Question;4-1. You have just taken out a;five-year loan from a bank to buy an engagement ring. The ring costs;$5000. You plan to put down $1000;and borrow $4000. You will need to make annual payments;of $1000 at the end of each year.;Show the timeline of the loan from your perspective. How would;the timeline differ if you created;it from the bank?s perspective?;4-2. You currently have a;four-year-old mortgage outstanding on your house. You make monthly;payments of $1500. You have just;made a payment. The mortgage has 26 years to go (i.e., it had;an original term of 30 years).;Show the timeline from your perspective. How would the timeline;differ if you created it from the;bank?s perspective?;4-3. Calculate the future value of;$2000 in;a. Five years at an interest rate;of 5% per year.;b. Ten years at an interest rate;of 5% per year.;c. Five years at an interest rate;of 10% per year.;d. Why is the amount of interest;earned in part (a) less than half the amount of interest earned;in part (b)?;a. Timeline;d. Because in the last 5 years you get interest on the;interest earned in the first 5 years as well as;interest on the original $2,000.;4-4. What is the present value of;$10,000 received;a. Twelve years from today when;the interest rate is 4% per year?;b. Twenty years from today when;the interest rate is 8% per year?;c. Six years from today when the;interest rate is 2% per year?;28Berk/DeMarzo ? Corporate;Finance, Second Edition;?2011 Pearson Education, Inc. Publishing as Prentice Hall;4-5. Your brother has offered to;give you either $5000 today or $10,000 in 10 years. If the interest;rate is 7% per year, which option;is preferable?.;4-6. Consider the following;alternatives;i. $100 received in one year;ii. $200 received in five years;iii. $300 received in ten years;a. Rank the alternatives from most;valuable to least valuable if the interest rate is 10% per;year.;b. What is your ranking if the;interest rate is only 5% per year?;c. What is your ranking if the;interest rate is 20% per year?;4-7. Suppose you invest $1000 in;an account paying 8% interest per year.;a. What is the balance in the;account after 3 years? How much of this balance corresponds to;?interest on interest??;b. What is the balance in the;account after 25 years? How much of this balance corresponds to;interest on interest?;simple interest 80 240 2000;interest on interest 0 19.712 3848.475;4-8. Your daughter is currently;eight years old. You anticipate that she will be going to college in 10;years. You would like to have;$100,000 in a savings account to fund her education at that time. If;the account promises to pay a;fixed interest rate of 3% per year, how much money do you need;to put into the account today to;ensure that you will have $100,000 in 10 years?;4-9. You are thinking of retiring.;Your retirement plan will pay you either $250,000 immediately on;retirement or $350,000 five years;after the date of your retirement. Which alternative should you;choose if the interest rate is;a. 0% per year?;b. 8% per year?;c. 20% per year?;30Berk/DeMarzo ? Corporate;Finance, Second Edition;?2011 Pearson Education, Inc. Publishing as Prentice Hall;4-10. Your grandfather put some;money in an account for you on the day you were born. You are now;18 years old and are allowed to;withdraw the money for the first time. The account currently has;$3996 in it and pays an 8% interest;rate.;a. How much money would be in the;account if you left the money there until your 25th;birthday?;b. What if you left the money;until your 65th birthday?;c. How much money did your;grandfather originally put in the account?;4-11. Suppose you receive $100 at;the end of each year for the next three years.;a. If the interest rate is 8%;what is the present value of these cash flows?;b. What is the future value in;three years of the present value you computed in (a)?;c. Suppose you deposit the cash;flows in a bank account that pays 8% interest per year. What;is the balance in the account at;the end of each of the next three years (after your deposit is;made)? How does the final bank;balance compare with your answer in (b)?;4-12. You have just received a;windfall from an investment you made in a friend?s business. He will be;paying you $10,000 at the end of;this year, $20,000 at the end of the following year, and $30,000;at the end of the year after that;(three years from today). The interest rate is 3.5% per year.;a. What is the present value of;your windfall?;b. What is the future value of;your windfall in three years (on the date of the last payment)?;4-13. You have a loan outstanding.;It requires making three annual payments at the end of the next;three years of $1000 each. Your;bank has offered to allow you to skip making the next two;payments in lieu of making one;large payment at the end of the loan?s term in three years. If the;interest rate on the loan is 5%;what final payment will the bank require you to make so that it is;indifferent between the two forms;of payment?;4-14. You have been offered a;unique investment opportunity. If you invest $10,000 today, you will;receive $500 one year from now;$1500 two years from now, and $10,000 ten years from now.;a. What is the NPV of the;opportunity if the interest rate is 6% per year? Should you take the;opportunity?;b. What is the NPV of the;opportunity if the interest rate is 2% per year? Should you take it;now?;4-15. Marian Plunket owns her own;business and is considering an investment. If she undertakes the;investment, it will pay $4000 at;the end of each of the next three years. The opportunity requires;an initial investment of $1000;plus an additional investment at the end of the second year of;$5000. What is the NPV of this;opportunity if the interest rate is 2% per year? Should Marian;take it?;4-16. Your buddy in mechanical;engineering has invented a money machine. The main drawback of;the machine is that it is slow. It;takes one year to manufacture $100. However, once built, the;machine will last forever and will;require no maintenance. The machine can be built;immediately, but it will cost;$1000 to build. Your buddy wants to know if he should invest the;money to construct it. If the;interest rate is 9.5% per year, what should your buddy do?;4-17. How would your answer to;Problem 16 change if the machine takes one year to build?;4-18. The British government has a;consol bond outstanding paying ?100 per year forever. Assume the;current interest rate is 4% per;year.;a. What is the value of the bond;immediately after a payment is made?;b. What is the value of the bond;immediately before a payment is made?;4-19. What is the present value of;$1000 paid at the end of each of the next 100 years if the interest;rate is 7% per year?;4-20. You are head of the Schwartz;Family Endowment for the Arts. You have decided to fund an arts;school in the San Francisco Bay;area in perpetuity. Every five years, you will give the school $1;million. The first payment will;occur five years from today. If the interest rate is 8% per year;what is the present value of your;gift?
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