# 14 finance problems

*label*Business

*timer*Asked: Jan 20th, 2016

**Question description**

Please help answer these questions. I found that they have similar problems online (google), but they are not the exact problems (different numbers) I would really appreciate your help. Please also show your work.

Your firm has identified three potential investment projects. The projects and their cash flows are shown here:

PROJECT A -15 CASH FLOW TODAY (MILLIONS) 20 CASH FLOW IN ONE YEAR (MILLIONS)

PROJECT B 7 CASH FLOW TODAY (MILLIONS) $3 CASH CLOW IN ONE YEAR (MILLIONS)

PROJECT C $25 CASH FLOW TODAY (MILLIONS) -$14 CASH FLOW IN ONE YEAR (MILLIONS)

Suppose all cash flows are certain and the risk-free interest rate is 6%.

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?

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Suppose Bank One offers a risk-free interest rate of 7.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 8.0% on both savings and loans.

a. What arbitrage opportunity is available?

b. Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposits?

c. What would you expect to happen to the interest rates the two banks are offering?

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Throughout the 1990s, interest rates in Japan were lower than interest rates in the United States. As a result, many Japanese investors were tempted to borrow in Japan and invest the proceeds in the United States. Explain why this strategy does not represent an arbitrage opportunity.

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The promised cash flows of three securities are listed here. If the cash flows are risk-free, and the risk-free interest rate is 4.0%, determine the no-arbitrage price of each security before the first cash flow is paid.

Security | Cash Flow Today ($) | Cash Flow in One Year ($) |

A | 400 | 400 |

B | 0 | 800 |

C | 800 | 0 |

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1. An Exchange-Traded Fund (ETF) is a security that represents a portfolio of individual stocks. Consider an ETF for which each share represents a portfolio of 2 shares of Hewlett-Packard (HPQ), one share of Sears (SHLD), and three shares of General Electric (GE). Suppose the current stock prices of each individual stock are as shown here:

STOCK: HPQ CURRENT MARKET PRICE: $35

STOCK: SHLD CURRENT MARKET PRICE: $36

STOCK: GE CURRENT MARKET PRICE: $17

a. What is the price per share of the ETF in a normal market?

b. If the ETF currently trades for $192, what arbitrage opportunity is available? What trades would you make? (ignore any transaction costs)

c. If the ETF currently trades for $222, What trades would you make? (ignore any transaction costs)

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What is the present value of $10,000 received

a. 12 years from today when the interest rate is 4% per year

b. 20 years from today when the interest rate is 8% per year

c. 6 years from today when the interest rate is 2% per year?

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You have just received a windfall from an investment you made in a friend’s business. He will be paying you $25,155 at the end of this year, $50,310 at the end of the following year, and $75,465 at the end of the year after that (three years from today). The interest rate is 8.6% per year.

a. What is the present value of your windfall?

b. What is the future value of your windfall in three years (on the date of the last payment?)

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You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from now, $1,500 two years from now, and $10,000 ten years from now.

a. What is the NPV of the investment opportunity if the interest rate is 8% per year? Should you take the opportunity

b. What is the NPV of the investment opportunity if the interest rate is 4% per year? Should you take the opportunity?

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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 $400. However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $4,000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 9.0% per year, what should your buddy do? What is your advice if the machine takes one year to build?

The NPV of the machine is $....

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Suppose you currently have $5,300 in your savings account, and your bank pays interest at a rate of 0.53% per month. If you make no further deposits or withdrawals, how much will you have in the account in 4 years?

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You have just made an offer on a new home and are seeking a mortgage. You need to borrow $632,000.

a. The bank offers a 30-year mortgage with fixed monthly payments and an interest rate of 0.54% per month. What is the amount of your monthly payment if you take this loan

b. Suppose you take the 30-year mortgage described in part (a). How much will you still owe on the mortgage after 10 years?

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You would like to buy a house that costs $350,000. You have 50,000 in cash that you can put down on the house, you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. You can afford to pay only $23,690 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a balloon payment; that is, you must repay the remaining balance on the mortgage. How much will this balloon payment be? The PV of this annuity is?

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You have an investment opportunity that requires an initial investment of $7,500 today and will pay $11,000 in one year. What is the IRR on this opportunity?

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Suppose you invest $2,250 today and receive $9,500 in five years.

a. What is the internal rate of return (IRR) of this opportunity

b. Suppose another investment opportunity also requires $2,250 upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first one, what is the amount you will receive each year?