Семинар 2. Работа с денежными потоками. Дисконтирование. NPV. Perpetuities, annuities.

Семинар 2. Работа с денежными потоками. Дисконтирование. NPV. Perpetuities, annuities.

К этому семинару нужно посмотреть Week 1, week 2

Обязательные задачи

1. (B&D, 8/3) Your firm has a risk-free investment opportunity where it can invest $160,000 today and receive $170,000 in one year. For what level of interest rates is this project attractive?

2. (B&D, 9/3) You run a construction firm. You have just won a contract to construct a government office building. It will take one year to construct it, requiring an investment of $10 million today and $5 million in one year. The government will pay you $20 million upon the building’s completion. Suppose the cash flows and their times of payment are certain, and the risk-free interest rate is 10%.

a. What is the NPV of this opportunity?

b. How can your firm turn this NPV into cash today?

3. (B&D, 14/4) You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from now, $1500 two years from now, and $10,000 ten years from now.

a. What is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?

b. What is the NPV of the opportunity if the interest rate is 2% per year? Should you take it now?

4. (B&D, 16/4) Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 9.5% per year, what should your buddy do?

Дополнительные задачи

5. (B&D, 10/3) Your firm has identified three potential investment projects. The projects and their cash flows are shown here:

Project	Cash Flow Today ($)	Cash Flow in One Year ($)
A	-10
B
C		-10

Suppose all cash flows are certain and the risk-free interest rate is 10%.

a. What is the NPV of each project?

b. If the firm can choose only one of these projects, which should it choose?

c. If the firm can choose any two of these projects, which should it choose?

6. (B&D, 8/4) Your daughter is currently eight years old. You anticipate that she will be going to college in 10 years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years?

7. (B&D, 9/4) You are thinking of retiring. Your retirement plan will pay you either $250,000 immediately on retirement or $350,000 five years after the date of your retirement. Which alternative should you choose if the interest rate is

a. 0% per year?

b. 8% per year?

c. 20% per year?

8. (B&D, 19/4) What is the present value of $1000 paid at the end of each of the next 100 years if the interest rate is 7% per year?

9. (B&D, 38/4) You have just made an offer on a new home and are seeking a mortgage. You need to borrow $600,000. a. The bank offers a 30-year mortgage with fixed monthly payments and an interest rate of 0.5% per month. What is the amount of your monthly payment if you take this loan? b. Alternatively, you can get a 15-year mortgage with fixed monthly payments and an interest rate of 0.4% per month. How much would your monthly payments be if you take this loan instead?

10. (B&D, 7/4) Suppose the interest rate is 8% APR with monthly compounding. What is the present value of an annuity that pays $100 every six months for five years?

11. (B&D, 12/4) Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley Davidson, what will your monthly payment be?

12. Рассчитайте чистую приведенную стоимость двухлетнего проекта, если инвестиционные затраты на него составляют 170 тыс. долларов (инвестиции осуществляются в году 0), прогнозируемые ежегодные потоки по проекту следующие: выручка составит 160 тыс. дол., фактические затраты составят 80 тыс. долл. (включая амортизацию в размере 40 тыс. долл.), эффективная ставка налога на прибыль 20%, ставка дисконтирования равна 15%.

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