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Business Finance
Assignment No.1 Problems: 1. The following are exercises in future (terminal) values: a. At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. At the end of five years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? c. At the end of six years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? d. At the end of three years, how much is an initial $100 deposit worth, assuming a quarterly00 compounded annual interest rate of (i) 100 percent? (ii) 10 percent? e. Why do your answers to Part (d) differ from those to Part (a)? f. At the end of 10 years, how much is a $100 initial deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly? (iv) continuously? 2. The following are exercises in present values: a. $100 at the end of three years is worth how much today, assuming a discount rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. What is the aggregate present value of $500 received at the end of each of the next three years, assuming a discount rate of (i) 4 percent? (ii) 25 percent? c. $100 is received at the end of one year, $500 at the end of two years, and $1,000 at the end of three years. What is the aggregate present value of these receipts, assuming a discount rate of (i) 4 percent? (ii) 25 percent? d. $1,000 is to be received at the end of one year, $500 at the end of two years, and $100 at the end of three years. What is the aggregate present value of these receipts assuming a discount rate of (i) 4 percent? (ii) 25 percent? e. Compare your solutions in Part (c) with those in Part (d) and explain the reason for the differences. 3. Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will provide him with a steady income over the next 12 years. He has heard that the local savings and loan association is currently paying 6 percent compound interest on an annual basis. If he were to deposit his funds, what year-end equal-dollar amount (to the nearest dollar) would he be able to withdraw annually such that he would have a zero balance after his last withdrawal 12 years from now? 4. You need to have $50,000 at the end of 10 years. To accumulate this sum, you have decided to save a certain amount at the end of each of the next 10 years and deposit it in the bank. The bank pays 8 percent interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
Business Finance 5. Same as Problem 4 above, except that you deposit a certain amount at the beginning of each of the next 10 years. Now, how much will you have to save each year (to the nearest dollar)? 6. Vernal Equinox wishes to borrow $10,000 for three years. A group of individuals agrees to lend him this amount if he contracts to pay them $16,000 at the end of the three years. What is the implicit compound annual interest rate implied by this contract (to the nearest whole percent)? 7. You have been offered a note with four years to maturity, which will pay $3,000 at the end of each of the four years. The price of the note to you is $10,200. What is the implicit compound annual interest rate you will receive (to the nearest whole percent)? 8. Sales of the P.J. Cramer Company were $500,000 this year, and they are expected to grow at a compound rate of 20 percent for the next six years. What will be the sales figure at the end of each of the next six years? 9. The H & L Bark Company is considering the purchase of a debarking machine that is expected to provide cash flows as follows:
1 $1,200
2 $2,000
3 $2,400
4 $1,900
END OF YEAR 5 6 $1,600 $1,400
7 $1,400
8 $1,400
9 $1,400
10 $1,400
Cash flow If the appropriate annual discount rate is 14 percent, what is the present value of this cash-flow stream? 10. Suppose you were to receive $1,000 at the end of 10 years. If your opportunity rate is 10 percent, what is the present value of this amount, if interest is compounded (a) annually? (b) quarterly? (c) continuously? 11. In connection with the United States Bicentennial, the Treasury once contemplated offering a savings bond for $1,000 that would be worth $1 million in 100 years. Approximately what compound annual interest rate is implied by these terms? 12. Selyn Cohen is 63 years old and recently retired. He wishes to provide retirement income for himself and is considering an annuity contract with the Philo Life Insurance Company. Such a contract pays him an equal-dollar amount each year that he lives. For this cash-flow stream, he must put up a specific amount of money at the beginning. According to actuary tables, his life expectancy is 15 years, and that is the duration on which the insurance company bases its calculations regardless of how long he actually lives. a. If Philo Life uses a compound annual interest rate of 5 percent in its calculations, what must Cohen pay at the outset for an annuity to provide him with $10,000 per year? (Assume that the expected annual payments are at the end of each of the 15 years.) b. What would be the purchase price if the compound annual interest rate is 10 percent? c. Cohen had $30,000 to put into an annuity. How much would he receive each year if the insurance company uses a 5 percent compound annual interest rate in its calculations? A 10 percent compound annual interest rate?
