FINance Management - Chapter 5

Your younger sister is just starting high school, and 4 years from today she should be entering college. Your father plans to start a college fund for her, beginning today. He will invest $6,000 per year in a mutual fund, beginning today, and he expects to earn an annual return of 9%. What is the expected value of the college fund when your sister enters college? $29,908.26

$29,908.26

What's the present value of a 4-year ordinary annuity of $1,000 plus an additional $2,000 at the end of Year 4 if the annual interest rate is 10%?

$4,535.89

What is the PV of an ordinary annuity with 5 annual payments of $10,000 each if the appropriate annual interest rate is 6%?

$42,123.64

What is the present value of the following uneven cash flow stream: $0 at t = 0, $200 at t = 1, $300 at t = 2, and $400 at t = 3 if the appropriate annual interest rate is 10%?

$730.28

Suppose you won a $75,000 after-tax cash prize in the lottery. You want to start a new business that you think will lose money for a while, after which it will be up and running and bringing in big bucks. You plan to invest the funds immediately in securities that are expected to earn 10% per year. Suppose you would need only $20,000 per year during the start-up period. How long could you operate before you would require cash from the new business, i.e., how long could you receive payments of $20,000 per year? The first withdrawal will be made a year from today, and your answer will contain a fraction of a year.

4.93 years

Is this statement true or false? If you calculated the value of an ordinary annuity, you could find the value of the corresponding annuity due by multiplying the FV of the ordinary annuity by (1 + I), because this would take into account that each annuity due payment occurs one year earlier.

TRUE

Longstreet Corporation's sales today are $10 million. If sales grow at a rate of 10% per year, how long will it take Longstreet's sales to hit $15 million? a. 4.25 years b. 3.83 years c. 4.68 years d. 5.66 years e. 5.14 years

a. 4.25 years

Longstreet Corporation's sales today are $10 million. Sales are expected to grow by $1 million in each of the next 5 years, so that sales in 5 years are expected to be $15 million. What average rate of annual growth does Longstreet expect over the next five years? a. 8.45% b. 9.23% c. 8.20% d. 8.70% e. 8.96%

a. 8.45%

A lender should prefer to lend at a rate of 10% with semiannual compounding, but a borrower would prefer a loan with a rate of 10%, annual compounding. True or false? a. True b. False

a. True

Is this statement true or false? A rational person should choose to receive cash flows from an annuity due of $1,000 per year rather than from a similar ordinary annuity. a. True b. False

a. True

Is this statement true or false? If one set up time lines for an ordinary annuity of $1,000 per year for 3 years and a 3-year, $1,000 annuity due, the primary difference between the two time lines is that the $1,000 payments for the annuity due would begin at t = 0 and end at t = 2, whereas the ordinary annuity's payments would begin at t = 1 and end at t = 3. a. True b. False

a. True

Is this statement true or false? If you calculated the value of an ordinary annuity, you could find the value of the corresponding annuity due by multiplying the FV of the ordinary annuity by (1 + I), because this would take into account that each annuity due payment occurs one year earlier. a. True b. False

a. True

Under an amortized loan, the periodic payments are all equal. However, the fraction of the payment that represents interest declines over time. True or false? a. True b. False

a. true

Assume that you must make a $1,000 payment one year from today. How much must you deposit today in a bank account that pays a 6% nominal rate, monthly compounding, to have the needed funds a year from now? a. $ 970.17 b. $ 941.91 c. $1,060.13 d. $1,029.25 e. $ 999.27

b. $ 941.91

What's the future value of this cash flow stream: $1,200 at the end of Year 1, $0 at the end of Year 2, and $500 at the end of Year 3? The appropriate annual interest rate is 12%. a. $1,955.15 b. $2,005.28 c. $2,055.41 d. $1,858.61 e. $1,906.27

b. $2,005.28

A perpetuity pays $5,000 per year, with the first payment coming one year from now. If the appropriate annual interest rate is 6%, what is the perpetuity's present value? a. $80,833.33 b. $83,333.33 c. $78,408.33 d. $85,833.33 e. $88,333.33

