This document contains an engineering economics exam with four sections and multiple questions in each section. The exam tests knowledge of topics like loan payments, capital budgeting, cost-benefit analysis, and mining investment analysis. It provides context for calculation questions, such as loan principal and interest amounts, net present value, weighted average cost of capital, and mining investment returns. The exam is designed to be completed within a specified time limit and without outside consultation.

1. Engineering Economics
j.zambujal.oliveira@ist.utl.pt
19.01.2001
Duration: 60 minutes (Partial Test – 2 groups)
120 minutes (Global Test – 4 groups)
This exam is to be executed without any consultation.
I.
Consider an annual payment of €3741 associated to a loan with a maturity of 5
years and a nominal interest rate of 6% by year.
(1). (30%) Determine the value of the principal, and the value of interest
paid at the end of the second year.
(2). (20%) What is the value of principal paid until the end of third year?
(3). (30%) If the payment periodicity of the last two years were by month,
what would be the payment?
(4). (20%) What will be the monthly payment if you consider a nominal
interest rate compounded monthly?
II.
A company is faced with making a decision on a large capital investment proposal.
The capital investment amount is €640000. Estimated annual revenue at the end
of each year in the eight-year study period is €200000. The estimated annual year-
end expenses are €42000 starting in year one. These expenses begin decreasing by
9.5% per year at the end of year four and continue decreasing through the end of
year eight. Suppose the government offers the company an 8-year, non-amortizing
€320000 loan to help the company to undertake the project (the residual is financed
by equity). The government offers an attractive rate of 10% when shares of similar
risk yield an expected return of 15%. The tax rate is 25%. Assuming a €20000
market value at the end of year eight and straight line depreciation, answer the
following questions:
(1). (30%) What is the weighted average cost of capital?
(2). (40%) Using the NPV and the MIRR (reinvestment rate eq. to wacc),
what is your conclusion about the acceptability of this proposal?
(3). (30%) How can you compare this investment with another that
generates €2 by each unit of investment?

2. Engineering Economics
j.zambujal.oliveira@ist.utl.pt
19.01.2001
III.
A new highway will provide the following benefits: (b1) Extra commerce (€50
million each year); (b2) Economic growth over a 10-year period (increase of €5
million in the 2nd. year and increase of 5% in the subsequent years); and (b3)
Decrease in accidents (savings of €0.8 million each year). The disadvantages are:
(d1) Destruction of farmland (€1.3 million each year); (d2) Decrease in commercial
activity (€0.7 million each year). Consider a time horizon of 15 years and assume
an annual interest rate of 7%.
(1). (60%) Calculate the yearly net benefit of building the superhighway.
The highway yield €0.05 per ton-km (600 million annual ton-km) in fees. The tax
revenues of the first year represent €2 million and will grow annually at an annual
rate of 3%. The annual maintenance costs of the highway correspond to €1.5
million.
(2). (40%) Assess the desirability of the proposed superhighway, based on a
construction cost of €280 million.
IV.
A Russian company owns a land in Siberian on which five palladium mines could
be constructed. Each mine costs 1 million Russian rubles (R). The yield of each
mine will be either 1,000 or 2,000 ounces (oz) of palladium with equal probability.
All the palladium will be extracted from the mine in the first year of operation,
after which the mines will be worthless (there are no exit costs). Palladium sells at
spot and one-year forward prices of R1500/oz. Variable production costs are
R500/oz. The appropriate discount rate is 10% per year. The government has
agreed to a 25% tax rate. Rather than investing in all five mines today, the Russian
could invest in one mine on an exploratory basis and then base subsequent
investment on the outcome of the first mine. Once the exploratory mine is in
operation, the output of the four additional mines will be known with certainty.
Palladium’s two-year forward price is R1500/oz and variable cost is R500/oz.
(1). (30%) Calculate the NPV of investing in all 5 mines as a “now-or-never”
alternative.
(2). (30%) Calculate the NPV (as of t = 0) of investing in a single mine and
then waiting one year before considering investment in the other 4 mines.
(3). (40%) What is the opportunity cost of immediate investment in all five
mines today?