2. Suppose are running a cab business and your current cab is expected to produc

Question

2. Suppose are running a cab business and your current cab is expected to produce a cash flow of S4,000 in one year and $3,000 in two years. After that it will have to be replaced. The resale value is S1,000 if you replace now, $500 next year, and zero otherwise. The best alternative is a new cab that will be optimally replaced every 3 years, giving the following cash flows (inclusive of the resale value in year 3): What is the minimum price P of the new cab such that you will replace the old cab in year 2? (Assume no taxes.)

Explanation / Answer

Calculation of Minimum Price :

Old Cab:

Year

Cash Flows Old Cab (CFO)

Cash Flows New Cab (CFN)

CFN-CFO

PVF (6%)

PV = CF*PVF

0

1

1

4000

8000

4000

0.943396

$ 3,773.58

2

4000

8000

4000

0.889996

$ 3,559.99

(3000+1000)

Price of the new cab (P)

$ 7,333.57

Calculation of Minimum Price :

Old Cab:

Year

Cash Flows Old Cab (CFO)

Cash Flows New Cab (CFN)

CFN-CFO

PVF (6%)

PV = CF*PVF

0

1

1

4000

8000

4000

0.943396

$ 3,773.58

2

4000

8000

4000

0.889996

$ 3,559.99

(3000+1000)

Price of the new cab (P)

$ 7,333.57

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