# Financial Exercises 6: Capital Budgeting

*by Clemens Werkmeister*

### 1. The Dean-approach

Joelle Doe is analyzing investment proposals of her department managers. The following table shows the initial investment and the cash flows of five proposals. The financial manager reported the following financial situation. The Doe Company can use credit F (at 6 %) and / or loan G (at 8 %). Both the credit and the loan are limited to 70.000 € each. Additionally, it could recur to credit H (at 12 %), within a limit of 100.000 €.

year | Cash flows of proposal | ||||

A | B | C | D | E | |

0 | -50.000 € | -30.000 € | -80.000 € | -75.000 € | 0 € |

1 | 20.000 € | -10.000 € | 30.000 € | 0 € | -75.000 € |

2 | 30.000 € | 50.000 € | 40.000 € | 0 € | 0 € |

3 | 20.000 € | 30.000 € | 45.000 € | 100.000 € | 100.000 € |

a. Calculate the Internal rate of return (IRR) of the proposals.

b. Build an investment and a financing curve, both with respect to the interest rates and the corresponding possible payments.

c. What are the investment budgets following the Dean-approach, and how should they be financed?

d. Evaluate this approach. What are the advantages, what the major shortcomings?

### 2. Capital Budgeting based on the Profitability Index (PI)

Joelle Doe decides to set a capital budget of 160.000 € and to use an average cost of capital of 10 %.

a. Calculate the NPV and the profitability index (the ratio of NPV and initial investment) for the five proposals of the Doe Company.

b. What is the investment program following this approach?

c. Evaluate your approach. What are the advantages, what the major shortcomings?

### 3. Capital budgeting based on integrated financial planning

Joelle Doe assumes that the financial conditions of Exercise 1 apply to the following periods too. She asks you to find the investment program with the highest final value.

a. Describe the characteristics of the investment budgeting problem.

b. What kinds of models can you use to find the optimal investment program?

c. Determine the investment program with the highest final value using a miexed integer programming approach.

d. Evaluate your approach. What are the advantages, what the major shortcomings?

### 4. Capital Budgeting with NPV, IRR and PI

Consider the following four investment proposals, their initial investment and their cash flows in year 1 and 2.

year | Cash flows | |||

A | B | C | D | |

0 | -20 € | -15 € | -10 € | -5 € |

1 | 30 € | 5 € | 5 € | -40 € |

2 | 5 € | 20 € | 15 € | 60 € |

a. Calculate the IRR, the NPV and the PI for the four proposals. Assume a cost of capital of 10 %.

b. Your budget for year 0 is 25. What investment programs would you build, if you were using the

- IRR (Internal rate of return)
- NPV (Net present value)
- PI (Profitability index)
- average PI of the portfolios?

c. What happens if your budget for year 0 is 15?

d. Based on your investment programs, discuss the advantages and problems of the three approaches.

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References:

Financial Resources Formulary

Financial Exercises