ECO 340 Problem Set 1 Spring 2015 Solut

ECO 340 Problem set 1 Spring 2015
Solutions

1. Is the following statement correct, incorrect or uncertain? Explain why.

“Because corporations do not actually raise any funds in secondary markets, these markets are less important than primary markets.”

While it is true that no new funds are raised in secondary markets, it is not true that these markets are less important than primary markets. Secondary markets provide liquidity to financial assets that is lacking in the primary market. This liquidity increases asset demand and hence asset prices which allows the issuer of the security (or stock) to receive a higher cash flow through the primary market. Without a secondary market investors would have less incentive to purchase financial assets. Second, the secondary market helps to establish the price of the asset in the primary market. For example, if a firm wanted to sell new shares of its stock the secondary market price of the stock serves as a benchmark for the new shares’ price.

2. Sixteen countries of the European Union use the Euro as their common currency. Using the functions of money described in chapter 3, what are the advantages of a common currency?

Money has 3 functions. It serves as a medium of exchange, a unit of account and as a store of value. Currency unions, such as the Euro, are aided by all three of these functions of money. By serving as a medium of exchange a common currency facilitates international transactions in the Eurozone. Without a common currency transaction between individuals in different Eurozone countries would have to take into account exchange rate fluctuations. The common currency eliminates the need to adjust for exchange rates.

The unit of account function of money aids transactions in Eurozone nations. The purpose of a unit of account is to allow people to compare the value of different goods using a common standard instead of having to memorize the relative value of these goods in terms of each other. As the number of goods traded rises the number of relative values that must be known rises as well. Since the Eurozone is a complex economy with millions of goods and services being traded a common currency eliminates the need to know the relative prices of these millions of goods.

Finally, since the Eurozone has a single central bank monetary variations in monetary policy in these member nations are eliminated. Since money serves as a store of value, a common currency will be less subject to inflation risk than will be the individual currencies of separate nations.

3. Suppose in August of 2015 a high school senior is offered on of the following two tuition vouchers: A voucher that pays $2000 for the upcoming academic year (2015) A voucher that pays $3000 2 academic years in the future (2017)

Assume that the student’s decision is based solely on the time value of money.

A) If the student chooses the first option what does that imply about the student’s discount rate? Explain or show how you reach your answer.

By choosing the first option the student demonstrates that receiving $2000 today is worth more than receiving $3000 dollars 2 years in the future. To find the student’s discount rate equate the current payment with the present value of the future payment and solve for i.

$2000 = $3000 / (1+ i )2 3000/2000 = ( 1 + i )2 (3000/2000)1/2 = 1+i 1.2247 = 1+i i = 22.47%

B) Which option would we expect students with a 25% discount rate to choose? Show how you arrive at your answer.

If the student’s discount rate is 25% then the present value of the $3000 2 years in the future is

PV = 3000/(1 + .25)2 = $1920

Thus the student will choose option A.

4. Which $10,000 bond has a higher yield to maturity: A 10 year bond selling at $9000 with a current yield of 10% or a 2 year bond selling at $9000 with a current yield of 4%?

I did not provide you with the formula for yield to maturity for a coupon bond so I am giving everyone full credit for this question. Most of you correctly found the yield to maturity using your financial calculators or excel. If you want to calculate it by hand the formula for yield to maturity for a coupon bond is:

Plugging in the values from the question gives a YTM for the 10 year bond of 11.75% and of the 2 year bond of 9.74%

5. Explain why the more distant a bond’s maturity the lower the rate of return that occurs as a result of an increase in the interest rate.

The rate-of-return to an existing bond falls as interest rates rise. This price is determined by the present value of the stream of cash flows stemming from the bond. The more distant the time to maturity of a bond the greater will be the effect of a change in interest rates on the bond’s price, and hence on the bond’s rate-of-return. For example the price of a coupon is given by the formula:

Since i is in the denominator of both of the terms on the right hand side of the equation, and since these terms are raised to a power, t, greater than one, the higher the number of years to maturity the greater will be the size of the denominators on the right hand side, make the total values of the terms on the right hand side fall. This lowers rate of return on the bond.