**FIN 362 – Capital Budgeting Exercises**

**Please use Excel to solve all problems.**

- Calculate the following project’s NPV, IRR, MIRR, payback, and discounted payback:

The project’s initial investment is $6,000. The project lives for five years. In the next five years, annual cash flow is $2,000 per year. The project’s cost of capital is 14%.

Note: For NPV and MIRR, please use two approaches: a) the formula approach; and b) the NPV and MIRR functions of Excel.

- You are evaluating whether to buy a new car or a used car. The new car costs $20,000, and requires an annual maintenance of $100 per year. You anticipate that the new car will last for 10 years. The old car costs $5,000, and requires an annual maintenance of $1,000 a year. You anticipate that the old car will last for 3 years. No matter which car you get, after the physical life of the car, you will have to abandon it and obtain another car. Assume that interest rate is 5% a year.
- Calculate the equivalent annual annuity for the new car and the old car.
- Which car should you get?
- Physical life vs. economic life: The Scampini Supplies Company recently purchased a new delivery truck. The new truck costs $22,500, and it is expected to generate after-tax cash flows of $6,250 per year. The truck has a 5-year expected life. The expected year-end after-tax salvage values are listed below. The project’s cost of capital is 10%.

Year |
Annual After-tax Cash Flow |
After tax salvage value |

0 |
-22,500 |
22,500 |

1 |
6,250 |
17,500 |

2 |
6,250 |
14,000 |

3 |
6,250 |
11,000 |

4 |
6,250 |
5,000 |

5 |
6,250 |
0 |

Should the firm operate the truck until the end of its 5-year physical life? If not, what is its optimal economic life?

- Growth Option: Martin Development Co. is deciding whether to proceed with project X. The cost would be $9 million in Year 0. There is a 50% chance that X would be hugely successful, and would generate annual after tax CF of $6 mil per year during years 1, 2, and 3. However, there is 50% chance that X would be less successful, and would generate only $1 mil per year for years 1, 2, and 3. If Project X is hugely successful, it would open the door to another investment project Y, that would require a $10 mil outlay at the end of Year 2, and would generate $20 mil inflow for the company at the end of year 3. The cost of capital for all projects is 11%.
- If the company does not consider the value of real options, what is project X’s NPV?
- What is project X’s NPV considering the growth option?
- Option of waiting (Investment timing option): Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $20 million. Kim expects that the hotel will produce positive cash flows of $3 million a year at the end of each of the next 20 years. The project’s cost of capital is 13%.
- What is the project’s NPV?
- While Kim expects the cash flows to be $3 million a year, it recognizes that the cash flows could in fact be much higher or lower, depending on whether the government imposes a large hotel tax. One year from now, it will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, and the annual CF will be $2.2 mil a year. If the tax is not imposed, then the annual CF will be $3.8 million. Kim is trying to decide whether to develop the hotel now or to wait for one year to find out whether the tax will be imposed. If Kim waits for a year, the initial investment will remain $20 million. Assume that all CF are discounted at 13%. Using decision tree analysis, should Kim proceed with the project today or should it wait for one year?

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