Question

A highway in a rural town has a dangerous curve. Improving the highway will cost $10 million today, at time t = 0. The discount rate is r = .05 and a planning horizon of 10 years has been adopted. It is known that the new bridge will create benefits (due to a decline in deaths) of $1.5 million per year for each of the 10 years from t = 1 to t = 10.

a. Compute the present value (today, at t = 0) of the benefit over 10 years from t = 1 to t = 10. Should the highway be improved?

b. Finally, let’s say the new highway, being safer than the old one, will also save one statistical life per decade. What should the value of the statistical life be in order to change the decision in part a.?

c. Now suppose a member of the city council argues successfully that the planning for this project should use a discount rate of r 0 = .03 rather than the original value of r = .05. Discuss how this change will affect the decision. How would you advise the council, as a staff economist, to select the “best” discount rate for the project?

Answer 1

PART 1

To decide whether a project should be undertaken or not, one of the means is through Net Present Value or NPV.

If the NPV is positive, project should be undertaken and vice versa.

As per the calculations below, the NPV is $1,582,602. The benefits are more than the cost. Hence, the highway should be improved.

discount rate	5%
present value formula	cash flows/(1+discount rate)^t
time 't'	0	1	2	3	4	5	6	7	8	9	10
(outflow)/inflow	(10,000,000)	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000
present value discounted at 5%	(10,000,000)	1,428,571	1,360,544	1,295,756	1,234,054	1,175,289	1,119,323	1,066,022	1,015,259	966,913	920,870
present value of outflows	(10,000,000)
present value of inflows	11,582,602
Net present value	1,582,602

PART 2

This part of question is valid if the answer in part 1 turns out to be a negative NPV. Then we would add more value because of the saving of 1 life in the span of 10 years and try to reach a positive NPV.

For example, if in part 1 answer

• Present value of inflows was $9,000,000 and present value of outflows $10,000,000. then NPV = -$1,000,000
• Now the value of life should be more than $1,000,000 like $1,500,000 so that now
• present value of inflows = $10,500,000 and outflows = $10,000,000 with a positive NPV of $500,000

PART 3

discount rate	5%	3%
present value formula	cash flows/(1+discount rate)^t
time 't'	0	1	2	3	4	5	6	7	8	9	10
(outflow)/inflow	(10,000,000)	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000	1,500,000
present value discounted at 5%	(10,000,000)	1,428,571	1,360,544	1,295,756	1,234,054	1,175,289	1,119,323	1,066,022	1,015,259	966,913	920,870
present value of outflows	(10,000,000)
present value of inflows	11,582,602
Net present value	1,582,602
present value discounted at 3%	(10,000,000)	1,456,311	1,413,894	1,372,712	1,332,731	1,293,913	1,256,226	1,219,637	1,184,114	1,149,625	1,116,141
Net present value	2,795,304

With a lower discount rate, NPV will be higher.

The discount rate has to reflect the target risk and cost of undertaking the project. This would entail the cost of debt and cost of equity, preference both.

One of the best measures of discount rate is Weighted Average Cost of Capital (WACC)