term: 2B

Engineering Economics: Financial Management for Engineers, taken in Spring 2019.


Brian P. Cozzarin

introduction to finance

8 Principles of Finance

5 Rules for Finance Modeling

time value of money

Opportunity cost of capital/money in the space of time: what you could’ve done with the money in that space of time.

i.e. in interest, different stocks…

Lock the reference with $Col$Row, or F4.

How to compare different opportunities? Calculate the NPV and IRR of investments.


Future value:

where is the number of periods. At higher interest rates, the curve is steeper.

In Excel: FV(rate, number of periods, equal payment per term [optional], -present value)

note that present value is negative.


Present value: if you are promised money in the future, how much is it worth today? Taking inflation into account

Note that present value and future value are mirror images.

Present value:

As interest rate increases, present value decreases. i.e. present value at 6% is higher than present value with 35%. See formula.

On Excel, PV computes present value or series of constant payment (annuity stream, ex lottery payouts), all payments are equal. Make negative so that the PV function produces a positive answer.


On Excel, NPV computes the present value, not the net present value.

This present value is for unequal payments over time, use PV for constant or equal payments over time.


Payments on flat loan payments. Repays a constant amount over the term, resulting into the total of the loan.

Use Excel’s PMT to compute loan payments. Parameters needed: rate , number of periods , principal value or loan total

Note that is a negative number so that the PMT returns a positive payment.

i.e Saving for an amount 3 methods:

Goal Seek computes X.



measures to evaluate investment opportunities

Whether to undertake a single investment?:

Ranking investments:

NPV and IRR sometimes give conflicting conclusions. When there is a conflict, use NPV. Why?


Hence prefer NPV compared to IRR.

Caveat using the NPV as criterion: they need to have the same lifespan.


Net present value: NPV of a series of future cash flows is the present value of the cash flow, minus the initial investment required

In other words: whether or not it’s worth spending the initial investment, depending of whether the net present value taking time into account is positive.

Investment is worthwhile if:


Internal rate of return, to evaluate new projects (i.e. getting a new computer? starting a new training program?) Represents the discount rate that we obtain if the investment’s NPV is 0. Equivalent to percentage gain.

Excel’s IRR: plotting NPV and seeing when the curve crosses the x-axis (x-intercept) is the IRR percentage.

IRR(values per year)


Modified IRR:


Equivalent annual cash flows


Profitability index

IRR is where the NPV crosses the x-axis.

i.e. should you build a bridge with a toll?? yes or no, just make an IRR analysis

loans and amortization tables

effective interest rates

capital budgeting: valuing business cash flows

what is risk

statistics for portfolios

portfolio diversification and risk

risk diversification and the efficient frontier

capital asset pricing model (CAPM) and the security market line (SML)

security market line and the cost of capital

efficient markets - general principles of security valuation

bond valuation

stock valuation