i. Define the annual percentage rate (APR). Suppose you borrow $3,621.15 and take out a loan with an 8% nominal interest rate. You must repay the loan with 48 monthly payments of $90 each. In addition, you must pay an initial loan processing fee of $100. What is the APR for this loan? j. Explain when you should use the: nominal rate (IOM), periodic rate (IPR), effective annual rate (EFF %), and annual percentage rate (APR). Can you think of a way to modify the APR so that it would be more helpful? If so, how would you calculate that rate? k. (1) Construct an amortization schedule for a $1,000, 10% annual rate loan with three equal installments. (2) During Year 2, what is the annual interest expense for the borrower, and what is the annual interest income for the lender? Hint: Construct an amortization schedule. 1. Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months (273 days) later? m. (1) Consider the time line shown here. Is the stream of cash flows an annuity? 0 100 2 100 3 Years H 100 (2) What is the value at the end of Year 3 of the previous cash flow stream if the quoted interest rate is 10%, compounded semiannually? (3) What is the PV of the same stream? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual com- pounding, when INOM EFF% IR) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM 2 -10%/25%? n. You have the chance to buy a guaranteed promissory note for $850. The note pays $1,000 in 15 months (i.e., exactly 456 days). You have $850 in a bank account that pays a 7% nominal rate compounded daily. Which is a better investment, the note or the bank account? Answer this question using three approaches: (1) compare your future value if you buy the note versus leaving your money in the bank; (2) compare the PV of the note with your current bank balance; and (3) compare the effective rate or return on the note with that of the bank account. Assume that you are nearing graduation and have applied for a job at a prestigious com- pany. The company's evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an or- dinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of Years 0 through 3. b. (1) What's the future value of an initial $100 after 3 years if it is invested in an ac- count paying 10% annual interest? (2) What's the present value of $100 to be received in 3 years if the appropriate inter- est rate is 10%? c. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% per year, how long will it take sales to double? d. If you want an investment to double in 3 years, what interest rate must it earn? c. What's the difference between an ordinary annuity and an annuity duc? What type of annuity is shown below? How would you change the time line to show the other type of annuity? 2 3 + H 100 100 100 g f. (1) What's the future value of a 3-year ordinary annuity of $100 if the appropriate interest rate is 10%? (2) What's the present value of the annuity? (3) What would the future and present values be if the annuity were an annuity duc? What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10%, compounded annually. 10% 2 3 + 0 100 300 300 -50 h. (1) Define the nominal rate (I), which also is called the stated rate and the quoted rate. Also define the periodic rate (1). If the nominal rate is 6% and is compounded quarterly, what is the periodic rate (1) If it is compounded monthly? PER (2) If the stated interest rate is constant, will the future value be larger or smaller if we compound an initial amount more often than annually (for example, semi- annually)? Why? (3) What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? (1) What is the effective annual rate (EFF %), also called the annual equivalent rate (AER)? What is the EFF % for a nominal rate of 12%, compounded semiannu- ally? Compounded quarterly? Compounded monthly? Compounded daily? (5) Can the effective annual rate ever be equal to the nominal (quoted) rate?

i. Define the annual percentage rate (APR). Suppose you borrow $3,621.15 and take out a loan with an 8% nominal interest rate. You must repay the loan with 48 monthly payments of $90 each. In addition, you must pay an initial loan processing fee of $100. What is the APR for this loan? j. Explain when you should use the: nominal rate (IOM), periodic rate (IPR), effective annual rate (EFF %), and annual percentage rate (APR). Can you think of a way to modify the APR so that it would be more helpful? If so, how would you calculate that rate? k. (1) Construct an amortization schedule for a $1,000, 10% annual rate loan with three equal installments. (2) During Year 2, what is the annual interest expense for the borrower, and what is the annual interest income for the lender? Hint: Construct an amortization schedule. 1. Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months (273 days) later? m. (1) Consider the time line shown here. Is the stream of cash flows an annuity? 0 100 2 100 3 Years H 100 (2) What is the value at the end of Year 3 of the previous cash flow stream if the quoted interest rate is 10%, compounded semiannually? (3) What is the PV of the same stream? (4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual com- pounding, when INOM EFF% IR) What would be wrong with your answers to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate, INOM 2 -10%/25%? n. You have the chance to buy a guaranteed promissory note for $850. The note pays $1,000 in 15 months (i.e., exactly 456 days). You have $850 in a bank account that pays a 7% nominal rate compounded daily. Which is a better investment, the note or the bank account? Answer this question using three approaches: (1) compare your future value if you buy the note versus leaving your money in the bank; (2) compare the PV of the note with your current bank balance; and (3) compare the effective rate or return on the note with that of the bank account. Assume that you are nearing graduation and have applied for a job at a prestigious com- pany. The company's evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an or- dinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of Years 0 through 3. b. (1) What's the future value of an initial $100 after 3 years if it is invested in an ac- count paying 10% annual interest? (2) What's the present value of $100 to be received in 3 years if the appropriate inter- est rate is 10%? c. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% per year, how long will it take sales to double? d. If you want an investment to double in 3 years, what interest rate must it earn? c. What's the difference between an ordinary annuity and an annuity duc? What type of annuity is shown below? How would you change the time line to show the other type of annuity? 2 3 + H 100 100 100 g f. (1) What's the future value of a 3-year ordinary annuity of $100 if the appropriate interest rate is 10%? (2) What's the present value of the annuity? (3) What would the future and present values be if the annuity were an annuity duc? What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10%, compounded annually. 10% 2 3 + 0 100 300 300 -50 h. (1) Define the nominal rate (I), which also is called the stated rate and the quoted rate. Also define the periodic rate (1). If the nominal rate is 6% and is compounded quarterly, what is the periodic rate (1) If it is compounded monthly? PER (2) If the stated interest rate is constant, will the future value be larger or smaller if we compound an initial amount more often than annually (for example, semi- annually)? Why? (3) What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? (1) What is the effective annual rate (EFF %), also called the annual equivalent rate (AER)? What is the EFF % for a nominal rate of 12%, compounded semiannu- ally? Compounded quarterly? Compounded monthly? Compounded daily? (5) Can the effective annual rate ever be equal to the nominal (quoted) rate?

Corporate Fin Focused Approach

5th Edition

ISBN:9781285660516

Author:EHRHARDT

Publisher:EHRHARDT

Chapter4: Time Value Of Money

Section: Chapter Questions

Problem 1cM

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