#### 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

- 1: Buy assets that add value; avoid buying assets that don’t add value.
- 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
- 5: GetFormula to spreadsheet

## 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:

where 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:

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 , 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**:

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

Goal Seek computes X.

### NPER

### RATE

## 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 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:

### 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)`

### MIRR

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