B In Class Exercises

B.1 Chapter 1 - Time Value of Money

B.1.1 In-Class Exercise 1: Classification of Cash-Flows

Classifications of Cash-flows

The timelines and descriptions A-H give possible patterns of cash-flows you will encounter in your personal finance decisions and in business. Matching a situation with a given cash-flow pattern will help you organize your thoughts and help you solve time value of money problems.

For each of the cash-flow patterns given, use the classifications A-H to categorize the known and unknown cash-flows shown on the time line. Questions 1 to 3 are answered for you as examples.

A Lump Sum today
B Lump Sum in the future
C Ordinary Level Annuity
D Ordinary Growing Annuity
E Level Annuity Due
F Growing Annuity Due
G Delayed Level Annuity
H Growing Delayed Annuity

For each of the cash-flow patterns given, use the classifications A-H to categorize the known and unknown cash-flows shown on the time line. Questions 1 to 3 are answered for you as examples.

  1. Classify the cash-flows shown according to the categories given.

Answer: Known Cash-Flows _____H________ Unknown Cash-flows ________A________

  1. Classify the cash-flows shown according to the categories given.

Answer: Known Cash-Flows _____H________ Unknown Cash-flows ________G________

  1. How much must you deposit today in your investment account in order to be able to withdraw $100, each year for 4 years, starting 5 years from now?

Answer: Known Cash-Flows _____G________ Unknown Cash-flows ________A________

  1. If you deposit $100 per year in your investment account, for 5 years, starting next year, how much will you have in your account 10 years from now?
Known Cash-Flows _____________  Unknown Cash-flows _______________

For questions 5 to 10, you will need to transfer the narrative onto the time line.

  1. You plan to go to graduate school starting in 5 years. The MBA program is two years long and will cost $25,000 per year. How much do you have to save in years 1 to 4 (equal amounts each year) to have enough to pay for your graduate school?
Known Cash-Flows _____________  Unknown Cash-flows _______________
  1. You inherit $100,000 from a family member. If you invest the $100,000 today, how much will you be able to withdraw 6 years from now?
Known Cash-Flows _____________  Unknown Cash-flows _______________
  1. You are managing the funds for the state lottery. The next payout is $10 million per year, for 5 years starting in 1 year. How much does the lottery have to invest today so that it will be able to make all of the $10 million payments?
Known Cash-Flows _____________  Unknown Cash-flows _______________
  1. You get a loan from a bank for $200,000 today. You will pay back the loan with 10 equal payments starting in 1 year. How big must the payments be to just payoff the loan?
Known Cash-Flows _____________  Unknown Cash-flows _______________
  1. You’ve won a lottery and have the choice between receiving $5 million each year for 5 years starting today, or a single lump sum today. How big must the lump sum today be in order for the two choices to have the same market value?
Known Cash-Flows _____________  Unknown Cash-flows _______________
  1. If you invest $10,000 per year for 6 years, starting today, how much will you have in 11 years?
Known Cash-Flows _____________  Unknown Cash-flows _______________

B.1.2 In-Class Exercise 2: Timeline → Present Value or Future Value (Lump Sum(s))

For each question below, draw in the cash-flows described in the narrative onto the time line. Then use the formula for present value or future value to solve for the desired cash-flow.

  1. If you invest $1000 now in a savings account that pays 3%, compounded annually, how much will you have after five years? (hint: future value)
  1. Which is worth more, $1000 today or $1100 in four years when the interest rate is 2% compounded annually? (hint: future value)
  1. Your bank account pays 2% compounded annually. How much would you have to deposit today in order to have $1200 in three years? (hint: present value)
  1. You take out a loan today for $10,000. The interest on the loan is 3% compounded annually. You will repay the loan in two equal payments in years one and two. How big are the payments? (hint: present value, two times)
  1. If you deposit $2500 two years from now in a bank account that pays 4% compounded annually, how much will you have five years from now? (hint: future value)
  1. You have a trust fund of $50,000. It is invested today in an account that pays 3.5% compounded annually. You plan to withdraw all the funds over the next two years in two equal payments. What is the size of each payments? (hint: present value, two times)
  1. You receive $1000 today and in one year. If you invest this money in an account that pays 3% compounded annually, how much will you have in the account in year eight? (hint: future value, two times)
  1. You have eight grandchildren and want to give each of them $500 for Christmas one year from now. Your investments earn 5% annually. How much do you have to deposit today to fund these gifts?
  1. Which has greater dollar value, $1000 received four years from now or $1200 received nine years from now when the interest rate is 3% compounded annually?

