FIN 3133 - Part Three
Choose in which category of debt instrument a three-month U.S. Treasury bill belongs.
Discount bond
Choose in which category of debt instrument a car loan belongs.
Fixed-payment loan
Would this possible difference be of more concern to you if you were considering making a loan to be paid back in 1 year or a loan to be paid back in 10 years?
This difference would affect the decision to take out aTh 1-year loan versus a 10-year loan because the real interest rate can change over 10 years.
Suppose that you are considering investing in a four-year bond that has a face value of $1,000 and a coupon rate of 5.3%. a.) If the market interest rate on similar bonds is 5.3%, the price of the bond is $
$1,000 P = C /1+i + C/(1+i)^2 .. + FV/(1+i)^n
c.) Now suppose that one year has gone by since you bought the bond, and you have received the first coupon payment. The market interest rate on similar bonds is still 4.8%. The price of the bond another investor will be willing to pay is $ The total return on the bond was
$1,027.33; 8.53% Rate of return = (coupon + capital gain or loss) / purchase price
b.) Suppose that you purchase the bond, and the next day the market interest rate on similar bonds falls to 4.8%. The price of the bond will be $
$1,035.62
Suppose that on January, 1, 2013, you purchased a coupon bond with the following characteristics: Face value: $1,000, Coupon rate: 8 3/4, Current yield: 7.7%, Maturity date: 2015 If the bond is selling for $910 on January 1, 2014, then the rate of return on this bond during the holding period of calendar year 2013 was
-12.22% First find the initial price. Initial price = coupon/current yield Then find the rate of return. Rate of return = current yield + (change in price/initial price)
The bond's current yield is
5.8%
What are the main reasons that lenders charge interest on loans? A. To compensate for inflation. B. To compensate for the opportunity cost of spending the funds being loaned. C. To compensate for default risk.
All of the above.
Choose in which category of debt instrument a mortgage loan belongs.
Fixed-payment loan
Why would money being barren mean that lenders should not charge interest on loans?
Money was to be used in exchange and not increaseMo (reproduce) by charging interest.
Which of the following is NOT a debt instrument? A. Coupon bonds B. Discount bonds C. Simple loans D. Stocks
Stocks
What are TIPS? Why would investors buy TIPS rather than conventional Treasury bonds?
TIPS are Treasury Inflation Protected Securities, which are securities that adjust the interest rate to compensate for inflation. Investors would buy TIPS to hedge against high expected inflation rates.
If David dies 58 years after buying the annuity, will the interest rate be higher or lower than if he dies after 29 years?
The interest rate should be HIGHER since David received the $11,000 annual payment for a longer period of time.
What is the yield to maturity?
The interest rate that equates the present value of future payments of an asset with its current value.
According to a New York Times article: "With yields on many municipal bonds extremely low ... even a small increase in their price, which would cause the yield to go ___, would cause a _____ of principal.
down; gain With yields on many municipal bonds extremely low, a small increase in their price would cause the yield to go down and cause a loss of principal.
The reporter also noted that, "regulations that took effect in 2012 ... allow companies to use corporate bond interest rates, rather than the lower ones of Treasury bonds, to calculate the discounted present value of an employee's future pension." If employers were still allowed to use the corporate bond interest rate in offering employees one-time payments for giving up their right to a monthly pension, the reporter might be ____ inclined to take the offer because the offer would be _____ than the offer calculated using Treasury bond rates.
less; lower The larger the interest rate, the smaller the present value. Since corporate bond rates are higher, the reporter should not take the offer because the offer will be lower than that calculated using Treasury bond rates.
Some companies offer their employees defined benefit pension plans. Under these plans, employees are promised a fixed monthly payment after they retire. The federal government regulates some aspects of these plans. A reporter for the Wall Street Journal wrote that under a former employer's pension plan she was to receive $423 per month beginning in 14 years when she turned 65 years old. She received a letter from her former employer offering a one-time payment of $32,088 in exchange for her agreeing not to receive the monthly pension payments. Suppose that the reporter's former employer expects that the reporter will live to be 85 years old. That means she would receive the pension payments for 20 years. The total amount she would receive would be $423 per month times 12 months per year times 20 years equals $101,520. Should she turn down the one-time payment?
Maybe, the present value of future payments depends on interest rates, which are unknown. In this case, although we know the total amount of monthly pension payments, we do not have enough information to evaluate each option. Although the total amount of her monthly payments is known, the present value of that series of future payments is unknown because the interest rate is unknown.
When the bond matures, the investor would receive a final payment of $?
$1,055 When the bond matures, the investor receives a final payment of the principal (par value) plus the coupon payment.
What is the present value of $1,300 to be received in two years if the interest rate is 8%?
$1,114.54 Present value formula: PV = FV / (1+i)^n
Suppose that Ford issues a coupon bonds at a price of $ 1,000, which is the same as the bond's par value. Assume the bond has a coupon rate of 5.5%, pays the coupon once per year, and has a maturity of 15 years. If an investor purchased this bond at the price of $ 1,000, for each year except the last year, the investor would receive a payment of $
$55 When an investor purchases the bond, each year the investor receives a coupon payment. The coupon payment is equal to the coupon rate times the par value. Here it is $ 1,000 times 5.5% equals $55. Remember when doing the computation to use the decimal form of the percentage coupon rate, (5.5/100).
What would you prefer to receive if the interest rate is 14%? A. $78 two years from now B. $85 three years from now C. $96 four years from now D. $71 one year from now
$71 one year from now
Assume that the interest rate is 7%. What would you prefer to receive? A. $67 one year from now B. $83 three years from now C. $74 two years from now D. $91 four years from now
$91 four years from now
d.) Now suppose that two years have gone by since you bought the bond and that you have received the first two coupon payments. At this point, the market interest rate on similar bonds unexpectedly rises to 11%. The price of the bond another investor will be willing to pay is $ The total return on the bond was Suppose that another investor had bought the bond at the price you calculated in (c). The total return would have been
$910.95; -3.11%, -5.68%
Consider the case of a two-year discount bond -that is, a bond that pays no coupon and pays its face value after two years rather than one year. Suppose the face value of the bond is $1,000, and the price is $800. What is the bond's yield to maturity?
11.8% Since a two-year discount bond pays no coupon and pays its face value after two years rather than one year, use the following formula to find the yield to maturity: Price = face value / (1+i)^2
Many retired people buy annuities. With an annuity, a saver pays an insurance company, such as Berkshire Hathaway Insurance Company, a lump-sum amount in return for the company's promise to pay a certain amount per year until the saver dies. With an ordinary annuity, when the buyer dies, there is no final payment to his or her heirs. Suppose that at age 70, David Alexander pays $110,000 for an annuity that promises to pay him $11,000 per year for the remaining years of his life. If David dies 29 years after buying the annuity, choose an equation that would allow you to calculate the interest rate that David received on his annuity.
110,000 = 11,000/(1+i) + 11,000/(1+i)^2...
Suppose that for a price of $930 you purchase a 7-year Treasury bond that has a face value of $1,000 and a coupon rate of 4%. If you sell the bond one year later for $1,140, what was your rate of return for that one-year holding period? The rate of return for the one-year holding period was
26.9% First find the coupon. Coupon = face value x coupon rate Rate of return = (coupon/initial price) + (change in price/initial price)
If another investor had bought the bond a year ago for the amount that was calculated in (b), the total return would have been
4.8%
Now suppose the price of the bond changes to $ 1,090. Assuming an investor purchased the bond at a price of $ 1,090, the investor would receive a current yield equal to
5.05% = (55/1,090) * 100% The current yield gives an approximate yield rate by taking the coupon payment divided by the price payed. The current yield = (coupon payment / price paid) X 100%
The current yield will be
5.6% Current yield = rate of return - rate of capital gain $58/$1,035.62 = 0.056
Suppose that on January 1, 2018, the price of a one-year Treasury billlong -with a face value of $1000- is $938.52. Investors expect that the inflation rate will be 5% during 2018, but at the end of the year, the inflation rate turns out to have been 1%. The nominal interest rate on the bill is (YTM formula) The expected real interest rate is The actual real interest rate is
6.55% YTM = (face value - price)/price 1.55% The expected real interest rate equals the difference of the nominal interest rate and the expected rate of inflation. 5.55% The actual real interest rate equals the difference of the nominal interest rate and the actual inflation rate. The nominal interest rate is 6.55%, and the actual rate of inflation is 1%.
When will the real interest rate differ from the expected real interest rate?
There will be a difference between the real interest rate and the expected real interest rate when future inflation is unknown.
Why is the yield to maturity a better measure of the interest rate on a bond than is the coupon rate?
Because the coupon rate does not take into account the present value adjusted yield on the purchase price.
Consider the following information on two U.S. Treasury bonds: Both mature 2018 Nov 15, same asked yield 2.26, Bond A Coupon: 3.375, Bond B Coupon: 4.750
Bond A has a low coupon rate and a lower price. Bond B has a higher coupon rate and a higher price. Because of the bond price formula, if coupon rates fall, the yield will fall, which requires prices to fall to keep the yield the same. If both bonds have the same risk profile, the law of one price brings bond yields to the same level.
Choose in which category of debt instrument a U.S. Treasury bond belongs.
Coupon bond
What is the difference between the primary market for a bond and the secondary market?
If a bond is purchased directly from the company issuing theIf bond, it was purchased in the primary market. If the bondholder decides to sell the bond to another investor, the transaction would take place in the secondary market.
A student asks: If a coupon bond has a face value of $1,000, I don't understand why anyone who owns the bond would sell it for less than $1,000. After all, if the owner holds the bond to maturity, the owner knows he or she will receive $1,000, so why sell for less?
If the market interest rate has decreased since purchasing theIf bond, the price of the bond will have risen relative to what you paid for it and you will realize a capital gain.
These examples have demonstrated two very important points: 1. If interest rates on newly issued bonds rise, the prices of existing bonds will fall. 2. If interest rates on newly issued bonds fall, the prices of existing bonds will rise.
In other words, yields to maturity and bond prices move in opposite directions. This relationship must hold because in the bond price equation, the yield to maturity is in the denominator of each term. If the yield to maturity increases, the present values of the coupon payments and the face value payment must decline, causing the price of the bond to decline. The reverse is true when the yield to maturity decreases. The economic reasoning behind the inverse relationship between bond prices and yields to maturity is that if interest rates rise, existing bonds issued when interest rates were lower become less desirable to investors, and their prices fall. If interest rates fall, existing bonds become more desirable, and their prices rise.
Ford Motor Company has issued bonds with a maturity date of November 1, 2046 that have a coupon rate of 7.40%, and coupon bonds with a maturity of February 15, 2047 that have a coupon rate of 9.80%. Why would Ford issue bonds with coupons of $74 and then a little more than a year later issue bonds with coupons of $98? Why didn't the company continue to issue bonds with the lower coupon?
It is likely that Ford had to increase the coupon rate because either the price increased or the interest rate fell.It
A certified financial planner notes that with an unsubsidized student loan the borrower has the choice of whether to make interest payments on the loan while still in college. She notes that making the interest payments rather than postponing them until after graduation is "always to your financial benefit ... because otherwise [the interest payments] will capitalize ...." Which of the following statements best reflects the planners position?
Making interest payments rather than postponing them until after graduation is always to your financial benefit because deferred interest payments increase the principal balance, effectively "capitalizing" the interest.
Norman Jones, an economic historian at the University of Utah, has described the view of the ancient Greek philosopher Aristotle on interest: Aristotle defined money as a good that was consumed by use. Unlike houses and fields, which are not destroyed by use, money must be spent to be used. Therefore, as we cannot rent food, so we cannot rent money. Moreover, money does not reproduce. A house or a flock can produce new value by use, so it is not unreasonable to ask for a return on their use. Money, being barren, should not, therefore, be expected to produce excess value. Thus, interest is unnatural. What did Aristotle mean in arguing that money is "barren"?
Money cannot produce other money; it does not have the capacity to reproduce itself like crops or livestock.
What is the difference between the nominal interest rate on a loan and the real interest rate?
Nominal interest rates do not adjust forNo prices; real interest rates adjust for prices.
Consider a bond with a face value of $1,000 that sells for an initial price of $900. It will pay no coupons for the first nine years and will then pay 14% coupons for the remaining 29 years. Choose an equation showing the relationship between the price of the bond, the coupon (in dollars), and the yield to maturity.
There will be a series of future payments starting 10 years from now. (formula not shown here)
Briefly explain why yields to maturity and bond prices move in opposite directions.
The equation for bond prices shows that the higher the purchase price of the bond, the lower the rate of return. Buying a bond at a high price means that the difference made between the purchase price and face value can be small and even negative. The higher the price, the lower the overall rate of return is.
Is charging interest generally an accepted practice in today's economy?
Yes, interest today is viewed as the cost of credit.
What is the difference between the yield to maturity on a coupon bond and the rate of return?
Yield to maturity is the return on a bond assuming the bondholder holds the bond for the full maturity. Rate of return is the return over a specific holding period that takes into account not just the coupon rate but the price change.
