Question

Rubber sidewalks made from ground up tires are said to be environmentally friendly and easier on people’s knees. RUBBERSIDEWALKS, Inc. of Gardena, California, manufactures the small rubberized squares that are being installed where tree roots, freezing weather, and snow removal have required sidewalk replacement or major repairs every 3 years. The District of Columbia spent $60,000 for a rubber sidewalk to replace broken concrete in a residential neighborhood lined with towering willow oaks. If a concrete sidewalk costs $28,000 and lasts only 3 years versus a 9-year life for the rubber sidewalks, what rate of return does this represent?

a) [hand calculation]

b) [Use MS Excel]

Answer 1

a. by hand

analysis period = 9 yrs

Incremental initial cost (rubber - concrete) = 60000 - 28000 = 32000

Incremental replacement cost (rubber - concrete) at EOY 3 = 0 - 28000 = -28000 (savings at EOY 3)

Incremental replacement cost (rubber - concrete) at EOY 6 = 0 - 28000 = -28000 (savings at EOY 6)

let i% be incremental ROR, then

28000*(P/F,i%,3) + 28000*(P/F,i%,6) = 32000

Dividing by 1000

28*(P/F,i%,3) + 28*(P/F,i%,6) = 32

using trail and error method

When i = 13%, value of 28*(P/F,i%,3) + 28*(P/F,i%,6) = 28*0.693050 + 28*0.480319 = 32.854318

When i = 14%, value of 28*(P/F,i%,3) + 28*(P/F,i%,6) = 28*0.674972 + 28*0.455587 = 31.655638

using interpolation

i = 13% + (32.854318-32) /(32.854318-31.655638)*(14%-13%)

i = 13% + 0.71% = 13.71%

by excel

Yrs	initial cost of concrete	initial cost of rubber	Incremental Cash flow
0	-28,000.00	-60000	-32,000.00
1	0.00	0	0.00
2	0.00	0	0.00
3	-28,000.00	0	28,000.00
4	0.00	0	0.00
5	0.00	0	0.00
6	-28,000.00	0	28,000.00
7	0.00	0	0.00
8	0.00	0	0.00
9	0.00	0	0.00
		IRR	13.71%

Showing formula in Excel

Yrs	initial cost of concrete	initial cost of rubber	Incremental Cash flow
0	-28000	-60000	=O8-N8
1	0	0	=O9-N9
2	0	0	=O10-N10
3	-28000	0	=O11-N11
4	0	0	=O12-N12
5	0	0	=O13-N13
6	-28000	0	=O14-N14
7	0	0	=O15-N15
8	0	0	=O16-N16
9	0	0	=O17-N17
		IRR	=IRR(P8:P17)