B.1.3 In-Class Exercise 3: Monthly Compounding — Present Value or Future Value (Lump Sum(s))

For each question below, draw a time line and put in the known and unknown cash-flows. Then use the cash-flow classification (A-H) you learned earlier to classify the known and unknown cash-flows. Finally, solve for the desired cash-flow(s).

  1. If you invest $10,000 now in an account that pays an APR of 3% but is compounded monthly, how much will you have in the account after 10 years?

  2. You will have a tuition bill of $5000 due in eight months. How much would you have to invest today to fully pay for the tuition if you can earn 3% APR, compounded monthly, on the investment?

  3. If you deposit $10,000 today and $10,000 in one month, in an account that earns 4% APR, compounded monthly, how much will you have in the account 8 months from now?

  4. If you deposit $10,000 in month 3 and $10,000 in month 5, in an account that earns 3% APR, compounded monthly, how much will you have in the account 8 months from now?

  5. How much would you have to invest in months 1 and month 2 in an account that earns 7% APR, compounded monthly, to have $20,000 in 12 months (i.e., 12 months from today)?

  6. A loan charges 5% APR, compounded monthly. What is the effective annualized interest rate?

B.1.4 In-Class Exercise 4: Present Value of Annuity Formula (PVA)

For each of the questions given, draw in the cash-flows described by the narrative. Then use the PVA formula to solve for the cash-flow requested.

\[PVA = (PMT)\left(\frac{1}{R}\right)\left[1-\frac{1}{(1+R)^{N}}\right]\]

  1. You have an investment that pays $1000 in year one, year two and year three. The investment pays 4% compounded annually. What is the present value of this investment?
  1. You take out a bank loan for $20,000 today. You need to pay the loan back over the next 10 years with 10 equal payments. If the interest rate on the loan is 5% how big are the payments?
  1. Cash flow A consists of a level annuity of three payments of $1000 starting in year three and a lump sum of $10,000 in year four. If the interest rate is 3%, what is the present value of cash flow A?

  2. You are planning to save for your child’s college education which will start in 18 years. You expect the tuition to be $30,000 in years 18 through 21. If your college savings account pays 4% compounded annually, how much do you have to deposit today to fund your child’s college education?

  3. You are the owner of a level annuity that pays $10,000 per year starting next year and going for 10 years. You would like to sell this annuity today. If the interest rate is 6%, how much can you sell the annuity for?

  4. You are planning to purchase a restaurant and are wondering how much to pay for it. You’ve estimated that the restaurant will generate $200,000 per year for the next 20 years. If you want to earn 10% on your investment, how much should you pay for the restaurant today?

  5. Unfortunately, as a result of your negligence, you cause the death of a CEO. Her annual compensation was $2 million per year and she was expected to continue working for an additional 10 years. Not counting pain-and-suffering (only compensation for lost wages) what is the present value of her lost earnings if the interest rate is 5%?

  6. Investment B consists of a level annuity of 20 payments of $10,000 in each year for the next 20 years starting a year from now plus a lump sum of $100,000 in year 20. If the interest rate is 4% compounded annually, what is the present value of investment B?

  7. You are planning to save for your child’s college education which will start in 18 years. You expect the tuition to be $30,000 in years 18 through 21. If your college savings account pays 4% compounded annually, how much do you have to deposit in years 1 to 17 to fully fund the tuition?

  8. You take out a bank loan for $20,000 today. You need to pay the loan back over the next 10 years. The bank realizes that you are new in your career so it offers to make the payments for the first 3 years lower than the remaining payments. The payments for years 4 to 10 are 10% higher than the payments for years 1 to 3. If the interest rate on the loan is 5% how big are the payments?

B.1.5 In-Class Exercise 5: Time Value of Money Story Problems

For each of the questions below. Draw the time line and cash-flows associated with the narrative. Use the time value of money (TVM) techniques you’ve learned to solve for the requested cash-flow.

  1. When you graduate you have a student loan balance of $24,000 with an interest rate of 4.6% APR, compounded monthly. If you pay-off the loan over 10 years with equal payments (120 months, starting the month after you graduate) how big are the monthly payments?

  2. When you graduate you have a student loan balance of $24,000 with an interest rate of 4.6% APR, compounded monthly. If you pay-off the loan over 5 years (60 months, starting the month after you graduate) how big are the monthly payments?

  3. Your annual bonus this year was $15,000. You decide to use the money to remodel your bathroom or install solar panels on your roof. In either case, you will spend the entire $15,000.

