Question

The right of way and the road bed for a new highway will cost $4.5 million.The pavement will cost $2.5 million and it has a much shorter life of 20 years. if the discount rate is 9% find the projects capitalized cost?

Answer 1

cost - Right of way and road bed	$ 4.5 million
cost -pavement	$2.5 million
Total cost of project is	$ 7 million	(sum of above)
Capitalized costs are not expensed in the period they were incurred but recognized over a period of time via depreciation or amortization
So the above cost is to be depreciated over life of asset of 20 years
Assuming straight line method of depreciation , Yearly cost for each year upto 20 years = $ 7000000/20 = $350000 per year
SO $350000 is depreciated over a period of 20 years of project (year 1 to year 20)
This cost of 20 years should be discounted to 9% at today value using present value annuity factor of 20 years for 9%
Present value annuity factor for 9% for 20 years = 0.178413 (refer annuity table or calulation below)
	Year 1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Depreciation	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000	3,50,000
Annuity factor	0.9174	0.8417	0.7722	0.7084	0.6499	0.5963	0.5470	0.5019	0.4604	0.4224	0.3875	0.3555	0.3262	0.2992	0.2745	0.2519	0.2311	0.2120	0.1945	0.1784
Present value (Multiply above)	3,21,101	2,94,588	2,70,264	2,47,949	2,27,476	2,08,694	1,91,462	1,75,653	1,61,150	1,47,844	1,35,636	1,24,437	1,14,163	1,04,736	96,088	88,154	80,876	74,198	68,071	62,451
Capitalised cost at Present value = sum of above				31,94,991
			i.e $ 3.194 million