Business Finance 13. The Happy Hang Glide Company is purchasing a building and has obtained a $190,000 mortgage loan for 20 years. The loan bears a compound annual interest rate of 17 percent and calls for equal annual installment payments at the end of each of the 20 years. What is the amount of the annual payment? 15. You have borrowed $14,300 at a compound annual interest rate of 15 percent. You feel that you will be able to make annual payments of $3,000 per year on your loan. (Payments include both principal and interest.) How long will it be before the loan is entirely paid off (to the nearest year)? 16. Lost Dutchman Mines, Inc. is considering investing in Peru. It makes a bid to the government to participate in the development of a mine, the profits of which will be realized at the end of five years. The mine is expected to produce $5 million in cash to Lost Dutchman Mines at that time. Other than the bid at the outset, no other cash flows will occur, as the government will reimburse the company for all costs. If Lost Dutchman requires a nominal annual return of 20 percent (ignoring any tax consequences), what is the maximum bid it should make for the participation right if interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) continuously? 17. Earl E. Bird has decided to start saving for his retirement. Beginning on his twenty-first birthday, Earl plans to invest $2,000 each birthday into a savings investment earning a 7 percent compound annual rate of interest. He will continue this savings program for a total of 10 years and then stop making payments. But his savings will continue to compound at 7 percent for 35 more years, until Earl retires at age 65. Ivana Waite also plans to invest $2,000 a year, on each birthday, at 7 percent, and will do so for a total of 35 years. However, she will not begin her contributions until her thirty-first birthday. How much will Earl’s and Ivana’s savings programs be worth at the retirement age of 65? Who is better off financially at retirement, and by how much? 18. When you were born, your dear old Aunt Minnie promised to deposit $1,000 in a savings account for you on each and every one of your birthdays, beginning with your first. The savings account bears a 5 percent compound annual rate of interest. You have just turned 25 and want all the cash. However, it turns out that dear old (forgetful) Aunt Minnie made no deposits on your fifth, seventh, and eleventh birthdays. How much is in the account now – on your twenty-fifth birthday? 20. Suppose that an investment promises to pay a nominal 9.6 percent annual rate of interest. What is the effective annual interest rate on this investment assuming that interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) monthly? (e) daily (365 days)? (f) continuously? 22. It took roughly 14 years for the Dow Jones Average of 30 Industrial Stocks to go from 1,000 to 2,000. To double from 2,000 to 4,000 took only 8 years, and to go from 4,000 to 8,000 required roughly 2 years. To the nearest whole percent, what compound annual growth rates are implicit in these three index-doubling milestones?
Assignment No.1 Problems: 1. The following are exercises in future (terminal) values: a. At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. At the end of five years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? c. At the end of six years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? d. At the end of three years, how much is an initial $100 deposit worth, assuming a quarterly00 compounded annual interest rate of (i) 100 percent? (ii) 10 percent? e. Why do your answers to Part (d) differ from those to Part (a)? f. At the end of 10 years, how much is a $100 initial deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly? (iv) continuously? 2. The following are exercises in present values: a. $100 at the end of three years is worth how much today, assuming a discount rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. What is the aggregate present value of $500 received at the end of each of the next three years, assuming a discount rate of (i) 4 percent? (ii) 25 percent? c. $100 is received at the end of one year, $500 at the end of two years, and $1,000 at the end of three years. What is the aggregate present value of these receipts, assuming a discount rate of (i) 4 percent? (ii) 25 percent? d. $1,000 is to be received at the end of one year, $500 at the end of two years, and $100 at the end of three years. What is the aggregate present value of these receipts assuming a discount rate of (i) 4 percent? (ii) 25 percent? e. Compare your solutions in Part (c) with those in Part (d) and explain the reason for the differences. 3. Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will provide him with a steady income over the next 12 years. He has heard that the local savings and loan association is currently paying 6 percent compound interest on an annual basis. If he were to deposit his funds, what year-end equal-dollar amount (to the nearest dollar) would he be able to withdraw annually such that he would have a zero balance after his last withdrawal 12 years from now? 4. You need to have $50,000 at the end of 10 years. To accumulate this sum, you have decided to save a certain amount at the end of each of the next 10 years and deposit it in the bank. The bank pays 8 percent interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