    1. If you install solar panels, you will save $100 per month on your electric bill, each month, for 120 months, starting next month.

    2. If you remodel your bathroom, you expect to increase the value of the house by $9,000 today.

    If your investments earn 4% APR (compounded monthly), which alternative adds more to (or subtracts less from) your wealth in present value terms and by how much?

  4. Your currently owe $1400 on your credit card that charges 15% APR compounded monthly. You can pay this balance off in 12 months (12 equal payments, the first payment next month) or pay it off all at once today.

    If you pay it off today, how much do you save in PV terms if your savings account earns 2% APR compounded monthly?

  5. The current US National Debt is about $58,000 per taxpayer. Let’s say you will work and be taxed the same amount each month (starting next month) for the next 45 years. How much is your tax bill assuming your investments earn 4% APR compounded monthly?

  6. Asset A provides the following cash-flows:

The interest rate appropriate for Asset A is 4%.

What would you pay for Asset A today?

What is the PV of Asset A?

B.1.6 In-Class Exercise 6: Time Value of Money — Funding Problems

Each of the problems below falls into one of several types of “funding” problems. These can be described as

  • Lump sum funds lump sum

  • Lump sum funds ordinary annuity

  • Lump sum funds delayed annuity

  • Ordinary Annuity funds a future lump sum

  • Ordinary Annuity funds a delayed annuity

For each question, draw the time line, categorize the type of problem and solve for the requested cash-flow.

Question 1 Type of Problem =

How much would you have to invest today to fund two equal payments in years 1 and 2 of $500 each if the interest rate is 5% APR (compounded annually)?

Question 2 Type of Problem =

If you earn 2% APR (compounded annually) on your investments, how much do you have to invest today to “Fund” a payment of $400 due in 3 years?

Question 3 Type of Problem =

How much would you have to invest today to fund four equal payments in years 1, 2, 3 and 4 of $200 each if the interest rate is 6% APR (compounded annually)?

Question 4 Type of Problem =

You earn 8% APR (compounded annually) on your investments. How much do you have to invest today to “Fund” a payment of $1,000 due in 4 years?

Question 5 Type of Problem =

If you earn 6% APR (compounded annually) on your investments, how much do you have to invest today to “Fund” a payment of $500 due in 3 years?

Question 6 Type of Problem =

How much would you have to invest today to fund three equal payments in years 1, 2 and 3 of $100 each if the interest rate is 3% APR (compounded annually)?

Question 7 Type of Problem =

Your child is planning attend summer camp for three months, starting 7 months from now. The cost for camp is $1,000 per month, each month, for the three months she will attend.

If your investments earn 5% APR (compounded monthly), how much must you invest today such that your investment will grow to just cover the cost of the camp?

Question 8 Type of Problem =

During your retirement you will need $4,000 per month, each month, for 300 months. You plan on retiring 60 months from today. If your investments earn 6% APR (compounded monthly), how much would you need to have today to fully fund your retirement?

B.1.7 In-Class Exercise 7: Time Value of Money — Valuation, Funding, Choosing among Alternatives

For each of the questions given, draw the time line, indicate the type of problems and/or the relevant concept. Then solve for the requested cash-flow. Example types of problems/concepts included

• Valuation

• Funding

• Choosing among alternatives

  1. You need to fund a tuition payment of $5,215 in 12 months. You plan to make 12 equal monthly payments, starting next month to your savings account to go toward your tuition. If your savings account pays 2% APR compounded monthly, how big must the payments be?

    Type of Problem or Relevant Concept:

  2. What is the market value of Investment A if it pays $1000 per month for 27 months and the interest rate is 2% APR compounded monthly?

    Type of Problem or Relevant Concept:

  3. You need to pay a tuition bill of $4,447 in 8 months. If your investment account pays 4% APR compounded monthly, how much do you have to deposit today to fund the tuition payment?

    Type of Problem or Relevant Concept:

  4. You purchase a new car for $42,713. You finance the purchase with a 4 year loan which consists of 48 equal monthly payments starting next month. The interest on the loan in 2.4% APR compounded monthly. What are your monthly payments? Type of Problem or Relevant Concept:

  5. You take out an 18-year mortgage for $169,927 with an interest rate of 6.4% APR compounded monthly. What are your monthly payments?

    Type of Problem or Relevant Concept:

  6. You need to fund a payment of $18,882 due in 27 months. If your investment account pays 2.7% APR compounded monthly, how much do you have to deposit today to fully fund this payment?

    Type of Problem or Relevant Concept:

  7. You spent $1,913 on Christmas gifts and put the purchases on your credit card. Your credit card has a 14.5% APR compounded monthly. If you want to pay off your credit card balance in 23 months, how big are the monthly payments?

    Type of Problem or Relevant Concept:

  8. Investment A pays $1,926 per month for the next 12 months

    Investment B pays $698 per month for the next 24 months.

    If the interest rate is 5.1% APR compounded monthly, what is the difference in the market price of the two assets?

    Type of Problem or Relevant Concept:

  9. You want to buy a car that’s currently priced at $23,969. The price of the car in one year will be $21,000 since it will be last year’s model. You currently don’t have anything in your bank account. Consequently, if you buy the car today you will borrow $23,969 from your parents who will charge you 3.2% APR, compounded monthly. You will repay the entire loan balance in one year if you decide to buy the car today. How much will you save (viewed as of one year from now) if you wait to buy the car?

    Type of Problem or Relevant Concept:

  10. How much would you pay today for an investment that provides you $100 each year for the next five years and $1,100 six years from now if the interest rate is 4.9%?

    Type of Problem or Relevant Concept:

  11. How much would you have to deposit today in a bank account that pays 5.4% compounded annually to fund 9 yearly payments of $1,085 with the first payment starting five years from now?

    Type of Problem or Relevant Concept:

B.1.8 In-Class Exercise 8: Time Value of Money — Incorporating Inflation

For each of the questions given, solve for the cash-flows requested. The following will be useful formulas for these types of problems.

\[\text{Nominal Price} = (\text{real price})\times(\text{price level}) \] \[(1+\text{Nominal Rate %}) = (1+\text{real rate %})\times(1+\text{inflation rate %}) \]

  1. The price of gasoline is currently $2.30 per gallon. If the price is expected to increase at a rate of 3% per year, how much do you expect a gallon of gas to cost in 4 years?

  2. The price of a vacation home is currently $300,000. If the price of vacation homes is increasing at a rate of 5% per year, how much would a vacation home cost in 10 years?

  3. You purchase a painting today for $8,000. Paintings by this artist are expected to increase in value by 4% per year. How much do you expect the painting to be worth in 5 years?

  4. The nominal price (per pound) of apples for each year is shown in the time line below. Calculate the real price of apples for each year (as seen from year 2001)

  1. The nominal price of a gallon of gasoline for each year is shown in the time line below. Calculate the real price of gasoline for each year (as seen from year 2001)

6a. When Kevin started working 30 years ago, his salary was $50,000. His current salary is $175,000. How much has Kevin’s salary increased in nominal terms over the 30 years?

6b. When Kevin started working, the price level was 118, while the current price level is 286. How much has Kevin’s salary increased in real terms over the 30 years?

6c. What was Kevin’s average per year percentage raise in real terms over the 30 years?

  1. In 1975 the price of a new house was $48,000. In 2015 the price of a new house is $270,200. How much has the price of housing increased over the entire 40 years in percentage terms?

  2. In 1975 the price of a new house was $48,000. In 2015 the price of a new house is $270,200. How much has the price of housing increased on average per year over the 40 years in percentage terms?

  3. In 1975 median income was $12,686, while in 2015 median income was $51,759. In 1975 the price level was 32, while in 2015 the price level was 140. What was real income in 2015?

  4. In 1975 the minimum wage was $2.10, while in 2015 it was $4.91. In 1975 the price level was 32, while in 2015 the price level was 140. What was real minimum wage in 2015?

  5. If electricity costs $0.18 per KWH today and the price of electricity is expected to increase at 1.87% per year for the next 10 years, how much will electricity cost in 10 years per KWH?

B.1.9 In-Class Exercise 9: Time Value of Money — Incorporating Inflation into Funding Problems

  1. The average price of a compact car in 2018 is $20,484. If inflation on compact cars is 3% per year, how much will a compact car cost in 2023?

  2. The average annual tuition for a public university in 1998 was $3,168. In 2018, the average annual tuition for a public university is $10,691. How much (as a percentage) has the tuition cost increased over the entire period? How much (as a percentage) has the tuition cost increase on average per year?

  3. You plan to retire five years from today. Your current utility bills are $3,650 per year. How much will your utility bills be when you retire if utility costs are rising at 3% per year?

  4. You plan to retire in five years. You would like to maintain your current level of consumption which is $48,000 per year. You will need to have 30 years of consumption during your retirement. You can earn 5% per year (nominal terms) on your investments. In addition, you expect inflation to be 3% inflation per year, from now and through your retirement. How much do you have to invest each year, starting next year, for four years, in real terms to just cover your retirement needs?

