Question

Problem 1
Find the internal rate of return (IRR) of a project that costs $10,000 and brings net
revenue of $8,000 each year for two consecutive years.

Problem 2
Two projects are proposed to a young start-up company. Project A will cost
$250,000 to implement and is expected to have annual net cash flows of $75,000.
Project B will cost $150,000 to implement and should generate annual net cash
flows of $52,000. The company is very concerned about their cash flow. Using the
payback period, which project is better, from a cash flow standpoint? If the discount
rate is 10% what is the discounted payback period.

Problem 3
A four-year financial project has net cash flows of $20,000; $25,000; $30,000; and
$35,000 in the next four years. It will cost $65,000 to implement the project all of
which is needed at the beginning of the project. After the fourth year, the project will
have no residual value. Find the net present value of the project assuming 20%
discount rate. What is the profitability index of the project?

Problem 4
The annual maintenance on the parking lot is $5000. What expenditure would be
justified for resurfacing if no maintenance is required for the first 5 years, $2000 per
year for the next 10 years, $3000 per year for the next 5 years and $5000 a year
thereafter? Assume the cost of money is 6%.

Problem 5
Mr. Jones wishes to establish a fund for his newborn child’s education. The fund
pays $60,000, $67,000, $75,000 and $83,000 on the child’s 18th, 19th, 20th, and 21st
birthdays respectively. The fund will be set up by the deposit of a fixed sum on the
child’s 1st through 17th birthdays. The fund earns 6 percent annual interest. What is
the required annual deposit?

Problem 6
A company is pursuing following cost-reduction projects at the same time.
1. Project A requires an investment of $10 million. It is expected to yield a cost
savings of $30 million in the first year and another $10 million in the second
year.
2. Project B requires an investment of $5 million. It is expected to produce a
cost savings of $5 million in the first year and another $20 million in the
second year.
3. Project C needs an investment of $5 million. It is expected to produce a cost
savings of $5 million in the first year and another $15 million in the second
year.
After the second year, there will be no benefit from these projects. The cost of
capital is 10 percent. Determine the ranking of these projects on the basis of the
evaluation criteria of NPV, IRR and Benefit-cost ratio.

Problem 7
a) An electric utility plans to build a large hydro project, to begin operation at the start
of 2020. The ultimate project capacity will be 400 MW, but only 200 MW is required
to serve load growth from 2020 until the end of 2024, and then the last 200 MW will
be commissioned at the start of 2025. The foundations for the last 2×100-MW units
will be constructed initially, but the power house would be completed and the
turbine-generator units would be installed later at an additional cost of $60 million.
An alternative would be to include the last two units in the initial construction
contract at an additional cost of only $45 million. The equipment suppliers and
contractors could offer a lower price if all units were built in one stage due to
economies of scale and thereby avoiding the cost of remobilisation required if the
last units were built separately. Furthermore there is an opportunity to export the
surplus generation produced by these last two units at an annual revenue of $ 4
million/yr, received at the end of each year from 2020 to 2024. Assume that the
additional operation and maintenance costs of these last two units are $500,000/yr
payable at the end of each year, the inflation rate is zero, the equipment lifetime is
indefinite and the discount rate is 12%. Is it more economic to commission the last
two units in 2020 or in 2025?
b) Re-evaluate the alternative schemes described in the above problem with a
discount rate of 15% instead of 12%. Which scheme is more economic now?

Problem 8
You are considering a good-looking Toyota hybrid car priced $60,000 or an elegant luxury
BMW car at $50,000. The fuel efficiency is rated at 20 km/liter for the Toyota and 10
km/liter for the BMW. The annual maintenance cost for both cars is about 0.5% of the car
price. The fuel price in the local market is selling at $1.00 per liter. The cars are to be
driven about 20,000 kms per year. You plan to keep your car for five years only. At the fifth
year, the resale values of the Toyota and the BMW are about 40 percent and 30 percent
respectively, of their original prices.
i) Assuming a discount rate of 5% and no escalation of fuel prices which car is the
better choice from the standpoint of cost?
ii) Will your decision change if the discount rate is 10%?

Problem 9
Determine the cost of electricity in US cents/kWh for a coal-fired power station of
total capacity 500 MW, with the following cost and energy data:
- Initial annual 5-years capital outlay 100, 200, 200, 100 and 100 MUS$
- Discount rate 8%
- 25 years lifetime, assume salvage value of 50 MUS$.
- Annual O&M cost: 1% of the total outlay (i.e. 1% of 700 MUS$)
- Annual consumption of coal is 1 million tons
- 1 ton of coal costs US$ 50.00 and produce 2500 kWh of energy
- No inflation and real escalation of fuel
Assume that all the costs and the benefit occur at the end of each year. Note that
after the final disbursement of capital cost the power plant is brought on-line hence
the benefit, O&M and fuel costs are realized after one year of plant being in
operation.

Answer 1

Answer of Problem 1:

Initial Investment = $10,000
Annual Revenue = $8,000
Period = 2 years

Let IRR be i%

NPV = -$10,000 + $8,000 * PVA of $1 (i%, 2)
0 = -$10,000 + $8,000 * PVA of $1 (i%, 2)

Using financial calculator:
N = 2
PV = -10000
PMT = 8000
FV = 0

I = 37.98%

IRR of the project is 37.98%