#### 2019-05-01 term: 2B

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

# meta

Brian P. Cozzarin

• Homework 5%
• Tutorial quiz 5%
• Programming assignment 20 + 5%
• Midterm 30%
• Final 40%

## introduction to finance

8 Principles of Finance

• 2: Cash is king.
• 3: The time dimension of financial decisions is important.
• 4: Know how to compute the cost of financial alternatives.
• 5: Minimize the cost of financing.
• 6: Take risk into account.
• 7: Markets are efficient and deal well with information.
• 8: Diversification is important.

5 Rules for Finance Modeling

• 1: Put important variables in one place. Critical parameters == value drivers.
• 2: Don’t hardcode numbers
• 3: No blank columns
• 4: No auto-jump cells

## 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.

### FV

Future value: $principal \times (1 + rate)^{N}$

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

• Beginning of year: interest is not applied
• End of year: interest is applied

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

note that present value is negative.

### PV

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: $principal \div (1 + rate)^{N}$

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.

• Type 0: end-of-period payments
• Type 1: beginning-of-period payments

### NPV

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.

### PMT

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 $r$, number of periods $N$, principal value or loan total $PV$

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

i.e Saving for an amount 3 methods:

• 1: trial and error
• 2: goal seek
• 3: Excel’s PMT function

Goal Seek computes X.

## measures to evaluate investment opportunities

#### Whether to undertake a single investment?:

• 1: determine if the IRR of the project > the initial investment.
• 2: calculate whether the net present value NVP > 0

#### Ranking investments:

• 1: A over B if $NPV_A > NPV_B$.

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

NPV

Hence prefer NPV compared to IRR.

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

### NPV

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: $NPV>0$

### IRR

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:

### EAC

Equivalent annual cash flows

### PI

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