  5. You plan to retire in five years. You would like to maintain your current level of consumption which is $48,000 per year. You will need to have 30 years of consumption during your retirement. You can earn 5% per year (nominal terms) on your investments. In addition, you expect inflation to be 3% inflation per year, from now and through your retirement. How much do you have to invest each year, starting next year, for four years, in nominal terms to just cover your retirement needs?

  6. You have an investment that has the following nominal cash-flows.

    If inflation averages 2% per year over this same time period, what is your average per year real rate of return?

  7. You are managing an investment portfolio and sell an “inflation protected” annuity that pays $1,000 per month (in real terms) for twenty-five years, starting next month. You forecast that inflation will be 0.25% per month over the twenty-five years.

    If you earn 5% APR (nominal terms) on your investments, how much do you need to invest today to fully fund the annuity?

  8. You are managing an investment portfolio and sell an “inflation protected” annuity that pays $1,000 per month (in real terms) for twenty-five years, starting next month. You forecast that inflation will be 0.25% per month over the twenty-five years.

    Assume that after you sell the annuity, your inflation forecasts are correct. What would be the first three annuity payments in nominal terms?

  9. You need $50,000 in today’s buying power, five years from now. You can earn 2% APR in real terms on your investments. How much do you have to invest, in nominal terms (the same amount each year), starting next year, for 4 years, to just meet your needs, if you expect inflation to be 3% per year?

  10. You need $50,000 in today’s buying power, five years from now. You can earn 2% APR in real terms on your investments. How much do you have to invest, in real terms (the same amount each year), starting next year, for 4 years, to just meet your needs, if you expect inflation to be 3% per year?

  11. You need $50,000 in today’s buying power, five years from now. You can earn 2% APR in real terms on your investments. How much do you have to invest, in nominal terms (a different amount each year), starting next year, for 4 years, to just meet your needs, if you expect inflation to be 3% per year?

B.1.10 In-Class Exercise 10: Time Value of Money — Review Questions

  1. You expect that you will need to replace your furnace in two years at a cost of $15,000. How much must you save today in an account that pays 3% APR (compounded monthly) to exactly pay the $15,000 in two years?

    Type of problem?

  2. You expect that you will need to replace your furnace in two years at a cost of $15,000. How much must you save, each month for 24 months, starting next month (the same amount each month) if your savings account pays 3% APR (compounded monthly)?

    Type of problem?

  3. You expect that you will need to replace your furnace in two years at a cost of $15,000. How much must you save, each month for 12 months, starting 12 months from today (the same amount each month) if your savings account pays 3% APR (compounded monthly)?

    Type of problem?

  4. You plan to spend a semester abroad in France. You will live in France for 6 months starting 12 months from now. Each month in France will cost you $6,000. How much must you invest each month, for 6 months, starting next month to exactly pay for your trip if your investments earn 3% APR (compounded monthly)?

    Type of problem?

  5. You manage an investment fund that sells annuities. You sell a 20 year ordinary level annuity that makes monthly payments of $1,000 per month. If interest rates are 5% APR (compounded monthly) what is the current price of this annuity?

    Type of problem?

  6. You would like to purchase a vacation home when you retire 5 years from now. The current cost of the homes that interest you is $600,000, however, you expect their price to rise at 3% per year for the next 5 years. How much must you save each year in nominal terms (the same amount each year) for the next 5 years, starting next year, to just be able to pay for the vacation home if you earn 4% APR (compounded annually) on your investments?

    Type of problem?

  7. You would like to purchase a vacation home when you retire 5 years from now. The current cost of the homes that interest you is $600,000, however, you expect their price to rise at 3% per year for the next 5 years. How much must you save each year in nominal terms (a growing annuity) for the next 5 years, starting next year, to just be able to pay for the vacation home if you earn 4% APR (compounded annually) on your investments?

    Type of problem?

  8. You currently have two loans outstanding: a car loan and a student loan. The balance on your car loan is $15,000 and requires that you pay $450 per month, starting next month for 36 more months. The balance on your student loan is $20,000 and requires that you pay $212 per month, starting next month for the next 120 months.

    A debt consolidation company gives you the following offer: It will pay off the balances of your two loans today and then charge you $620 per month for the next 60 months, starting next month.

    If your investments earn 7% APR, compounded monthly, how much would you save or lose by taking the debt consolidation company’s offer?

