ECON $360$

Problem Set

Instructions: Complete the following problems on separate paper. Show your work and explain.

$1.$ Initial Investment Growth:

$$ You invest $$3,000$ in a certificate of deposit $($CD$)$ that offers an annual interest rate of $4\%.$ Calculate the

amount of money you will have after $5$ years.

$2.$ College Savings Plan:

$$ You start a college savings plan for your child and deposit $$500$ at the start of each and every year into

an account with an annual interest rate of $6\%.$ If you continue this for $10$ years, how much will be in the

account at the end of $10$ years?

$3.$ Real Estate Investment:

$$ You purchase a real estate property for $$150,000.$ The property is expected to appreciate at an annual

rate of $3\%.$ Calculate the estimated value of the property after $8$ years.

$4.$ Business Valuation

$$ Assume a business earns a profit of $$1$ million every year and is expected to do so for a very long time.

Assume the market interest is $9\%.$ The owner wants to sell the business. One way of finding a sales

price is to compute the present value of this income stream. Compute this present value.

$5.$ Face Value and Interest Rate:

$$ You are considering purchasing a zero$-$coupon bond with a face value of $$1,000$ and an annual interest

rate of $7\%.$ What is the present value of this bond if it matures in $6$ years?

$6.$ Varying Maturity Periods:

$$ You come across two zero$-$coupon bonds with the same face value of $$1,200.$ One has an annual interest

rate of $6\%$ and matures in $10$ years, while the other has an annual interest rate of $8\%$ and matures in $5$

years. Compare the present values of these two bonds.

$7.$ Capital Investment Decision

$$ Assume the market interest rate is $8\%$ and your company is considering the purchase of a new computer

system that will increase productivity and profits at your company. The new system has a $6-$year expected

life span, and expected revenues generated from it over the life span include: $$1$ million at the end of

year $1$; $$10$ million at the end of year $2$; $$20$ million at the end of year $3$; $$8$ million at the end of year $4$;

and $$1$ million at the end of the $5$th year. After that, the system breaks down and is worthless. Find the

present value of this system to your company as you consider buying it now.

$8.$ Valuation Issues

$$ In the previous question $($#$7)$ you computed the price your company would pay for the computer system.

Explain why you might not want to pay this much. $($I$.$E$.$ what are some problems with this method of

computing the value of the system?$)$ Explain.

$9.$ Investing in Stocks

$$ I buy $$12,000$ in stocks at $20\%$ margin. The stock goes up $20\%.$ What is my profit? Explain.

$10.$ Investing in Stocks

$$ I buy $$21,000$ in stocks at $25\%$ margin. The stock goes down $35\%.$ What is my profit? Explain.

$11.$ Investing in Stocks

$$ The stock price of IBM today is $$70$ per share. But you believe it will go down. Explain what you would

do to try and earn a return. Then explain what your return would be if the stock goes down to $$45$ per

share. And what would your return be if instead, the price went up to $$90$ per share.

$12.$ Interest Rates and Present Value

$$ When the Federal Reserve raises the interest rate, the prices of many stocks fall. Explain why.