1. Allen Auto Group owns corner property that can serve as a parking lot for cus
ID: 2806453 • Letter: 1
Question
1. Allen Auto Group owns corner property that can serve as a parking lot for customers. The parking lot can be made of concrete or asphalt. Concrete will cost $375K initially, have an estimated monthly maintenance cost of $200 starting at the end of the first month of the eighth year, and will last for 20 years. Asphalt is cheaper to install at $250K, costs $700 per month starting at the end of the second year, and will last 10 years and. Using MARR=12% per year compounded quarterly and a 20 year planning horizon, should the parking lot be of concrete or asphalt? a. Use present worth analysis to solve the problem assuming that the projects may be repeated. Solve the problem using the factors. Make sure to explicitly recommend one of the options. (ANS: $- 381,930.16 vs. $-371.961.09 – select asphalt) b. Compute the 10 year annual equivalent for the asphalt option using the factors. (ANS: $-44,635.33) c. Compute the 20 year annual equivalent for the asphalt option using the factors assuming that the project can be repeated with the same costs and compare it to the results in part b. (ANS: $- 44,635.33) d. Solve the problem using the Rate of Return Analysis. (ANS: i* = 0.91%, select asphalt)
Explanation / Answer
Given interest rate=12% compounded quarterly, but the payments are made monthly, hence monthly effective rate is to be determined which is as follows:
Effective annual rate=(1+r)^n-1
n=number of compounding done in one year.
=(1+.12/4)^4-1
=12.55%.
But monthly rate is to be determined =(1+r)^1/12 -1
=1.1255^1/12 -1
=0.99%=rate
The monthly maintenance is paid from end of first month of eighth year=13*12=nper
Monthly payment=$200=pmt.
So, the present value for concreta @ 0.99% monthly rate=$375,000+PV(0.99%,13*12,-200,,0)
=$375,000+$15,855.71
=$390,855.71.
For Asphalt option it is as follows:
0.99%=rate
The monthly maintenance is paid from end of last month of second year=1+(12*8)=nper
Monthly payment=$700=pmt.
Present value of monthly payments
=PV(0.99%,(8*12)+1,-700,,0)
=$43,510.93.
As the project can be repeated, present value of maintenance costs at the end of 10 years for the next 10 years=$43,510.93-------(1)
Present value to be determined for year 0=$43,510.93/(1+12.55%)^10
=$13,338.57.--------(2)
Again $250,000 is invested at the end of 10th year.Therefore, present value of this investment=$250,000/1.1255^10
=$76,645.209.-----------(3)
Total investment in Asphalt=$250,000+(1)+(2)+(3)
=$383,494.71.
As the present value of investment in Asphalt is low, it shoule be opted.
Answer for question no.b:
10 year Annual equivalent for the asphalt option =Present value of cash outflow for 10 years/Present value annuity factor for 10 years
Present value annuity factor for 10 years=1-(1+r)^-n/r
=((1-(1+.1255)^-10)/.1255
=5.52525.
10 year present value of cash outflow=($250,000+$43,510.93)/5.52525
=$53,121.72.
Answer for question no.c:
Equivalent annual worth for 20 years is Present value of annual cash outflows for 20 years/Present value annuity for 20 years.
Present value annuity for 20 years =(1-(1+0.1255)^-(20))/0.1255
=7.219188.
Present value of cash outflows for 20 years=$383,494.71
Equivalent present value for 20 years=$383,494.71/7.219188.
=$53,121.58.
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