    Type of problem?

  9. A bookstore offers you the following deal: you pay $35 today (in January) and you get 10% off the price of everything you purchase in December (for simplicity assume exactly 12 months from now). If your savings account earns 5% APR (compounded monthly), how much do you have to buy in December to just break-even on the offer?

    Type of problem?

  10. You go to a fancy restaurant each month, starting today, for a total of 12 months. On average you spend $150 per meal. The restaurant offers to sell you a discount card today for $75. The card will give you a 10% discount on each of your meals, including today’s meal. If your investments earn 5% APR (compounded monthly) should you pay-as-you-go or should you buy the discount card? How much is the difference in PV terms?

    Type of problem?

B.2 Chapter 2 - Introduction to Bonds

B.2.1 In-Class Exercise 11: Bond Terms and Concepts

  1. What is a bond?

  2. Define each of the terms associated with a bond. Include an example to illustrate.

    2a. What is the bond’s price? How is it determined?

    2b. What is the bond’s dollar coupon?

    2c. What is the bond’s coupon rate?

    2d. What is the bond’s par value?

    2e. What is the bond’s face value?

    2f. What is the bond’s maturity date?

    2g. What is the bond’s yield to maturity?

  3. How does the bond’s price relate to the time-value of money (TVM)? Explain with an example.

  4. Based on your answer in #3, how does the bond’s price change when interest rates increase? Explain with an example.

  5. Based on your answer in #3, how does the bond’s price change when interest rates decrease?

  6. All assets provide a return to their owners in the form of either income or price change or both. What we call the income and where if comes from depends on the type of asset. For example,

    the income from a bond is called interest and comes from coupons
    
    the income from a stock is called dividend income and comes from dividends
    
    the income from rental property comes from rent and is called rent

    Explain the term current yield with an example. How does this relate to income or price change as described above?

    Explain the term capital gains/loss with an example. How does this relate to income or price change as described above?

B.2.2 In-Class Exercise 12: Bond Calculations – Price, Yield to Maturity and Yield to Call

  1. What is the price of a bond with the following features?

     Face Value                  $1,000
     Coupon Rate                 10% (stated as an ANNUAL rate)
     Semiannual coupon payments
     Maturity                    5 years
     YTM                         6% (Stated as an APR)

    N =____________ I/Y =____________ PMT =____________ FV =____________ PV =____________

  2. What is the price of a bond with the following features?

     Face Value                  $1,000
     Coupon Rate                 8% (stated as an ANNUAL rate)
     Semiannual coupon payments
     Maturity                    9 years
     YTM                         5% (Stated as an APR)

    N =____________ I/Y =____________ PMT =____________ FV =____________ PV =____________

  3. What is the YTM of a bond with the following features?

     Face Value                  $1,000
     Coupon Rate                 4% (stated as an ANNUAL rate)
     Semiannual coupon payments
     Maturity                    10 years
     Price                       $851.23

    N =____________ I/Y =____________ –> YTM =____________

    PMT =____________ FV =____________ PV =____________

  4. What is the YTM of a bond with the following features?

     Face Value                  $1,000
     Coupon Rate                 8% (stated as an ANNUAL rate)
     Semiannual coupon payments
     Maturity                    30 years
     Price                       $1,000

    N =____________ I/Y =____________ –> YTM =____________

    PMT =____________ FV =____________ PV =____________

  5. You own a bond with the following features:

     Face Value                  $1,000
     Coupon Rate                 6% (stated as an ANNUAL rate)
     Semiannual coupon payments
     Maturity                    15 years
     Current bond price          $1,104.65
     The bond is callable after seven years with the call price of $1,100. 

What is the yield to call if the bond is called at seven years (state as an APR)?

  1. You own a bond with the following features:

     Face Value                  $1,000
     Coupon Rate                 8% (annual)
     Semiannual coupon payments
     Maturity                    15 years
     Current bond price          $1,100
     The bond is callable after ten years with the call price of $1,090. 

If the market interest rate is 6% in ten years when the bond can be called, should the firm call the bond and if it does, how much will it save or lose by calling the bond?

  1. You own a bond with the following features:

     Face Value                  $1,000
     Coupon Rate                 8% (annual)
     Semiannual coupon payments
     Maturity                    30 years
     Current bond price          $985
     The bond is callable after ten years with the call price of $1,090. 

If the market interest rate is 7% in ten years when the bond can be called, should the firm call the bond and if it does, how much will it save or lose by calling the bond?

