Question

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. Table 1 shows the forecasted cash flow from the toll road.

	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

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. Explain your calculations showing for each year the applicable discount rate and for each block the present value.

PS:please calculate in order to see and understand the PV for each block

Answer 1

		Beginning of year 2006=Year0
		End of year 2006=Year 1
		End of year 2007=Year 2
	Present Value (PV) of Cash Flow:
	(Cash Flow)/((1+i)^N)
	i=Discount Rate=6%=0.06
	N=Year of Cash Flow
	P=Present Values at beginning of Block are calculated using PV function of excel with Rate=C,Nper=A,Pmt=-B)
				N	A	B	C	P	PV=P/(1.06^N)
		Blockof years	Beginning of Block	Number of years fromPresent	Number of years in the block	Annual net Cash inflow	DiscountRate	Present Value at beginning of Block	Present Value of cash flow at beginning 2006
		2006-2015	2006	0	10	700.00	6%	$5,152	$5,152
		2016-2025	2016	10	10	1,128.40	6%	$8,305	$4,638
		2026-2035	2026	20	10	1,801.00	6%	$13,256	$4,133
		2036-2045	2036	30	10	2,357.50	6%	$17,351	$3,021
		2046-2055	2046	40	10	2,928.80	6%	$21,556	$2,096
		2056-2065	2056	50	10	3,598.00	6%	$26,482	$1,438
		2066-2075	2066	60	10	3,511.00	6%	$25,841	$783
		2076-2081	2076	70	5	2,232.20	6%	$9,403	$159
				Total	75			SUM	$21,420
	SUM of PV at beginning of 2006	$21,420
	Present Value of concession	$21,420