# National Guard Armory’s Investment Options Essay

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Updated: May 7th, 2021

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

 Year Year Year Year Year Year Year Year Year Year Year Year Year Year Year Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Benefits 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Costs \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 Discount rate (r) % 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% Discount factor 1 /(1+r)ⁿ 1.00 0.962 0.92 0.89 0.85 0.82 0.79 0.76 0.73 0.70 0.68 0.65 0.62 0.60 0.58 0.56

### 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

 Year Year Year Year Year Year Year Year Year Year Year Year Year Year Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Cost (Future Value) \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 \$ 275,000 Rate 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% Present Value \$ 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 Sum of Present Value \$ 3,057,556.54 Annual Present Value of Maintenance Cost \$ 203,837.10

### 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

 15 Years Present Value \$3,057,557 Initial Cost Rehabilitation Cost \$4,000,000 Discounted Benefit of Maintenance \$(942,443)

### Calculation

Discounted Benefit (Consumer Surplus) = \$3,057,557 – \$4,000,000 = \$(942,443)

## Cost-Benefit Ratio for the Proposal

 Initial Cost Rehabilitation Cost \$4,000,000 Discounted Benefit \$942,443 Cost-Benefit Ratio 41/4

### 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.

 Cost of Delay Sum of Present Value Additional Cost 15 Years \$3,057,557 – 16 Years \$3,204,381 \$146,825 17 Years \$3,345,559 \$141,178

### 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.

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