B.2.3 In-Class Exercise 13: Price risk and Reinvestment Risk

Example 1

Example 2

Example 3

Example 4

B.2.4 In-Class Exercise 14: Bond Concept Questions

  1. When interest rates decrease, the “price risk” __________ the bondholder AND the “reinvestment risk” ______________ the bondholder.

    1. hurts; hurts

    2. benefits; benefits

    3. hurts; benefits

    4. benefits; hurts

  2. All assets potentially give return to their owners from which two sources?

    1. Income and Yield

    2. Income and Capital Gain/Loss

    3. Capital Gain and Price Appreciation

    4. Income and Return

  3. The cash-flows of a typical bond correspond to which TVM concepts?

    1. The PV of an annuity

    2. The PV of a lump sum

    3. The PV of an annuity PLUS the PV of a lump sum

    4. The PV of a delayed annuity PLUS the PV of a lump sum

  4. Bond Features

     Bond Price                  $1,038
     Maturity                    4 years
     Coupon Rate                 3%
     Face Value                  $1,000
     YTM                         2.00%
     Coupon dates (Annual)   

    Based on the bond features, the current yield of the bond above is

    1. 2.89%
    2. 2.00%
    3. 3.00%
    4. 2.76%
  5. If a bond is held to maturity, then its price risk will be

    1. zero

    2. positive

    3. negative

  6. Firms issue (sell) bonds to raise capital. In a typical bond arrangement,

    1. the firm is the borrower and investors are the lenders

    2. the firm is the lender and investors are the borrowers

  7. The YTM on a bond is 6% and is expected to remain at 6%. You calculated that the bond’s one period current yield is 9%. Based on this information, the one period expected capital gain/loss is : Note: Gains are shown as positive and losses as negative.

    1. -6%
    2. -3%
    3. 0%
    4. 9%
  8. At maturity a bond will sell ___________

    1. above its par value
    2. below its par value
    3. at its yield to maturity
    4. at its par value
  9. If a bond is selling at a PREMIUM and the yield to maturity (YTM) on the bond stays constant for the life of the bond, then the bond’s price will:

    1. rise during the bond’s life
    2. fall during the bond’s life
    3. remain at par for the bond’s life
  10. As the owner of a callable bond, you are more likely to have the bond “called away” from you, in a _____________ interest rate environment.

    1. rising
    2. falling
    3. constant
    4. not enough information to tell
  11. Bond Features

    Maturity                    10 years
    Coupon Rate                 5%
    Face Value                  $1,000
    Annual Coupons 

The bond can be called in year 6

The market interest rate in year 6 = 3.00%

The call price is equal to $1,050

How much would the company save or lose if it calls the bond in year 6?

  1. Bond Features:

    Maturity                    6 years
    Coupon Rate                 5%
    Face Value                  $1,000
    Price                       $1,100
    Coupon (annual)

What is the YTM (annual) of the above bond?

B.3 Chapter 3 - Components of the Interest Rate

B.3.1 In-Class Exercise 15: Components of the Interest Rate

  1. Assets that are NOT liquid tend to be
    1. Heterogeneous
    2. Homogenous
  2. Which of the following contributes to the real riskless interest rate?
    1. Production Opportunities
    2. Expected Inflation
    3. Default Risk
    4. Price risk
    5. Reinvestment risk
  3. In the expression (Nominal Interest Rate for given asset)= (Nominal Riskless Interest Rate) + (Risk Adjustments) , the nominal riskless interest rate is
    1. A market wide rate
    2. An asset specific rate
  4. Investor and consumers ultimately are concerned with
    1. Real rates of return
    2. Nominal rates of return
    3. Compound rates of return
    4. Simple rates of return
  5. Illiquid assets tend to be
    1. Heterogeneous with high information costs
    2. Heterogeneous with low information costs
    3. Homogeneous with high information costs
    4. Homogeneous with low information costs
  6. There are actually many interest rates in the economy. However, we can talk about THE interest rate because
    1. Interest rates tend to move together, that is, when one interest rate increases all of them tend to increase and when one interest rate decreases all of them tend to decrease.
    2. The interest rate on long-term government bonds is the key interest rate to follow.
    3. The interest rate on short-term government bonds is the key interest rate to follow.
  7. Conceptually, interest is analogous to a
    1. rental fee
    2. consumption fee
    3. risk fee
  8. Which of the following is one reason households save?
    1. Delayed consumption
    2. Production opportunities
    3. Public works

B.3.2 In-Class Exercise 16: Term Structure - Expectations Calculations

  1. Find the expected interest rates implied by the current term structure, A, B, and C.
  1. Find the expected interest rates implied by the current term structure, A, B, and C.
  1. Find the expected interest rates implied by the current term structure, A, B, and C.
  1. Find the expected interest rates implied by the current term structure, A, B, and C.
  1. Find the expected interest rates implied by the current term structure, A, B, and C.
  1. Find the expected interest rates implied by the current term structure, A, B, and C.

