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ECN226 Capital Markets 1 – 2012
Questions and Answers
Question 1
a)
The current yield of a bond is the bond’s annual coupon payment divided by the bond’s price.
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 =
𝐵𝑜𝑛𝑑′𝑠 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑃𝑟𝑖𝑐𝑒
The coupon rate of a bond determines the amount of each coupon payment expressed as an APR.
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 =
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
A premium bond is where the current price of the bond is greater than the par value. For premium
bonds, the coupon rate is greater than the current yield. If the current price of the bond is greater
than the face value, then the current yield has a larger denominator than the coupon rate. This is
evident from the equations above.
b)
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( ) ( ) ( )
𝑃𝑉 = + ( )
+ ( )
+ ...+ ( )
( ) ( ) ( )
𝑃𝑉 = (1 + ( )
+ ( )
+ ...+ ( )
)
The terms in the brackets is simply a geometric series which starts at 1 and grows at a rate
(1+g)/(1+r). Applying the formula for the summation of a geometric series with infinite
terms:
𝑃𝑉 = ( )
𝑃𝑉 = ( )
𝑃𝑉 =
c) The duration of a bond is the weighted average time to each payment made by the bond. The
duration of a bond is defined as:
𝐷 = 𝑤 × 𝑡
Where wt is the weight of each payment:
𝐶𝐹
(1 + 𝑟)
𝑤 =
𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒
One of the factors that affect the weight is the cash flow in period t (the higher the cash flow, the
smaller the duration). There is a negative relationship between coupon payments and the duration
of the bond.
Holding maturity constant, a bond’s duration is lower when the coupon rate is higher. Further,
holding the coupon rate constant, a bond’s duration generally increases with its time to maturity.
Holding all other factors constant (ceteris paribus), the duration of a coupon bond is higher when
the bond’s yield to maturity is lower.
d)
The price earnings ratio is defined as follows:
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒
𝑃𝑟𝑖𝑐𝑒 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑅𝑎𝑡𝑖𝑜 =
𝐸𝑃𝑆
Since the two firms have the same EPS, the only factor that would cause their price earnings
ratio to be different would be a different current stock price. The current stock price can be
calculated as follows:
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
ECN226 Capital Markets 1 – 2012
Questions and Answers
Question 1
a)
The current yield of a bond is the bond’s annual coupon payment divided by the bond’s price.
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 =
𝐵𝑜𝑛𝑑′𝑠 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑃𝑟𝑖𝑐𝑒
The coupon rate of a bond determines the amount of each coupon payment expressed as an APR.
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 =
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
A premium bond is where the current price of the bond is greater than the par value. For premium
bonds, the coupon rate is greater than the current yield. If the current price of the bond is greater
than the face value, then the current yield has a larger denominator than the coupon rate. This is
evident from the equations above.
b)
, FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
( ) ( ) ( )
𝑃𝑉 = + ( )
+ ( )
+ ...+ ( )
( ) ( ) ( )
𝑃𝑉 = (1 + ( )
+ ( )
+ ...+ ( )
)
The terms in the brackets is simply a geometric series which starts at 1 and grows at a rate
(1+g)/(1+r). Applying the formula for the summation of a geometric series with infinite
terms:
𝑃𝑉 = ( )
𝑃𝑉 = ( )
𝑃𝑉 =
c) The duration of a bond is the weighted average time to each payment made by the bond. The
duration of a bond is defined as:
𝐷 = 𝑤 × 𝑡
Where wt is the weight of each payment:
𝐶𝐹
(1 + 𝑟)
𝑤 =
𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒
One of the factors that affect the weight is the cash flow in period t (the higher the cash flow, the
smaller the duration). There is a negative relationship between coupon payments and the duration
of the bond.
Holding maturity constant, a bond’s duration is lower when the coupon rate is higher. Further,
holding the coupon rate constant, a bond’s duration generally increases with its time to maturity.
Holding all other factors constant (ceteris paribus), the duration of a coupon bond is higher when
the bond’s yield to maturity is lower.
d)
The price earnings ratio is defined as follows:
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒
𝑃𝑟𝑖𝑐𝑒 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑅𝑎𝑡𝑖𝑜 =
𝐸𝑃𝑆
Since the two firms have the same EPS, the only factor that would cause their price earnings
ratio to be different would be a different current stock price. The current stock price can be
calculated as follows:
