage offers you a lease deal and two different options for purchasing the car. You are completely indifferent among these cars except for their costs. Once you have decided which car to take, you will always take the same car again at the end of its useful life. The pre-tax residual value (salvage value) for the car at the end of its useful life is equal to (100 / n) % of the purchase price, where n is equal to the lifetime of the car. All cars are fully depreciated according to its lifetime on a straight-line basis with no half-year convention. The discount rate is 7% and the tax rate is 20%. Assume that you pay the price of the car up front, and the annual costs at the end of the year. The costs of leasing occur at the end of each period. (For example, if you purchase Car B, you pay $18,000 in year 0 and $1,000 in year 1, year 2, etc. If you lease car A, you pay $4,650 in year1, year 2, etc.) Note: consider all relevant cash flows for this problem.

Lease A Purchase B Purchase C

Purchase price --- $18,000 $45,000

Total annual costs* $4,650 $900 ---

Lifetime of the car 3 years 5 years 18 years

* Includes all after-tax costs like fuel, wear and tear, maintenance, etc.

Using the Equivalent Annual Cost (EAC) method, which of the cars should you decide to drive always?

ANSWER:

First find the relevant cash flows associated with each purchase option:

Purchase B:

Depreciation tax shield = 20% × $3,600 = $720

After-tax salvage value = $3,600 – 20% × $3,600 = $2,880

PVB = 18,000 + [pic]$16,684.64

EACB ( [pic]16,684.64 ( EACB = $4,069.23

Purchase C:

Depreciation tax shield = 20% × $2,500 = $500

After-tax salvage value = $2,500 – 20% × $2,500 = $2,000

PVC = 45,000 + [pic]$39,378.73

EACC ( [pic]39,378.73 ( EACC =...