B.4 Chapter 4 - Stock Characteristics

B.4.1 In-Class Exercise 17: Stock Valuation – Constant Dividend Growth

  1. \(D_0\)=$2.25 \(R\)=5% \(g\)=2%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$3.25 \(R\)=4% \(g\)=3%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$2.25 \(R\)=3% \(g\)=0%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$4.25 \(R\)=2% \(g\)=1%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$7.25 \(R\)=4% \(g\)=-1%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$7.25 \(R\)=4% \(g\)=-2%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$7.25 \(R\)=4% \(g\)=-1%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

  1. \(D_0\)=$5.25 \(R\)=7% \(g\)=6%

Find \(P_0\)

Find \(P_1\)

Find dividend yield from t=0 to t=1

Find the capital gain/loss from t=0 to t=1

Find total return form from t=0 to t=1

B.4.2 In-Class Exercise 18: Stock Valuation – Supernormal Growth

  1. Consider a stock with the following features:

The current dividend = $4.00

Dividend Growth from today to period 1 = 16.00%

Dividend growth from period 1 to period 2 = 11.00%

Dividend Growth from period 2 to period 3 = 8.00%

Dividend growth forever after period 3 = 3.00%

Discount rate= 5.74%

What is the current price?

What is the dividend yield from today to period 1?

What is the capital gains/loss from today to period 1?

What is the total return from today to period 1?

  1. Consider a stock with the following features:

The current dividend = $3.00

Dividend Growth from today to period 1 = 10.00%

Dividend growth from period 1 to period 2 = 8.00%

Dividend Growth from period 2 to period 3 = 7.00%

Dividend growth forever after period 3 = 3.00%

Discount rate= 6.00%

What is the current price?

What is the dividend yield from today to period 1?

What is the capital gains/loss from today to period 1?

What is the total return from today to period 1?

  1. Consider a stock with the following features:

The current dividend = $5.00

Dividend Growth from today to period 1 = 18.00%

Dividend growth from period 1 to period 2 = 16.00%

Dividend Growth from period 2 to period 3 = 12.00%

Dividend growth forever after period 3 = 5.00%

Discount rate= 9.00%

What is the current price?

What is the dividend yield from today to period 1?

What is the capital gains/loss from today to period 1?

What is the total return from today to period 1?

  1. Consider a stock with the following features:

The current dividend = $10.00

Dividend Growth from today to period 1 = 5.00%

Dividend growth from period 1 to period 2 = 5.00%

Dividend Growth from period 2 to period 3 = 5.00%

Dividend growth forever after period 3 = 3.00%

Discount rate= 4.00%

What is the current price?

What is the dividend yield from today to period 1?

What is the capital gains/loss from today to period 1?

What is the total return from today to period 1?

B.5 Chapter 5 - Capital Budgeting and wealth Creation

B.5.1 In-Class Exercise 19: Capital Budgeting – NPV and IRR

  1. Cash flows:
  • What is the NPV of project A?
  • What is the IRR of project A?
  • What is the NPV of project B?
  • What is the IRR of project B?
  1. Cash flows:
  • What is the NPV of project A?
  • What is the IRR of project A?
  • What is the NPV of project B?
  • What is the IRR of project B?
  1. Cash flows:
  • What is the NPV of project A?
  • What is the IRR of project A?
  • What is the NPV of project B?
  • What is the IRR of project B?

B.5.2 In-Class Exercise 20: Capital Budgeting – MIRR

  1. Given the cash-flows shown in the table, what is the MIRR for cash-flow A?
  1. Given the cash-flows shown in the table, what is the MIRR for cash-flow A?
  1. Given the cash-flows shown in the table, what is the MIRR for cash-flow A?
  1. Given the cash-flows shown in the table, what is the MIRR for cash-flow A?

Assume the project is financed using debt. The cost of debt is 1% after tax.

B.5.3 In-Class Exercise 21: Capital Budgeting – Payback Period

Problem 1

Problem 2

B.6 Chapter 6 - Cost of Capital

B.6.1 In-Class Exercise 22: Cost of Capital Calculations

With the information provided, fill-in the missing cells in the table.