Question

A 50-meter tunnel must be constructed as part of a new aqueduct system for a city. Two alternatives are being considered. One is to build a full-capacity tunnel now for $500,000. The other alternative is to build a half-capacity tunnel now for $300,000 and then to build a second parallel half-capacity tunnel 20 years hence for $400,000. The cost of repair of the tunnel lining at the end of every 10 years is estimated to be $20,000 for the full-capacity tunnel and $16,00 for each half-capacity tunnel.

Determine whether the full-capacity tunnel or the half-capacity tunnel should be constructed now. Solve the problem by B/C ratio analysis using a 5% interest rate and a 50-year analysis period. There will be no tunnel lining repair at the end of the 50 years.

Answer 1

OPtion-1 -1 Full- CaPacity tunnel CompataBionop total as on today :- -# Initial inveltme af Cont ruction - S00000 Co stofthe Projet + Preset vaaue ef Resair® Cot 16, 2.34 inared NOte -0 . Total Present value of Pro je ct the 516,234 Note- The Reair Cot Should incuYed af end f evey 10hear after the it was given there Condtruction and RePair Cot at the ond f dear వ no The RePair cot shouldincured af fhe ear, 30 yeaY Year, 20t Jear : The Present valuet lining and re Pair Cot is going to Com Ated ellow Cnd ef 0th } and 40 fu deav Presevalue Pref the Cast Cot Iincred $ 20/000 O.6134 $1,227.80

$7,538 o. 364 o 2314 201000 30 4, 628 2,840 o 1420 4-0 Totl Present Value f 16, 234 Qining RePair Cost how oPthon- 2 Halb- Cafacity tunnel and HaltCafacity tunnel aeler 20-eare Compatution f fotl Cost ef the Prouec on foday itial ot Conttuction f Hl- $300,000 tunnel today Ca fa city Presevaleue uf cot ef CojiKa ction =f150360 second half-Cafacity tunnel at the ($4,00, 000 o. 364) 26

C) Preset value ef Oiving aud 2780 Resaire Co t -wote-2 .. Tofal Presef due f the 13 $A,53,540 Pojece rhe refoaire aud linivg cot Note On halt-Cafaciy tunnel which Second Was Contucted ct the end ef doth yeur (wi be nCuel in only 3othgear and 4-0f year Уeat Preset Value ftor Lining and Refair Coy preset value On 2halb2nhoalbTofal Cafa ci ty Cafa Ci ta tunnel tunnel Cost inurel 982. 24 1600 1600 16 00 1600 o.3769 60304- 30 4-0- 48 o. 23/4 1600 1600 32 O0 4 54. 4-0 O.J420 4-0 1600 1600 32 O0 Totl Pv liuiny ond refaiWs Colf =

Con clusion V Coyt Projec 1 altesnive- Ful cafauita tunnel = $5,16,234 Per 2nd lternabive- two half-Calacita - $453,540 tunneles halb-cafauity and another halb- cafacity It wo advised to Coutyu c tunnel one now tunnel after 20-eares because it Coyts outflow wha Comfared finanial a deser fll-Cafa uita tunnel today to bulding
It was advised to opt for the alternative 2 , that is the constitution of half tunnels is more economical than the constitution of one single full capacity tunnel today.

Disclaimer:-

In the 11th linne of the problem it was given the lining and repair cost is 1,600$ , But the cama is ther after two zeros i.e $16,00

While solving the problem it was taken as 1,600$ only but there is a chance it may be $16,000

The answer may change it was $16,000