Washington Countys Board of Representatives is considering the construction of a longer runway at the county airport. Currently, the airport can handle only private aircraft and small commuter jets. A new, long runway would enable the airport to handle the midsize jets used on many domestic flights. Data pertinent to the boards decision appear below.

Cost of acquiring additional land for runway$ 72,000Cost of runway construction219,420Cost of extending perimeter fence30,460Cost of runway lights40,600Annual cost of maintaining new runway28,800Annual incremental revenue from landing fees41,120

In addition to the preceding data, two other facts are relevant to the decision. First, a longer runway will require a new snowplow, which will cost $104,000. The old snowplow could be sold now for $10,200. The new, larger plow will cost $12,400 more in annual operating costs. Second, the County Board of Representatives believes that the proposed long runway, and the major jet service it will bring to the county, will increase economic activity in the community. The board projects that the increased economic activity will result in $68,080 per year in additional tax revenue for the county.

In analyzing the runway proposal, the board has decided to use a 10-year time horizon. The countys hurdle rate for capital projects is 12 percent.

Use Appendix A for your reference.

Note: Use appropriate factor(s) from the tables provided.

PR 16-45 (Algo) Internal Rate of Return; Even Cash Flows (Section 1) (LO 16-1, 16-3)

Required:

1. Compute the initial cost of the investment in the long runway.

2. Compute the annual net cost or benefit from the runway.

3-a. Determine the IRR on the proposed long runway.

3-b. Should it be built considering IRR?

Future Value and Present Value Tables

Table I

Future Value of $1.00(1 + r)ⁿn

Period4%6%8%10%12%14%20%11.0401.0601.0301.1001.1201.1401.20021.0821.1241.1661.2101.2541.3001.4403l.1251.1911.2601.3311.4051.4821.72841.1701.2631.3611.4641.5741.6892.07451.2171.3381.4691.61l1.7621.9252.48861.2651.4191.5871.7721.9742.1952.98671.3161.5041.7141.9492.2112.5023.58381.3691.5941.8512.1442.4762.8534.30091.4231.690l.9992.3592.7733.2525.16010l.4801.7912.1592.5943.1063.7076.192111.5401.8982.3322.8533.4794.2267.430121.6012.0 122.5133.1393.8964.8188.91613l.6652.1332.7203.4524.3645.49210.69914l.7322.2612.9373.7984.8876.26112.839151.8012.3973.1724.1775.4747.13815.407202.1913.2074.6616.7239.64613.74338.338303.2435.74410.06317.45029.96050.950237.380404.30110.28621.72545.26093.051188.8801,469.300

Table II

Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity)(((1+r)ⁿn 1) r)

Period4%6%8%10%12%14%20%11.0001.0001.000l.0001.0001.0001.00022.0402.0602.0802.1002.1202.1402.22033.1223. 1843.2463.3103.3743.4403.64044.2474.3754.5064.6414.7794.9215.36855.4165.6375.8676.1056.3536.6107.44266.6336.9757.3367.7168.1158.5369.93077.8988.3948.9239.48710.08910.73012.91689.2149.898I0.637Il.43612.30013.23316.499910.583ll.49112.48813.58014.77616.08520.7991012.00613.18114.48715.93817.54919.33725.9591113.48614.97216.64618.53120.65523.04532.1501215.02616.87018.97721.38524.13327.27139.5801316.62718.88221.49524.52328.02932.08948.4971418.29221.01524.21527.97632.39337.58159.1961520.02423.27627.15231.77337.28043.84272.0352029.77836.77345.76257.27675.05291.025186.6903056.08579.058113.283164.496241.330356.790l,181.9004095.026154.762259.057442.597767.0901.342.0007,343.900

Table III

Present Value of $1.00 (1 (1+r)ⁿn)

Period4%6%8%10%12%14%16%18%20%22%24%26%28%30%32%1.962.943.926.909.893.877.862.847.833.820.806.794.781.769.7582.925.890.857.826.797.769.743.718.694.672.650.630.610.592.5743.889.840.794.751.712.675.641.609.579.551.524.500.477.455.4354.855.792.735.683.636.592.552.516.482.451.423.397.373.350.3295.822.747.681.621.567.519.476.437.402.370.341.315.291.269.2506.790.705.630.564.507.456.410.370.335.303.275.250.227.207.1897.760.665.583.513.452.400.354.314.279.249222.198.178.159.1438.731.627.540.467.404.351.305.266.233.204.179.157.139.123.1089.703.592.500.424.361.308.263.225.194.167.144.125.108.094.08210.676.558.463.386.322.270.227.191.162.137.116.099.085.073.06211.650.527.429.350.287.237.195.162.135.112.094.079.066.056.04712.625.497.397.319.257.208.168.137.112.092.076.062.052.043.03613.601.469.368.290.229.182.145.116.093.075.061.050.040.033.02714.577.442.340.263.205.160.125.099.078.062.049.039.032.025.02115.555.417.315.239.183.140.108.084.065.051.040.031.025.020.01620.456.312.215.149.104.073.051.037.026.019.014.010.007.005.00430.308.174.099.057.033.020.012.007.004.003.002.001.001 40.208.097.046.022.011.005.003.001.001

Table IV

Present Value of Series of $1.00 Cash Flows 1/r (1 (1 (1+rⁿn)))

Period4%6%8%10%12%14%16%18%20%22%24%25%26%28%30%10.9620.9430.9260.9090.8930.8770.8620.8470.8330.8200.8060.8000.7940.7810.76921.8861.8331.7831.7361.6901.6471.6051.5661.5281.4921.4571.4401.4241.3921.36132.7752.6732.5772.4872.4022.3222.2462.1742.1062.0421.9811.9521.9231.8681.81643.6303.4653.3123.1703.0372.9142.7982.6902.5892.4942.4042.3622.3202.2412.16654.4524.2123.9933.7913.6053.4333.2743.1272.9912.8642.7452.6892.6352.5322.43665.2424.9174.6234.3554.1113.8893.6853.4983.3263.1673.0202.9512.8852.7592.64376.0025.5825.2064.8684.5644.2884.0393.8123.6053.4163.2423.1613.0832.9372.80286.7336.2105.7475.3354.9684.6394.3444.0783.8373.6193.4213.3293.2413.0762.92597.4356.8026.2475.7595.3284.9464.6074.3034.0313.7863.5663.4633.3663.1843.019108. 1117.3606.7106.1455.6505.2164.8334.4944.1923.9233.6823.5713.4653.2693.092118.7607.8877.1396.4955.9385.4535.0294.6564.3274.0353.7763.6563.5443.3353.147129.3858.3847.5366.8146.1945.6605.1974.7934.4394.1273.8513.7253.6063.3873.190139.9868.8537.9047.1036.4245.8425.3424.9104.5334.2033.9123.7803.6563.4273.2231410.5639.2958.2447.3676.6286.0025.4685.0084.6114.2653.9623.8243.6953.4593.2491511.1189.7128.5597.6066.8116.1425.5755.0924.6754.3154.0013.8593.7263.4833.2682013.59011.4709.8188.5147.4696.6235.9295.3534.8704.4604.1103.9543.8083.5463.3163017.29213.76511.2589.4278.0557.0036.1775.5174.9794.5344.1603.9953.8423.5693.3324019.79315.04611.9259.7798.2447.1056.2345.5484.9974.5444.1663.9993.8463.5713.333