The main purpose of this project is to evaluate the investment options available for the replacement of a National Guard Armory. Therefore, the main objective of this project is to determine the consumer surplus of the project.
Discount Factor for Each Year
Calculation
Discount factor for year 0=1/ (1+.04)0 = 1/1 = 1
Discount factor for year 1=1/ (1+.04)1= 1/1.04 = 0.962
Discount factor for year 2=1/ (1+.04)2 = 1/1.0816 = 0.920
Discount factor for year 3= 1/ (1+.04)3= /1.1248 = 0.890
Discount factor for year 4=1/ (1+.04)4= 1/1.1698 = 0.850
Discount factor for year 5=1/ (1+.04)5 = 1/1.2166 = 0.820
Discount factor for year 6= 1/ (1+.04)6=1/1.2653 = 0.790
Discount factor for year 7=1/ (1+.04)7= 1/1.3159 = 0.760
Discount factor for year 8=1/ (1+.04)8 = 1/1.3685 = 0.730
Discount factor for year 9= 1/ (1+.04)9=1/1.423 = 0.700
Discount factor for year 10=1/ (1+.04)10= 1/1.480 = 0.680
Discount factor for year 11=1/ (1+.04)11 = 1/1.5394 = 0.650
Discount factor for year 12= 1/ (1+.04)12=1/1.601= 0.620
Discount factor for year 13=1/ (1+.04)13= 1/1.665 = 0.600
Discount factor for year 14=1/ (1+.04)14 = 1/1.7316 = 0.580
Discount factor for year 15= 1/ (1+.04)15 = 1/1.8009 = 0.560
The calculation of the discount factor shows that the present value of future cash flows will be determined for estimating the benefit of rehabilitation. It could be noted that the value of the discount factor decreases over the project life.
Present Value and Annual Present Value of Maintenance cost
Calculation
Present Value Year 1 $275000/ (1.04)1= $264,423
Present Value Year 2 $275, 000/ (1.04)2= $254,253
Present Value Year 3 $275000/ (1.04)3= $244,474
Present Value Year 4 $275, 000/ (1.04)4= $235,071
Present Value Year 5 $275000/ (1.04)5= $226,030
Present Value Year 6 $275, 000/ (1.04)6= $217,336
Present Value Year 7 $275000/ (1.04)7= $208,977
Present Value Year 8 $275, 000/ (1.04)8= $200,940
Present Value Year 9 $275000/ (1.04)9= $193,211
Present Value Year 10 $275, 000/ (1.04)10= $185,780
Present Value Year 11 $275000/ (1.04)11= $178,635
Present Value Year 12 $275, 000/ (1.04)12= $171,764
Present Value Year 13 $275000/ (1.04)13= $165,158
Present Value Year 14 $275, 000/ (1.04)14= $158,806
Present Value Year 15 $275,000/ (1.04)15= $152,698
Sum of all present values = $264,423 + $254,253 + $244,474 + $235,071 + $226,030 + $217,336 +$208,977+ $200,940+ $193,211+ $185,780 + $178,635 + $171,764 + $165,158 + $158,806 + $152,698 = $3,057,556.54
Annual Present Value = $ 3,057,556.54 / 15 = $203,837.10
Discounted Benefit of Rehabilitating
Calculation
Discounted Benefit (Consumer Surplus) = $3,057,557 – $4,000,000 = $(942,443)
Cost-Benefit Ratio for the Proposal
Calculation
Benefit from the Project = $4,000,000:$(942,443) = 41/4
The State of Massachusetts should avoid investing in the rehabilitation facility as the investment amount is higher than the sum of present values of maintenance cost. Therefore, the consumer surplus favors the decision to maintain the armory. The cost-benefit ratio indicates that the demand for the project (rehabilitation cost) is approximately four times higher than the discounted benefit. Therefore, the State of Massachusetts should not choose rehabilitation. If the present value of the existing investment is lower than the initial value of the new investment, then the company should avoid the latter (Vallabhaneni, 2016). The existing project has only one operating expense, which are the maintenance costs of $275,000 annually.
The cost of delay is important to understand the effect of time on the forecasted outcome of a business decision. It represents the consequences of delaying the project completion after the projected time (Higham, Bridge & Farrell, 2016), i.e., 15 years in this case. However, there is a possibility of a delay by one or two years. Therefore, the estimated cost of potential delays is presented below.
Calculation
Cost of delay at end of the 16th year = $3,057,557 + [$275,000/ (1.04)16] = $3,204,381
Cost of delay at the end of the 17th year = $3,057,557 + $146,825 + [$275,000/ (1.04)17] = $3,345,559
The calculation of the cost of delay of this project shows that each additional year beyond the estimated time will incur more cost. The additional cost is the maintenance cost of $275,000 that will incur every year. However, it can be noticed that the sum of present value of these two scenarios (16th and 17th years) will change by a different amount. The main cause is that the future value of each year cost will be discounted by using a different discount factor. The additional cost will also change the values of discounted benefits and cost-benefit ratio. Therefore, it is suggested that the State of Massachusetts should complete the project within time to avoid additional costs.
References
Higham, A., Bridge, C. & Farrell, P. (2016). Project finance for construction. New York, NY: Taylor & Francis.
Vallabhaneni, S. R. (2016). Wiley CIAExcel exam review 2016: Part 3, internal audit knowledge elements. Hoboken, NJ: John Wiley & Sons.