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Finance
• A coupon bond with a coupon rate of 8% and a face value of $1,000. Coupons
are paid out annually and the bond has 1 year to maturity. The current coupon
has just been paid out. The current price of the bond is $1018.772.
• A zero coupon bond with a face value of $1,000 and 2 years to maturity. The
bond trades at $907.029.
• An annuity that pays $50 every year for the next 3 years. The next payment will
be a year from now and the last payment will be 3 years from now. The annuity
is currently worth $136.967.
All these securities are risk-free. Note that there is no direct borrowing and lending
here, so if you want to borrow (lend) you need to sell (buy) an appropriate bond.
(c) Expectations theory of interest rates. He wonders
what the price of the zero coupon bond will be in a year. Compute the expected price for him.
(d) RBC offers a forward rate over year 2, f2, of 4%. That rate is good for a loan or
deposit of $10,000. Can you make money and eat a free lunch at RBC’s expense? If so, how?
are paid out annually and the bond has 1 year to maturity. The current coupon
has just been paid out. The current price of the bond is $1018.772.
• A zero coupon bond with a face value of $1,000 and 2 years to maturity. The
bond trades at $907.029.
• An annuity that pays $50 every year for the next 3 years. The next payment will
be a year from now and the last payment will be 3 years from now. The annuity
is currently worth $136.967.
All these securities are risk-free. Note that there is no direct borrowing and lending
here, so if you want to borrow (lend) you need to sell (buy) an appropriate bond.
(c) Expectations theory of interest rates. He wonders
what the price of the zero coupon bond will be in a year. Compute the expected price for him.
(d) RBC offers a forward rate over year 2, f2, of 4%. That rate is good for a loan or
deposit of $10,000. Can you make money and eat a free lunch at RBC’s expense? If so, how?
Finance
The yields to maturity on five zero coupon bonds are given below:
Years to Maturity: 1 year (yield of 12%), 2 years (yield of 14%), 3 years (yield of 15%), 4 years (yield of 15.5%), and 5 years (yield of 15.7%)
(a) What is the implied forward rate for the third year?
(b) What is the yield to maturity of a 5-year annual coupon bond with a coupon
rate of 5%. Also, find the yield to maturity of a 5-year annual coupon bond
with a coupon rate of 10%. Which one is higher, why?
Years to Maturity: 1 year (yield of 12%), 2 years (yield of 14%), 3 years (yield of 15%), 4 years (yield of 15.5%), and 5 years (yield of 15.7%)
(a) What is the implied forward rate for the third year?
(b) What is the yield to maturity of a 5-year annual coupon bond with a coupon
rate of 5%. Also, find the yield to maturity of a 5-year annual coupon bond
with a coupon rate of 10%. Which one is higher, why?
Finance
Today is his 24th birthday. He plans to retire at 65 years old and he expects to live for another 20 years afterwards. He wants an income of $30,000 per year during his retirement years, to be paid annually on his birthday (starting from his 65th birthday). He plans to save some amount at each birthday from the age 25 to 64. He thinks about saving a constant amount for the first 10 years and then increases his saving at 3% each year until the last one before his retirement. The bank provides two types of accounts. One account pays 6.9%/year compounded quarterly. The other account pays 7%/year compounded annually?
(a) Which account would you recommend? Why?
(b) After choosing the proper account, how much should your brother save each year
for the first 10 years?
(c) What is the balance of your brother’s account right after he makes his deposit in
his saving account on his 50th birthday?
(a) Which account would you recommend? Why?
(b) After choosing the proper account, how much should your brother save each year
for the first 10 years?
(c) What is the balance of your brother’s account right after he makes his deposit in
his saving account on his 50th birthday?
Finance
Suppose there are two investors: A and B. Both plan to retire after T years but save for their
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.
Finance
This is part c, d, and e to question #70426
(c) Your boss strongly believes in the expectations theory of interest rates. He wonders
what the price of the zero coupon bond will be in a year. Compute the
expected price for him.
(d) RBC offers a forward rate over year 2, f2, of 4%. That rate is good for a loan or
deposit of $10,000. Can you make money and eat a free lunch at RBC’s expense?
