The Georgia Transportation Directorate is considering a public-private partnersh

Question

The Georgia Transportation Directorate is considering a public-private partnership with Young Construction as the prime contractor using a DBOMF contract for a new 22.51-mile toll road on the outskirts of Atlanta's suburban area. The design includes three 4-mile-long commercial/ retail corridors on both sides of the toll road. Highway construction is expected to require 5 years at an average cost of $3.91 million per mile. The discount rate is 4% per year, and the study period is 30 years. Evaluate the economics of the proposal using (a the modified B/C analysis from the State of Georgia perspective and (b) the profitability index from the Young corporate viewpoint in which disbenefits are not included Initial estment: $88 million distributed over 5 years; $4 million now and in year 5 and 20 million in each of years 1 through 4 Annual M&O; cost: $1 million per year, plus an additional $3 million each fifth year, includ- ing year 30 Annual revenue/benefits: Include tolls and retail/commercial growth; start at $2 million in year 1, increasing by a constant $0.5 million annually through year 10, and then increasing by a constant $1 million per year through year 20 and remaining constant thereafter Estimable disbenefits: Include loss of business income, taxes, and property value in sur- rounding areas; start at $10 million in year 1, decrease by $0.5 million per year through year 21, and remain at zero thereafter

Explanation / Answer

INITIAL INVESTMENT Present Worth (PW) of investment=(investment)/(91+i)^N) i=discount rate=4%=0.04, N=year of investment N A B=A/(1.04^N) Year Investment PW of investment 0 $4,000,000 4000000 1 $20,000,000 19230769.23 2 $20,000,000 18491124.26 3 $20,000,000 17779927.17 4 $20,000,000 17096083.82 5 $4,000,000 3287708.427 Present Worth of total initial investment PW= $            79,885,613 Modified B/C analysis from State of Georgia perspective Year wise Benefits, Disbenefits and M&O costs are given below N A B C D=A-B-C E=D/(1.04^N) Year RevenueBenefit Disbenefit M&O Cost Net benefit PW of net benefit 1 $2,000,000 $10,000,000 $1,000,000 ($9,000,000) -8653846.154 2 $2,500,000 $9,500,000 $1,000,000 ($8,000,000) -7396449.704 3 $3,000,000 $9,000,000 $1,000,000 ($7,000,000) -6222974.511 4 $3,500,000 $8,500,000 $1,000,000 ($6,000,000) -5128825.146 5 $4,000,000 $8,000,000 $4,000,000 ($8,000,000) -6575416.854 6 $4,500,000 $7,500,000 $1,000,000 ($4,000,000) -3161258.103 7 $5,000,000 $7,000,000 $1,000,000 ($3,000,000) -2279753.44 8 $5,500,000 $6,500,000 $1,000,000 ($2,000,000) -1461380.41 9 $6,000,000 $6,000,000 $1,000,000 ($1,000,000) -702586.7356 10 $6,500,000 $5,500,000 $4,000,000 ($3,000,000) -2026692.506 11 $7,500,000 $5,000,000 $1,000,000 $1,500,000 974371.3973 12 $8,500,000 $4,500,000 $1,000,000 $3,000,000 1873791.149 13 $9,500,000 $4,000,000 $1,000,000 $4,500,000 2702583.388 14 $10,500,000 $3,500,000 $1,000,000 $6,000,000 3464850.497 15 $11,500,000 $3,000,000 $4,000,000 $4,500,000 2498690.262 16 $12,500,000 $2,500,000 $1,000,000 $9,000,000 4805173.581 17 $13,500,000 $2,000,000 $1,000,000 $10,500,000 5390419.081 18 $14,500,000 $1,500,000 $1,000,000 $12,000,000 5923537.452 19 $15,500,000 $1,000,000 $1,000,000 $13,500,000 6407672.725 20 $16,500,000 $500,000 $4,000,000 $12,000,000 5476643.354 21 $16,500,000 $0 $1,000,000 $15,500,000 6801920.833 22 $16,500,000 $0 $1,000,000 $15,500,000 6540308.493 23 $16,500,000 $0 $1,000,000 $15,500,000 6288758.166 24 $16,500,000 $0 $1,000,000 $15,500,000 6046882.852 25 $16,500,000 $0 $4,000,000 $12,500,000 4688960.028 26 $16,500,000 $0 $1,000,000 $15,500,000 5590683.111 27 $16,500,000 $0 $1,000,000 $15,500,000 5375656.837 28 $16,500,000 $0 $1,000,000 $15,500,000 5168900.805 29 $16,500,000 $0 $1,000,000 $15,500,000 4970096.928 30 $16,500,000 $0 $4,000,000 $12,500,000 3853983.35 Present worth of Total Net Benefits $            51,234,701 Benefit cost Ratio(51234701/79885613) 0.641350787 B-C Ratio less than 1, hence not recommended CALCULATION OF PROFITABILITY INDEX FOR YOUNG CORPORATE N A B C=A-B D=C/(1.04^N) Year RevenueBenefit M&O Cost Net cash inflow Present value of net cash inflow(4%discount) 1 $2,000,000 $1,000,000 $1,000,000 961538.4615 2 $2,500,000 $1,000,000 $1,500,000 1386834.32 3 $3,000,000 $1,000,000 $2,000,000 1777992.717 4 $3,500,000 $1,000,000 $2,500,000 2137010.478 5 $4,000,000 $4,000,000 $0 0 6 $4,500,000 $1,000,000 $3,500,000 2766100.84 7 $5,000,000 $1,000,000 $4,000,000 3039671.253 8 $5,500,000 $1,000,000 $4,500,000 3288105.923 9 $6,000,000 $1,000,000 $5,000,000 3512933.678 10 $6,500,000 $4,000,000 $2,500,000 1688910.422 11 $7,500,000 $1,000,000 $6,500,000 4222276.055 12 $8,500,000 $1,000,000 $7,500,000 4684477.872 13 $9,500,000 $1,000,000 $8,500,000 5104879.732 14 $10,500,000 $1,000,000 $9,500,000 5486013.287 15 $11,500,000 $4,000,000 $7,500,000 4164483.77 16 $12,500,000 $1,000,000 $11,500,000 6139944.02 17 $13,500,000 $1,000,000 $12,500,000 6417165.573 18 $14,500,000 $1,000,000 $13,500,000 6663979.634 19 $15,500,000 $1,000,000 $14,500,000 6882315.149 20 $16,500,000 $4,000,000 $12,500,000 5704836.828 21 $16,500,000 $1,000,000 $15,500,000 6801920.833 22 $16,500,000 $1,000,000 $15,500,000 6540308.493 23 $16,500,000 $1,000,000 $15,500,000 6288758.166 24 $16,500,000 $1,000,000 $15,500,000 6046882.852 25 $16,500,000 $4,000,000 $12,500,000 4688960.028 26 $16,500,000 $1,000,000 $15,500,000 5590683.111 27 $16,500,000 $1,000,000 $15,500,000 5375656.837 28 $16,500,000 $1,000,000 $15,500,000 5168900.805 29 $16,500,000 $1,000,000 $15,500,000 4970096.928 30 $16,500,000 $4,000,000 $12,500,000 3853983.35 TOTAL $   131,355,621 Profitability Index=(131355621/79885613) 1.644296346 At 4% discount rate, the project is acceptable Profitability indes is higher than 1

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