Question

Question from chapter 2 -3rtDa

	2006-2015	2016-2025	2026-2035	2036-2045	2046-2055	2056-2065	2066-2075	2076-2081
Revenues	1,746.60	2,604.60	3,908.20	5,453.60	7,588.60	10,749.00	14,656.20	11,797.90
Expenditures
General operating	468.80	771.00	1,267.80	2,084.90	3,428.60	5,638.30	9,272.10	8,227.90
Repairs and renovations	577.80	705.20	839.40	1,011.20	1,231.20	1,512.70	1,873.10	1,337.80
Total expenditures	1,046.60	1,476.20	2,107.20	3,096.10	4,659.80	7,151.00	11,145.20	9,565.70
Revenues over expenditures	700.00	1,128.40	1,801.00	2,357.50	2,928.80	3,598.00	3,511.00	2,232.20

In 2006 the State of Indiana in the USA sold a 75-year concession to operate and maintain the East-West Toll Road. Before doing so, it commissioned a consulting report that estimated the value of the concession.

Q: Calculate the present value of the concession using a discount rate of 6%. Cash flows are reported in Table 1 for each ten-year block up until 2066–2075 with the last block as five years (2076–2081). Assume in your calculations that cash flows are spread evenly during those blocks.

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U
2
3			2006-2015	2016-2025	2026-2035	2036-2045	2046-2055	2056-2065	2066-2075	2076-2081
4		Revenue over expenditures	$700.00	$1,128.40	$1,801.00	$2,357.50	$2,928.80	$3,598.00	$3,511.00	$2,232.20
5
6		Total Number of Year	75
7		Block	10	Years
8		Discount rate	6%
9
10		Present value of cash flows will be as follows:
11		Present value	=$700*(P/A,6%,10)+$1,128.40*(P/A,6%,10)*(P/F,6%,10)+$1,801*(P/A,6%,10)*(P/F,6%,20)+$2,357.50*(P/A,6%,10)*(P/F,6%,30)
12			+$2,928.80*(P/A,6%,10)*(P/F,6%,40)+$3,598*(P/A,6%,10)*(P/F,6%,50)+$3511*(P/A,6%,10)*(P/F,6%,60)+$2232.2*(P/A,6%,5)*(P/F,6%,70)
13			$21,419.70	=PV(D8,D7,-1,0)*(D4+E4*(1/((1+D8)^10))+F4*(1/((1+D8)^20))+G4*(1/((1+D8)^30))+H4*(1/((1+D8)^40))+I4*(1/((1+D8)^50))+J4*(1/((1+D8)^60)))+K4*PV(D8,5,-1,0)*(1/((1+D8)^70))
14
15		Hence present value is	$21,419.70
16
17