If so, how?
(e) Bank of Montreal offers a forward rate over year 3, f3, of 3%. That rate is good
for a loan or deposit of $10,000. Can you make money and eat a free lunch at
Bank of Montreal’s expense? If so, how?
(c) Your boss strongly believes in the expectations theory of interest rates. He wonders
what the price of the zero coupon bond will be in a year. Compute the
expected price for him.
(d) RBC offers a forward rate over year 2, f2, of 4%. That rate is good for a loan or
deposit of $10,000. Can you make money and eat a free lunch at RBC’s expense?
If so, how?
(e) Bank of Montreal offers a forward rate over year 3, f3, of 3%. That rate is good
for a loan or deposit of $10,000. Can you make money and eat a free lunch at
Bank of Montreal’s expense? If so, how?
Finance
The yields to maturity on five zero coupon bonds are given below:
Years to Maturity: 1 year (yield of 12%), 2 years (yield of 14%), 3 years (yield of 15%), 4 years (yield of 15.5%), and 5 years (yield of 15.7%)
(a)What is the implied forward rate for the third year?
(b) Compute the yield to maturity of a 5-year annual coupon bond with a coupon
rate of 5%. Also compute the yield to maturity of a 5-year annual coupon bond
with a coupon rate of 10%. Which one is higher, why?
Years to Maturity: 1 year (yield of 12%), 2 years (yield of 14%), 3 years (yield of 15%), 4 years (yield of 15.5%), and 5 years (yield of 15.7%)
(a)What is the implied forward rate for the third year?
(b) Compute the yield to maturity of a 5-year annual coupon bond with a coupon
rate of 5%. Also compute the yield to maturity of a 5-year annual coupon bond
with a coupon rate of 10%. Which one is higher, why?
Finance
Suppose there are two investors: A and B. Both plan to retire after T years but save for their
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.
Finance
• A coupon bond with a coupon rate of 8% and a face value of $1,000. Coupons
are paid out annually and the bond has 1 year to maturity. The current coupon
has just been paid out. The current price of the bond is $1018.772.
• A zero coupon bond with a face value of $1,000 and 2 years to maturity. The
bond trades at $907.029.
• An annuity that pays $50 every year for the next 3 years. The next payment will
be a year from now and the last payment will be 3 years from now. The annuity
is currently worth $136.967.
All these securities are risk-free. Note that there is no direct borrowing and lending
here, so if you want to borrow (lend) you need to sell (buy) an appropriate bond.
(a) Find the term structure of spot interest rates (i.e., r1, r2 and r3: rates for the
next 1, 2, and 3 years).
(b) Find the term structure of forward interest rates (i.e., rates between years 0 and
1, between years 1 and 2, and between years 2 and 3).
are paid out annually and the bond has 1 year to maturity. The current coupon
has just been paid out. The current price of the bond is $1018.772.
• A zero coupon bond with a face value of $1,000 and 2 years to maturity. The
bond trades at $907.029.
• An annuity that pays $50 every year for the next 3 years. The next payment will
be a year from now and the last payment will be 3 years from now. The annuity
is currently worth $136.967.
All these securities are risk-free. Note that there is no direct borrowing and lending
here, so if you want to borrow (lend) you need to sell (buy) an appropriate bond.
(a) Find the term structure of spot interest rates (i.e., r1, r2 and r3: rates for the
next 1, 2, and 3 years).
(b) Find the term structure of forward interest rates (i.e., rates between years 0 and
1, between years 1 and 2, and between years 2 and 3).
Finance
Thelma and Louie, Inc., started the year with a balance of retained earnings of $550 million and ended the year with retained earnings of $600 million. The company paid dividends of $40 million to the preferred stockholders and $80 million to common stockholders.
Calculate Thelma and Louie’s net income for the year. (Enter your answer in millions of dollars.)
Net income $
Calculate Thelma and Louie’s net income for the year. (Enter your answer in millions of dollars.)
Net income $
Finance
If the corporate tax rate were to decrease, from a purely WACC perspective, what would a business want to do?
