## PV

## Payment2PV

A chemical engineer believes that by modifying the structure of a certain water treatment polymer, his company would earn an extra $5000 per year. At an interest rate of 10% per year, how much could the company afford to spend now to just break even over a 5 year project period? (A) $11,170 (B) 13,640 (C) $15,300 (D) $18,950

## FV

## Payment2FV

An industrial engineer made a modification to a chip manufacturing process that will save her company $10,000 per year. At an interest rate of 8% per year, how much will the savings amount to in 7 years? (A) $45,300 (B) $68,500 (C) $89,228 (D) $151,500

## IRR

Year | NCF |

0 | -20 |

1 | 7 |

2 | 7 |

3 | 15 |

The interest rate at which the present worth and equivalent uniform annual worth are equal to 0.

## LinearProgramming

## LinearProgWithButton

## ProjectSelection

Project | Init. Invest | Annual NCF | Life | PW |

A | -25,000 | 6,000 | 4 | |

B | -20,000 | 9,000 | 4 | |

C | -50,000 | 15,000 | 4 | |

Budget | 70000 | |||

## ProjSelectionWithButton

Project | Init. Invest | Annual NCF | Life | PW |

A | -25,000 | 6,000 | 4 | |

B | -20,000 | 9,000 | 4 | |

C | -50,000 | 15,000 | 4 | |

Budget | 70000 | |||

## ProjectSelection2

Project | Init. Invest | Annual NCF | Life | PW |

A | -8,000 | 3,000 | 4 | |

B | -15,000 | 2,930 | 9 | |

C | -8,000 | 2,680 | 5 | |

D | -8,000 | 2,540 | 4 | |

E | -10,000 | 3,200 | 5 | |

F | -12,000 | 3,400 | 6 | |

G | -9000 | 2,930 | 5 | |

H | -11000 | 3,400 | 5 | |

I | -5000 | 1,500 | 5 | |

J | -6000 | 1,900 | 5 | |

Budget | 42000 | |||

Constraint 1: Projects E and G cannot be selected together due to resource limitation. | ||||

Constraint 2: Either project B or J must be selected, but not both. |

Maximize ($15)Chairs($20)Tables

subject to

Large Bricks:Chairs2Tables6

Small Bricks:2Chairs2Tables8

and

Chairs0, Tables0.

Chapter 7

Choosing Innovation Projects

7-‹#›

Overview

Methods of choosing innovation projects range from informal to highly structured, and from entirely qualitative to strictly quantitative.

Often firms use a combination of method to more completely evaluate the potential (and risk) of an innovation project.

7-‹#›

The Development Budget 1

Most firms face serious constraints in capital and other resources they can invest in projects.

Firms thus often use capital rationing: they set a fixed R&D budget and rank order projects to support.

R&D budget is often a percentage of previous year’s sales.

Percentage is typically determined through industry benchmarking, or historical benchmarking of firm’s performance.

7-‹#›

Quantitative Methods for Choosing Projects 1

Commonly used quantitative methods include discounted cash flow methods and real options.

Discounted Cash Flow (DCF).

Net Present Value (NPV): Expected cash inflows are discounted and compared to outlays.

7-‹#›

F/P and P/F for Spreadsheets

Future value F is calculated using FV function:

FV(i%,n,,P)

Present value P is calculated using PV function:

PV(i%,n,,F)

Note the use of double commas in each function

7-‹#›

5

Example: Finding Future Value

A person deposits $5000 into an account which pays interest at a rate of 8% per year. The amount in the account after 10 years is closest to:

(A) $2,792 (B) $9,000 (C) $10,795 (D) $12,165

The cash flow diagram is:

FV(i%,n,,P)

7-‹#›

6

Example: Finding Present Value

A small company wants to make a single deposit now so it will have enough money to purchase a backhoe costing $50,000 five years from now. If the account will earn interest of 10% per year, the amount that must be deposited now is nearest to:

(A) $10,000 (B) $ 31,050 (C) $ 33,250 (D) $319,160

The cash flow diagram is:

7-‹#›

7

Quantitative Methods for Choosing Projects 2

Internal Rate of Return (IRR): The discount rate that makes the net present value of investment zero.

Calculators and computers perform by trial and error.

Potential for multiple IRR if cash flows vary.

Strengths and Weaknesses of DCF Methods:

Strengths.

Provide concrete financial estimates.

Explicitly consider timing of investment and time value of money.

Weaknesses.

May be deceptive; only as accurate as original estimates of cash flows.

May fail to capture strategic importance of project.

7-‹#›

Internal Rate of Return

The interest rate at which the present worth and equivalent uniform annual worth are equal to 0.

(For borrowing) The interest rate paid on the unpaid balance of a loan such that the payment schedule makes the unpaid loan balance equal to 0 when the final payment is made.

(For investment) The interest rate earned on the un-recovered investment such that the payment schedule makes the un-recovered investment equal to 0 at the end of the investment life.

7-‹#›

9

Combining Quantitative and Qualitative Information 2

Data Envelopment Analysis (DEA) uses linear programming to combine measures of projects based on different units (for example, rank versus dollars) into an efficiency frontier.

Projects can be ranked by assessing their distance from efficiency frontier.

As with other quantitative methods, DEA results only as good as the data utilized; managers must be careful in their choice of measures and their accuracy.

7-‹#›

Linear Programming

Weekly supply of raw materials:

6 Large Bricks

8 Small Bricks

Products:

Table Chair

Profit = $20/Table Profit = $15/Chair

2 large

2 small

1 large

2 small

7-‹#›

Linear Programming

Linear programming uses a mathematical model to find the best allocation of scarce resources to various activities so as to maximize profit or minimize cost

Objective function: Mathematical statement of profit (or cost) for a given solution

Decision variables: Amounts of either inputs or outputs

Constraints: Limitations that restrict the available alternatives

Parameters: Numerical constants

7-‹#›

Select projects to maximize PW at i 15% and b $70,000

Project | Initial investment, $ | Annual NCF, $ | Life, years | Salvage value, $ |

A | 25,000 | 6,000 | 4 | 4,000 |

B | 20,000 | 9,000 | 4 | 0 |

C | 50,000 | 15,000 | 4 | 20,000 |

7-‹#›

Maximize

($

15

)

Chairs

+

($

20

)

Tables

subject to

Large Bricks:

Chairs

+

2

Tables

£

6

Small Bricks:

2

Chairs

+

2

Tables

£

8

and

Chairs

³

0

,

Tables

³

0

.