Worksheet 5: First year rate of return

Worksheet 5: First year rate of return

Explanation sheet for first year rate of return

This worksheet is used to calculate the first year rate of return for the preferred project option.

1 Preferred project option Enter the preferred project option from worksheet 4, row (12).
2 PV of total net cost Enter the PV of total net cost of the preferred option from worksheet 3, row (18).
3 Mid-point of first year benefits Enter the mid-point of the first year of benefits relative to time zero by adding six months to the end of construction. For example, if the end of construction is 1¾ years after time zero, the mid-point of the first year of benefits is 2¼ years after time zero.
4 Discount factor (SPPWF) of first year of benefits Enter the SPPWF corresponding to the mid-point of the first year of benefits from table A1.2 in appendix A1.
5 Annual benefits of preferred option (at time zero) Enter the undiscounted (time zero) value of the net annual benefits for the preferred option from worksheet 2, column (4).
6 Annual benefit of the do minimum (at time zero) Enter the undiscounted (time zero) value of the net annual benefits for the do minimum from worksheet 2, column (4).
7 Annual net benefit of preferred option (at time zero) Enter the undiscounted (time zero) value of the net annual benefit by subtracting the do minimum value (5) from the preferred option value (6).
8 Growth rate Enter the growth rate at time zero from worksheet 1.
9 PV of benefits in first year Calculate the PV of the first year benefits using the formula shown on the worksheet.
10 PV of total net benefits in first year Sum the PV of all the net benefits to get the PV total net benefits in the first year.
11 FYRR Calculate the first year rate of return by dividing the PV of the first year of benefits (10) by the PV of the total net costs (2). Express this as a percentage by multiplying the result by 100.

First year rate of return - EXAMPLE

1 Preferred project option D
2 Present value of total net costs $500,000
3 Mid point of first year of benefits (relative to time zero) 2.25
4 Discount factor (SPPWF) for first year of benefits 0.8070

Benefit Annual benefits of preferred option Annual benefits of do minimum Net annual benefit
(at time zero)		 Growth rate
(decimal)		 PV of benefits in first year
(5) (6) (7) (8) (9)=[1.0+(3)x (8)]x(4)x(7)
Travel time savings 200,000 100,000 100,000 0.02 84,330
Vehicle operating cost savings 100,000 50,000 50,000 0.02 42,170
Accident cost savings 250,000 200,000 50,000 0.01 41,260
Reduced driver frustration N/A 0.02
Vehicle emissions reductions 5,000 2,500 2,500 0.02 2,110
External impacts
Vehicle emissions 50,000 30,000 20,000 0.02 16,140
10 Sum of present value of benefits in first year $186,010
11 First year rate of return [(8)/(2) × 100] 37%

Worksheet 5 (54 kb)

Explanation for worksheet 5 (32.4 kb)