cost-benefit analysis

[Analysis] The Site C hydroelectric dam is a controversial, expensive project. It was chosen from a set of many power generation alternatives that included wind generators, combined gas cycle plants, and more. One reason given for choosing Site C was that, given the 5% real discount rate used by B.C. Hydro, Site C provided energy at a reasonable cost of about $80 per MWh. (The other options ranged from a bit less than $60 to over $90.)

In 2015, economist Robert McCullough published his opinion that the 5% real discount rate was too low, and that 12% would be more appropriate. Using a 12% real discount rate (and changing nothing else), the cost of energy from Site C goes up to $150 per MWh, and the clear winner among the alternatives becomes a natural gas plant, with costs of about $55 per MWh.

a. (8 marks) A hydroelectric dam like Site C has very high initial costs, but once the dam is built, has very low operating costs. A natural gas plant has very low initial costs, but very high yearly fuel costs. Why would using a low discount rate (such as 5% instead of 12%) make the Site C dam look good and the gas cycle plant look bad? Explain briefly (25 words or less).

B.According to McCullough, BC Hydro said that it uses the 5% discount rate for its own investments because that is what it costs the company to borrow money. It can borrow directly from the province of BC, and its debt is guaranteed by the government. Do you agree that this means 5% is a good choice for the discount rate? Briefly explain your reasoning. (20 words or less)

C. McCullough’s sources justify the higher 12% rate on the basis of risk: the risk of the project failing, and the risk of international supply of capital drying up in the future, raising the cost of borrowing. Because of BC Hydro’s government guarantees, these risks may be small for Site C. List at least one other reason why the social discount rate for Site C might be higher than BC Hydro’s 5% cost of borrowing, and briefly explain your reasoning (20 words or less).

You work for a charity providing clean well-water to isolated communities. You are trying to decide whether it is worthwhile to build a well in the town of Tionalfic. There would be an initial cost of $8,000 to dig the well, and your charity would have to pay an additional $1,000 dollars for a replacement pumps 8 years in the future.

The well provide clean water for 15 years. The benefits from this clean water are estimated to be worth $1,500 a year. It would take a year for the first benefits to be seen.

(See the appendix for this information in table form. Year 0 is the present.)

Your charity is very small, and has very little money on hand. It can borrow money at a rate of 4% per year. Because of your charity’s need to borrow money, you use 4% as your MARR.

a. (2 marks) Calculate the present worth of the well’s costs, to the nearest cent. Use D(r,N).

Present Worth of Costs: $ ___________________________

b. (2 marks) Calculate the present worth of the well’s benefits, to the nearest cent. Use S(r,N).

Present Worth of Benefits: $ ___________________________

c. (1 mark) Use your answers to a. and b. to calculate a BCR to two decimal places. (It’s just the present worth of benefits over the present worth of costs).

(Discounted) Benefit/Cost Ratio: ___________________________

d. (1 mark) Use your answers to a. and b. to calculate the NPV to two decimal places.

Net Present Value $ ___________________________

e. (2 marks) Use your answer to part d. and S(r,N) to calculate the equivalent annual worth of the project (use N = 15).

Equivalent Annual Worth: $ _______________________

Data Table for Question 3

Year	Costs	Benefits	Bribe
0	$8,000
1		$2,000	$2,000
2		$2,000
3		$2,000
4		$2,000
5		$2,000
6		$2,000
7		$2,000
8	$1,200	$2,000
9		$2,000
10		$2,000
11		$2,000
12		$2,000
13		$2,000
14		$2,000
15		$2,000

f. (2 marks) Is the project worthwhile? Explain briefly (10 words or less).

Worthwhile? Yes/No

Reason:

A manufacturer of bottled water approaches your charity with an offer. If you do NOT build the well, one year from today she will pay your charity a bribe of $2,000. This manufacturer is known to always pay her bribes, so there is no risk. You can have either the bribe OR the well. The two projects are mutually exclusive.

g. (3 marks) Use the repeated lives method to compare the NPV of the bribe to the NPV of digging the well. Should you accept the bribe? Show your work and explain briefly (10 words or less). (Hint: You can use S(r,N) to make your repeated life calculations very quick.)

Accept the Bribe? Yes/No

Reason:

h. (2 marks) Compare the annual worth of the well from part e. to the annual worth of the bribe. Should you accept the bribe? Show your work and explain briefly. (10 words or less.) (Hint: You shouldn’t need to perform any additional mathematical operations. You have all the information you need.)

Accept the Bribe? Yes/No

Reason: