EC1008: Chapter 4 questions and answers
A $1,100-face-value bond has a 5% coupon rate, its current price is $1,040, and it
is expected to increase to $1070 next year. Calculate the current yield, the
expected rate of capital gains, and the expected rate of return. Ans✓✓✓-The
coupon payment C = $55, thus the current yield is $55/$1040 = 0.053, or 5.3%.
The expected rate of capital gain, g = ($1070 - $1040)/$1040 = 30/1040 = 0.028,
or 2.9%. The expected rate of return, R = iC + g = 5.3% + 2.9% = 8.2%.
A financial adviser has just given you the following advice: "Long-term bonds are a
great investment because their interest rate is over 20%." Is the financial adviser
necessarily right? Ans✓✓✓-No. If interest rates rise sharply in the future, long-
term bonds may suffer such a sharp fall in price that their return might be quite
low, possibly even negative.
A lottery claims its grand prize is $15 million, payable over 5 years at $3,000,000
per year. If the first payment is made immediately, what is this grand prize really
worth? Use an interest rate of 7% Ans✓✓✓-In present value terms, the lottery
prize is worth $3,000,000 + $3,000,000/(1.07) + $3,000,000/(1.07)^2 +
$3,000,000/(1.07)^3 + $3,000,000/(1.07)^4 = $13,161,634
Assume you just deposited $1,250 into a bank account. The current real interest
rate is 1%, and inflation is expected to be 5% over the next year. What nominal
rate would you require from the bank over the next year? How much money will
you have at the end of one year? If you are saving to buy a fancy bicycle that
currently sells for $1,300, will you have enough money to buy it? Ans✓✓✓-The
required nominal rate would be: i = rr +π e
= 1% + 5% = 6%.
At this rate, you would expect to have $1,250 x 1.06, or $1,325 at the end of the
year. Can you afford the bicycle? It is uncertain. This depends on whether the
price of the bicycle increases with inflation.
, Calculate the present value of a $1,300 discount bond with seven years to
maturity if the yield
to maturity is 8% Ans✓✓✓-PV = FV /(1 + i)^n , where FV = 1300, i = 0.08, n = 7.
PV = 1300/(1+0.08)^7 . Thus, PV = 758.54.
Consider a coupon bond that has a $900 par value and a coupon rate of 6%. The
bond is currently selling for $860.15 and has two years to maturity. What is the
bond's yield to maturity (YTM)? Ans✓✓✓-$860.15 = $54/(1 + i) + $54/(1 + i)^2 +
$900/(1 + i)^2. Solving for i gives a yield to maturity of 0.085, or 8.5%.
Do bondholders fare better when the yield to maturity increases or when it
decreases? Why? Ans✓✓✓-When the yield to maturity increases, this represents
a decrease in the price of the bond. If the bondholder were to sell the bond at a
lower price, the capital gains would be smaller (capital losses larger) and
therefore the bondholder would be worse off.
If interest rates decline, which would you rather be holding, long-term bonds or
short-term bonds? Why? Which type of bond has the greater interest-rate risk?
Ans✓✓✓-You would rather be holding long-term bonds because their price
would increase more than the price of the short-term bonds, giving them a higher
return. Longer-term bonds are more susceptible to higher price fluctuations than
shorter-term bonds, and hence have greater interest-rate risk.
If mortgage rates rise from 5% to 10% but the expected rate of increase in
housing prices rises from 2% to 9%, are people more or less likely to buy houses?
Ans✓✓✓-People are more likely to buy houses because the real interest rate
when purchasing a house has fallen from 3% (5-2%) to 1% (10-9%) and is thus
lower, even though nominal mortgage rates have risen. (If the tax deductibility of
A $1,100-face-value bond has a 5% coupon rate, its current price is $1,040, and it
is expected to increase to $1070 next year. Calculate the current yield, the
expected rate of capital gains, and the expected rate of return. Ans✓✓✓-The
coupon payment C = $55, thus the current yield is $55/$1040 = 0.053, or 5.3%.
The expected rate of capital gain, g = ($1070 - $1040)/$1040 = 30/1040 = 0.028,
or 2.9%. The expected rate of return, R = iC + g = 5.3% + 2.9% = 8.2%.
A financial adviser has just given you the following advice: "Long-term bonds are a
great investment because their interest rate is over 20%." Is the financial adviser
necessarily right? Ans✓✓✓-No. If interest rates rise sharply in the future, long-
term bonds may suffer such a sharp fall in price that their return might be quite
low, possibly even negative.
A lottery claims its grand prize is $15 million, payable over 5 years at $3,000,000
per year. If the first payment is made immediately, what is this grand prize really
worth? Use an interest rate of 7% Ans✓✓✓-In present value terms, the lottery
prize is worth $3,000,000 + $3,000,000/(1.07) + $3,000,000/(1.07)^2 +
$3,000,000/(1.07)^3 + $3,000,000/(1.07)^4 = $13,161,634
Assume you just deposited $1,250 into a bank account. The current real interest
rate is 1%, and inflation is expected to be 5% over the next year. What nominal
rate would you require from the bank over the next year? How much money will
you have at the end of one year? If you are saving to buy a fancy bicycle that
currently sells for $1,300, will you have enough money to buy it? Ans✓✓✓-The
required nominal rate would be: i = rr +π e
= 1% + 5% = 6%.
At this rate, you would expect to have $1,250 x 1.06, or $1,325 at the end of the
year. Can you afford the bicycle? It is uncertain. This depends on whether the
price of the bicycle increases with inflation.
, Calculate the present value of a $1,300 discount bond with seven years to
maturity if the yield
to maturity is 8% Ans✓✓✓-PV = FV /(1 + i)^n , where FV = 1300, i = 0.08, n = 7.
PV = 1300/(1+0.08)^7 . Thus, PV = 758.54.
Consider a coupon bond that has a $900 par value and a coupon rate of 6%. The
bond is currently selling for $860.15 and has two years to maturity. What is the
bond's yield to maturity (YTM)? Ans✓✓✓-$860.15 = $54/(1 + i) + $54/(1 + i)^2 +
$900/(1 + i)^2. Solving for i gives a yield to maturity of 0.085, or 8.5%.
Do bondholders fare better when the yield to maturity increases or when it
decreases? Why? Ans✓✓✓-When the yield to maturity increases, this represents
a decrease in the price of the bond. If the bondholder were to sell the bond at a
lower price, the capital gains would be smaller (capital losses larger) and
therefore the bondholder would be worse off.
If interest rates decline, which would you rather be holding, long-term bonds or
short-term bonds? Why? Which type of bond has the greater interest-rate risk?
Ans✓✓✓-You would rather be holding long-term bonds because their price
would increase more than the price of the short-term bonds, giving them a higher
return. Longer-term bonds are more susceptible to higher price fluctuations than
shorter-term bonds, and hence have greater interest-rate risk.
If mortgage rates rise from 5% to 10% but the expected rate of increase in
housing prices rises from 2% to 9%, are people more or less likely to buy houses?
Ans✓✓✓-People are more likely to buy houses because the real interest rate
when purchasing a house has fallen from 3% (5-2%) to 1% (10-9%) and is thus
lower, even though nominal mortgage rates have risen. (If the tax deductibility of