Business Finance 5. Same as Problem 4 above, except that you deposit a certain amount at the beginning of each of the next 10 years. Now, how much will you have to save each year (to the nearest dollar)? 6. Vernal Equinox wishes to borrow $10,000 for three years. A group of individuals agrees to lend him this amount if he contracts to pay them $16,000 at the end of the three years. What is the implicit compound annual interest rate implied by this contract (to the nearest whole percent)? 7. You have been offered a note with four years to maturity, which will pay $3,000 at the end of each of the four years. The price of the note to you is $10,200. What is the implicit compound annual interest rate you will receive (to the nearest whole percent)? 8. Sales of the P.J. Cramer Company were $500,000 this year, and they are expected to grow at a compound rate of 20 percent for the next six years. What will be the sales figure at the end of each of the next six years? 9. The H & L Bark Company is considering the purchase of a debarking machine that is expected to provide cash flows as follows:
1 $1,200
2 $2,000
3 $2,400
4 $1,900
END OF YEAR 5 6 $1,600 $1,400
7 $1,400
8 $1,400
9 $1,400
10 $1,400
Cash flow If the appropriate annual discount rate is 14 percent, what is the present value of this cash-flow stream? 10. Suppose you were to receive $1,000 at the end of 10 years. If your opportunity rate is 10 percent, what is the present value of this amount, if interest is compounded (a) annually? (b) quarterly? (c) continuously? 11. In connection with the United States Bicentennial, the Treasury once contemplated offering a savings bond for $1,000 that would be worth $1 million in 100 years. Approximately what compound annual interest rate is implied by these terms? 12. Selyn Cohen is 63 years old and recently retired. He wishes to provide retirement income for himself and is considering an annuity contract with the Philo Life Insurance Company. Such a contract pays him an equal-dollar amount each year that he lives. For this cash-flow stream, he must put up a specific amount of money at the beginning. According to actuary tables, his life expectancy is 15 years, and that is the duration on which the insurance company bases its calculations regardless of how long he actually lives. a. If Philo Life uses a compound annual interest rate of 5 percent in its calculations, what must Cohen pay at the outset for an annuity to provide him with $10,000 per year? (Assume that the expected annual payments are at the end of each of the 15 years.) b. What would be the purchase price if the compound annual interest rate is 10 percent? c. Cohen had $30,000 to put into an annuity. How much would he receive each year if the insurance company uses a 5 percent compound annual interest rate in its calculations? A 10 percent compound annual interest rate?
Business Finance 13. The Happy Hang Glide Company is purchasing a building and has obtained a $190,000 mortgage loan for 20 years. The loan bears a compound annual interest rate of 17 percent and calls for equal annual installment payments at the end of each of the 20 years. What is the amount of the annual payment? 15. You have borrowed $14,300 at a compound annual interest rate of 15 percent. You feel that you will be able to make annual payments of $3,000 per year on your loan. (Payments include both principal and interest.) How long will it be before the loan is entirely paid off (to the nearest year)? 16. Lost Dutchman Mines, Inc. is considering investing in Peru. It makes a bid to the government to participate in the development of a mine, the profits of which will be realized at the end of five years. The mine is expected to produce $5 million in cash to Lost Dutchman Mines at that time. Other than the bid at the outset, no other cash flows will occur, as the government will reimburse the company for all costs. If Lost Dutchman requires a nominal annual return of 20 percent (ignoring any tax consequences), what is the maximum bid it should make for the participation right if interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) continuously? 17. Earl E. Bird has decided to start saving for his retirement. Beginning on his twenty-first birthday, Earl plans to invest $2,000 each birthday into a savings investment earning a 7 percent compound annual rate of interest. He will continue this savings program for a total of 10 years and then stop making payments. But his savings will continue to compound at 7 percent for 35 more years, until Earl retires at age 65. Ivana Waite also plans to invest $2,000 a year, on each birthday, at 7 percent, and will do so for a total of 35 years. However, she will not begin her contributions until her thirty-first birthday. How much will Earl’s and Ivana’s savings programs be worth at the retirement age of 65? Who is better off financially at retirement, and by how much? 18. When you were born, your dear old Aunt Minnie promised to deposit $1,000 in a savings account for you on each and every one of your birthdays, beginning with your first. The savings account bears a 5 percent compound annual rate of interest. You have just turned 25 and want all the cash. However, it turns out that dear old (forgetful) Aunt Minnie made no deposits on your fifth, seventh, and eleventh birthdays. How much is in the account now – on your twenty-fifth birthday? 20. Suppose that an investment promises to pay a nominal 9.6 percent annual rate of interest. What is the effective annual interest rate on this investment assuming that interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) monthly? (e) daily (365 days)? (f) continuously? 22. It took roughly 14 years for the Dow Jones Average of 30 Industrial Stocks to go from 1,000 to 2,000. To double from 2,000 to 4,000 took only 8 years, and to go from 4,000 to 8,000 required roughly 2 years. To the nearest whole percent, what compound annual growth rates are implicit in these three index-doubling milestones?
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