Question

2) A proposed civic center is estimated to cost $10,000,000 and have a life of 45 years. The maintenance costs are estimated to be: Paint & normal repairs: $20,000/yr (billed and paid at the end of first year and each succeeding year) and increase 10%/year over the 45 year life. Replace air conditioner, floor tiles, seat upholstery every 15 year: the cost 15 years from now is estimated at $2,000,000 and the cost is expected to double for the replacement required at the end of the 30. year. After 45 years it is estimated the entire civic center will have a salvage value of $500,000 a) If the civic center will be financed with 45-year revenue bonds at 8% to be paid off in equal annual installments, how annual revenue is required to pay off the bonds plus paint, repairs and replacements as listed above? b) Any subsidy is needed?

please solve without spreadsheet

Answer 1

Equal annual installment on the bond
using the PV of ordinary annuity formula,
PV= Pmt.*(1-(1+r)^-n)/r
10000000=Pmt.*(1-1.08^-45)/0.08
Solving the above, we get the equal annual pmt. As
Pmt.=10000000/((1-1.08^-45)/0.08)=
825872.85		825873
1.PV of Paint & normal repair expenses for 45 years
Using PV of growing annuity formula,
Annual exp./(r-g)*(1-((1+g)/(1+r))^8)
ie. 20000/(8%-10%)*(1-(1.1/1.08)^45)=	-1283504
2.PV of the two replacements at end of 15 & 30 yrs.
2000000/1.08^15=	-630483
4000000/1.08^30=	-397509
3.Salvge at end of 45 yrs.
500000/1.08^45=	15664
NPV of the above(1+2+3)	-2295833
Equivalent annual cost of the above(NPV/Annuity Factor)
2295833/((1-1.08^-45)/0.08)=		189607
Minimum annual required		1015479