You have been transferred to Woop Woop for 5 years where there is no public tran
ID: 2812318 • Letter: Y
Question
You have been transferred to Woop Woop for 5 years where there is no public transport. You will need a car to commute to and from work. You can purchase a new Yugo automobile for $10,000.00 dollars or you can rent the same car for $220.00 per month. In either case you will be responsible for repairs and maintenance. If you expect to be able to sell the Yugo for $1,000.00 after 5 years and your discount rate is 9.00% per year, Which is the lower cost alternative? What is the monthly rental rate that would leave you indifferent between the two alternatives? a. b.Explanation / Answer
Step 1: Calculation of Present Value of buy option
Present Value of Uneven Cash flow can be calculated as
CF1/(1+I)^1 + CF2/(1+I)^2 ..........+ CFn/(1+I)^n
10000/(1.09)^1 + 1000/(1.09)^5
10000/1.09 + 1000/1.5386239549
9174.31192661+649.931386298
9824.24
Step 2: Calculation of Present Value of rent option
Present value of Annuity = A*[(1-(1+r)-n)/r]
Where
A - Annuity payment = 220
r - rate per period = 9%/12 = .75%
n - no. of periods = 5*12 =60
Present value of Annuity = 220* [(1-(1.0075)^-60)/.0075]
= 220* [(1-0.63869969859)/.0075]
= 220*48.1733735213
= 10598.14
a) Since the present value is lower for buy option, it is the lower cost alternative.
b) Let X be the monthly rental at which two options will be indifferent.
9824.24 = X* [(1-(1.0075)^-60)/.0075]
= X * 48.1733735213
X = 9824.24/48.1733735213
= 203.94
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