Question

1. Maintenance-free siding for a storage building costs $3.5 per square foot installed. Painted siding costs $2.5 per square foot, with a maintenance cost of $1.50 per square foot every five years. Determine the rate of interest at which the two choices have the same capitalized costs.     

Answer 1

Maintenance-free paint cost	$      3.50
Maintenance paint cost	$      2.50
Variance in maintenance cost	$      1.00
Maintenance cost	$      1.50
To keep both costs equal, the PV of maintenance cost at T5 should be equal to variance in paint cost at T0 as calculated above:
Maintenance cost after 5 years=	Variance in maintenance cost * (1+Interest rate)^time
1.5=	1*(1+Interest rate)^5
1.5^(1/5)=	(1+Interest rate)
1.085	(1+Interest rate)
Interest rate=	1.085-1
Interest rate=	8.50%