Question

20. An existing public park serving 1.8 Million visitor/year is to be improved. Initial cost is SR 2.25 Million and the annual operating and maintenance cost starts with SR 0.145 Million during the first year and increases 3%/year thereafter. The planning horizon is 20 years, the salvage value is 32% of the initial cost, and the interest rate is 12%. The minimum additional benefits/visit that will justify the facility improvement is closest to: a) SR 0.18 b) SR 0.30 c) SR 0.26 d) SR 0.20 21. Riyadh City is planning a public recreational facility with an initial cost of SR 72 Million and a maintenance cost of 800,000/year. Number of people expected to visit the facility is 90,000 person/year. 40% of visitors will receive a benefit of SR 12/visit, 45% will receive SR 18/visit, and 15% will receive SR 28/visit. For a 30-year planning horizon and 10% interest rate, the B/C ratio of the investment is closest to: a) 0.909 b) 0.984 c) 1.069 d) 1.163

Answer 1

20]

Incremental benefits each year = Annual benefits - Annual costs

Annual benefits = Visitors per year * Additional benefits per visit

Net benefits in year 0 = -Initial cost

Net benefits in years 1 to 19 = Incremental benefits

Net benefits in year 20 = Incremental benefits + salvage value

NPV is calculate using NPV function in Excel

First, we assume Additional benefits per visit to be SR 0.15, and calculate the NPV

NPV is -1,468,067

H K L M N O P Q R S T U V 1 Visitors per year 2 Additional benefits per visit 1,800,000 0.15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4 5 6 Initial Investment Initial Cost 2,250,000 7 8 OCF 9 Annual benefits 10 - Annual Costs 11 Incremental benefits 270,000 145,000 125,000 270,000 149,350 120,650 270,000 153,831 116,170 270,000 158,445 111,555 270,000 163,199 106,801 270,000 168,095 101,905 270,000 173,138 96,862 270,000 178,332 91,668 270,000 183,682 86,318 270,000 189,192 80,808 270,000 194,868 75,132 270,000 200,714 69,286 270,000 206,735 63,265 270,000 212,937 57,063 270,000 219,326 50,674 270,000 225,905 44,095 270,000 232,682 37,318 270,000 239,663 30,337 270,000 246,853 23,147 270,000 254,258 15,742 12 13 Terminal Cash Flow 14 Salvage Value 720,000 16 NPV Analysis 17 Net Benefits (2,250,000) 125,000 120,650 116,170 111,555 106,801 101,905 96,862 91,668 86,318 80,808 75,132 69,286 63,265 57,063 50,674 44,095 37,318 30,33723,147 735,742 19 NPV (1,468,067)

K L M N O 1 Visitors per year 2 Additional benefits per visit 1800000 0.15 1 2 3 4 5 6 7 8 9 10 11 12 13 4 5 6 Initial Investment Initial Cost 2250000 7 8 OCF 9 Annual benefits 10 - Annual Costs 11 Incremental benefits =$B$1$B$2 =$B$1*$B$2 =$B$1$B$2 =$B$1$B$2 =$B$1$B$2 =$B$1*$B$2 =$B$1$B$2 =$B$1$B$2 -$B$1$B$2 =$B$1$B$2 -$B$1$B$2 -$B$1$B$2 =$B$1*$B$2 145000 EC10*(1+3%) =D10*(1+3%) =E10*(1+3%) =F10*(1+3%) =G10*(1+3%) =H10*(1+3%) =110*(1+3%) = 10*(1+3%) =K10*(1+3%) =L10*(1+3%) =M10*(1+3%) =N10*(1+3%) =C9-C10 =D9-D10 E9-E10 =F9-F10 G9-G10 =H9-H10 =19-110 = 29-J10 =K9-K10 =L9-L10 =M9-M10 =N9-N10 =09-010 12 13 Terminal Cash Flow 14 Salvage Value 15 =-B6 =C11 -011 =E11 =F11 =G11 =H11 =111 -J11 -K11 =L11 -M11 =N11 -011 16 NPV Analysis 17 Net Benefits 18 19 NPV 20 =NPV(12%,C17:V17)+B17

Po S T U V 1 Visitors per year 2 Additional benefits per visit 3 4 5 Initial Investment 6 Initial Cost 7 8 OCF 9 Annual benefits 10 - Annual Costs 11 Incremental benefits 12 13 Terminal Cash Flow 14 Salvage Value =$B$1$B$2 =$B$1$B$2 =$B$1$B$2 =$B$1*$B$2 =$B$1$B$2 =$B$1$B$2 =$B$1$B$2 =010*(1+3%) =P10*(1+3%) =Q10*(1+3%) =R10*(1+3%) =510*(1+3%) =T10*(1+3%) =U10*(1+3%) =P9-P10 =Q9-010 =R9-R10 -S9-S10 =T9-T10 =U9-U10 =V9-V10 =B6.32% 16 NPV Analysis 17 Net Benefits =P11 =Q11 R11 =S11 =T11 =U11 =V11+V14 18 19 NPV

To justify the facility improvement, the NPV should be at least zero.

The Additional benefits per visit where NPV is zero is calculated using GoalSeek in Excel

B C D E F 1 Visitors per year 2 Additional benefits per visit 1,800,000 0.15 Goal Seek o 1 Set cell: SBS19 To value: By changing cell: SBS21 2,250,000 OK Cancel 5 Initial Investment 6 Initial Cost 7 8 OCF 9 Annual benefits 10 - Annual Costs 11 Incremental benefits 12 13 Terminal Cash Flow 14 Salvage Value 125,000 120,650 116,170 111,555 16 NPV Analysis 17 Net Benefits (2,250,000) 125,000 120,650 116,170 111,555 18 19 NPV (1,468,067)

The Additional benefits per visit where NPV is zero is SR 0.26

F G H K L M N O P Q R S T U V 1 Visitors per year 2 Additional benefits per visit 1,800,000 0.26 OD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4 5 6 Initial Investment Initial Cost 2,250,000 7 8 OCF 9 Annual benefits 10 - Annual Costs 11 Incremental benefits 466,543 145,000 321,543 466,543 149,350 317,193 466,543 153,831 312,713 466,543 158,445 308,098 466,543 163,199 303,344 466,543 168,095 298,448 466,543 173,138 293,405 466,543 178,332 288,211 466,543 183,682 282,861 466,543 189,192 277,351 466,543 194,868 271,675 466,543 200,714 265,829 466,543 206,735 259,808 466,543 212,937 253,606 466,543 219,326 247,218 466,543 225,905 240,638 466,543 232,682 233,861 466,543 239,663 226,880 466,543 246,853 219,690 466,543 254,258 212,285 12 13 Terminal Cash Flow 14 Salvage Value 720,000 15 16 NPV Analysis 17 Net Benefits (2,250,000) 321,543 317,193 312,713 308,098 303,344 298,448 293,405 288,211 282,861 277,351 271,675 265,829 259,808 253,606 247,218 240,638 233,861 226,880 219,690 932,285 19 NPV

The Additional benefits per visit where NPV is zero is SR 0.26

The answer is (c)