Problem 4 (3 points). Alternatives Cost Comparison (using PW) Of the two alterna

Question

Problem 4 (3 points). Alternatives Cost Comparison (using PW) Of the two alternatives below, which car should you buy? Compare these alternatives using present worth analysis. Assume an interest rate of 4%. Purchase Cost Lifetime Salvage Value Annual Gas & Maintenance $2,200 Ford S20,000 10 vears S500 Lexus S35,000 15 vears $2,250 $1,500 a) Over how many years should you compare these two alternatives? b) Draw the Ford cash flow diagram. c) What is the present worth of the Ford over the timeframe stated in (a)? d) Draw the Lexus cash flow diagram e) What is the present worth of the Lexus over the timeframe stated in (a)? f) Which car should you buy? Justify your answer

Explanation / Answer

(a) Comparison of the alternatives should be done for 10 years as the useful life of ford is 10 years and post 10 years whether there will be a new car or not of the same quality and brand is not possible to determine.

(b) Last year incorporates the $500 salvage value assuming that the car will be sold at the end of 10 years.

(c) PV= Cash flow for that time period/(1+rate)T

Rate =4%, Time perod T will vary from 0 to 10 for all the cash flows starting from Year 0 to Year 10

Sum of the Present value of the individual cash flows= $37,506.

This is the value of the Ford car to the owner.

(d) Last year incorporates the $2,250 salvage value assuming that the car will be sold at the end of 15 years.

(e) Using the same concept of present value as mentioned in (c), the present value of the car comes out to be $47,166. The assumption is that the car will be sold in Year 15 at the salvage value and not before that.

(f) Ford should be bought because in this case the present value is the net cash outflow in today's terms for the owner. Thus, if the owner is looking to buy a car in terms of price, the owner should invest in Ford rather than Lexus.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Cash Flow        (20,000)                 (2,200)      (2,200)      (2,200)      (2,200)      (2,200)      (2,200)      (2,200)      (2,200)      (2,200)      (1,700)

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