Question

A city is deciding whether it makes sense to invest in a light rail line. Engineers have projected that if the rail line were to be built, once completed it would reduce travel time for 2,000 commuters by 60 minutes per day (for each workday). The line will take four years to build. The costs of construction are projected to equal $25,000,000 per year, and the costs of operating the line are assumed to equal $2,000,000 per year. Assume that the project is to be evaluated over a 20 year time horizon, and Evermore uses its borrowing rate of 3% as the discount rate.

1. Assume that time is valued at $20 per hour per commuter. There are 5 workdays per week in a 52 week year. Calculate the monetary value of the reduced commute time projected to result from construction of the light rail line.
2. Using the spreadsheet template that is provided, calculate:
   1. the net present value of the project;
   2. The benefit-cost ratio.

	Years	1	2	3	4	5
Discount Rate
Value of Time per Hour
Annual Value Reduced Commuting Time
Present Value Reduced Commuting Time
Annual Capital Costs
Annual Operating Costs
Total Annual Costs
Present Value of Costs
Annual Net Benefits
Present Value of Net Benefits
Benefit-Cost Ratio

1. Now suppose that Evermore seeks federal funding for the project, and is told that in evaluating the project it needs to use the discount rate recommended by OMB for infrastructure projects. How would this change your results?

Answer 1

Step 1: Calculation of monetary value of the reduced commute time

Reduced Traveling Times in Hours per day (2000 Commuters * 1 hour (60 mins)) = 2000 hours

Number of Weeks in the year = 52 weeks

Number of Working Days = 5 days

Value of Time Saved = $20 per hour

Ans a) Monetary Value of Annual Savings = (2000 hours * 52 weeks * 5 days * $20) = $ 10,400,000

Step 2 : Calculation of Net Present Value of Project

Benefit Cost analysis

Years		Yr 1	Yr 2	Yr 3	Yr 4	Yr 5 to 20
Discount rate	3%
Value of Time per hour (2000 * $ 20)	$40,000
Annual Value Reduced Commuting Time (Note 1) (A)		-	-	-	-	$10,400,000.00
Present Value Reduced Commuting Time (Note 2) (C)		$0.00	$0.00	$0.00	$0.00	$116,067,915.16
Annual Capital Costs (Note 3)		$25,000,000.00	$25,000,000.00	$25,000,000.00	$25,000,000.00	-
Annual Operating Costs		-	-	-	-	$2,000,000.00
Total Annual Costs (B)		$25,000,000.00	$25,000,000.00	$25,000,000.00	$25,000,000.00	$2,000,000.00
Present Value of Costs (Note 2) (D)		$24,271,844.66	$23,564,897.73	$22,878,541.48	$22,212,176.20	$22,320,752.92
Annual Net Benefits (A) - (B)		($25,000,000.00)	($25,000,000.00)	($25,000,000.00)	($25,000,000.00)	$8,400,000.00
Present Value of Net Benefits (C) - (D)		($24,271,844.66)	($23,564,897.73)	($22,878,541.48)	($22,212,176.20)	$93,747,162.24
Benefit-Cost Ratio (C)/(D)		0	0	0	0	5.2

Net Present Value (NPV) = Sum of Present Value of Net Benefits

NPV = $819,702.17

Decision: Since NPV is positive meaning present value of cash inflows is greater than present value of cash outflows, accept the project

Notes :

1. Time horizon of the project is 20 years. During the Initial 4 years the Project is under construction and hence , there will be no savings due to reduced commuting time. From 5 year onwards till year 20 the annual savings due to reduced commute time is $10,400,000.

2. Present Value = Cash Flows * PVF (r,t) where, r = discount rate (3%) and t = Time period. Also, you can use the P.V. Formula** in excel to commute the same.

For Calculation of Present Value from 5 year to 20 year cash flows are multiplied with summation of PVF @3% from year 5 to year 2 (or PVAF(3%,20) - PVAF(3%,4)).

3. The costs of construction is $25,000,000 per year incurred in first 4 years in which line is constructed.

Step 3 : Calculation of Net Present Value of Project at discount rate notified by OMB for infrastructure projects ie.,7%

Benefit Cost analysis

Years		Yr 1	Yr 2	Yr 3	Yr 4	Yr 5 to 20
Discount rate	7%
Value of Time per hour (2000 * $ 20)	40000
Annual Value Reduced Commuting Time (Note 1) (A)		-	-	-	-	$10,400,000.00
Present Value Reduced Commuting Time (Note 2) (C)		$0.00	$0.00	$0.00	$0.00	$74,950,751.09
Annual Capital Costs (Note 3)		$25,000,000.00	$25,000,000.00	$25,000,000.00	$25,000,000.00	-
Annual Operating Costs		-	-	-	-	$2,000,000.00
Total Annual Costs (B)		$25,000,000.00	$25,000,000.00	$25,000,000.00	$25,000,000.00	$2,000,000.00
Present Value of Costs (Note 2) (D)		$23,364,485.98	$21,835,968.21	$20,407,446.92	$19,072,380.30	$14,413,605.98
Annual Net Benefits (A) - (B)		($25,000,000.00)	($25,000,000.00)	($25,000,000.00)	($25,000,000.00)	$8,400,000.00
Present Value of Net Benefits (C) - (D)		($23,364,485.98)	($21,835,968.21)	($20,407,446.92)	($19,072,380.30)	$60,537,145.11
Benefit-Cost Ratio (C)/(D)		0	0	0	0	5.2

Net Present Value (NPV) = Sum of Present Value of Net Benefits

NPV = $(24,143,136.30)

Decision: Since NPV is negative meaning present value of cash outflows is greater than present value of cash inflows, reject the project

Notes :

1. Time horizon of the project is 20 years. During the Initial 4 years the Project is under construction and hence , there will be no savings due to reduced commuting time. From 5 year onwards till year 20 the annual savings due to reduced commute time is $10,400,000.

2. Present Value = Cash Flows * PVF (r,t) where, r = discount rate (7%) and t = Time period. Also, you can use the P.V. Formula in excel to commute the same

For Calculation of Present Value from 5 year to 20 year cash flows are multiplied with summation of PVF @7% from year 5 to year 2 (or PVAF(7%,20) - PVAF(7%,4)).

3. The costs of construction is $25,000,000 per year incurred in first 4 years in which line is constructed.

** Present Value formula in excel

PV (rate, nper, pmt, [fv], [type]) where

rate = discount rate,

nper = time period that is 1, 2, 3 ..so on,

PMT = payment made each period, if any,

FV = Cash Flows,

type = When payments are due. 0 = end of period, 1 = beginning of period. Default is 0.