b. $83,333.33

A company's sales today are $50 million. If sales grow at 7% annually, what will they be (in millions of dollars) 20 years later? a. $174.85 b. $193.48 c. $188.64 d. $179.33 e. $183.93

b. 193.48 FV function

A bank states that it charges a 21% APR (or annual percentage rate) on credit card balances where the cardholder has been late making a payment. However, the bank compounds monthly. What EFF% is the bank charging? a. 21.77% b. 23.14% c. 23.83% d. 22.45% e. 21.12%

b. 23.14%

Suppose you won a $75,000 after-tax cash prize in the lottery. You want to start a new business that you think will lose money for a while, after which it will be up and running and bringing in big bucks. You plan to invest the funds immediately in securities that are expected to earn 10% per year. Suppose you would need only $20,000 per year during the start-up period. How long could you operate before you would require cash from the new business, i.e., how long could you receive payments of $20,000 per year? The first withdrawal will be made a year from today, and your answer will contain a fraction of a year. a. 5.42 years b. 4.93 years c. 5.97 years d. 6.56 years e. 4.44 years

b. 4.93 years

The U.S. government offers to sell you a bond for $362.45. No payments will be made until the bond matures 15 years from now, at which time it will be redeemed for $1,000. What annual interest rate would you earn if you bought this bond for $362.45? a. 6.32% b. 7.00% c. 6.65% d. 7.72% e. 7.35%

b. 7.00%

Which of the following statements regarding amortization is CORRECT? a. Mortgages, car loans, and student loan are not examples of amortized loans. b. An amortized loan is a type of loan that requires regular, fixed payments over the life of the loan with the loan balance decreasing over time. c. An amortization schedule provides information regarding the terms of the loan, such as the interest rate and the length of the loan (or maturity); however, it does not provide detailed information that the borrower can use to determine the breakdown of the loan payment into interest and principal repayment. d. All the above statements are true. e. None of the statements is true.

b. An amortized loan is a type of loan that requires regular, fixed payments over the life of the loan with the loan balance decreasing over time.

A dollar today is worth less than a dollar tomorrow. a. True b. False

b. False

The "cost" referred to in the concept of opportunity cost is always monetary. a. True b. False

b. False

Which of the following statements regarding annuities is NOT CORRECT? a. An annuity is a recurring payment, at set intervals, for a given amount of time. b. If the interest rate is greater than zero, then the future value of an ordinary annuity is greater than the future value of an annuity due. This occurs because the last payment of the ordinary annuity earns interest, while the last payment of the annuity due does not. c. An annuity due is like an ordinary annuity with the exception that payments occur at the beginning of each period, instead of at the end of each period. d. The general assumption in finance is that annuity payments occur at the end of the period, so this type of payment is referred to as an ordinary annuity.

b. If the interest rate is greater than zero, then the future value of an ordinary annuity is greater than the future value of an annuity due. This occurs because the last payment of the ordinary annuity earns interest, while the last payment of the annuity due does not.

A certificate of deposit has a cost of $2,000, three years to maturity, no cash flows until maturity, and an interest rate of 5%. Which of these time lines is correct? a. PV=? FV= 2000 b. PV= 2000 FV= ?

b. PV= 2000 FV= ?

What is discounting? a. The bank to bank lending rate b. Reducing the value of future cash flows c. Adding inflation risk d. Calculating the future value of a cash flow

b. Reducing the value of future cash flows

Suppose you deposited $1,000 in a credit union that pays a nominal rate of 7% with daily compounding and a 365-day year. How much could you withdraw after nine months, assuming this is three-fourths of a year? a. $ 980.69 b. $1,011.02 c. $1,053.90 d. $1,073.56 e. $ 951.27

c. $1,053.90

Suppose you bought a condo and took out a 30-year, $100,000 amortized loan at a nominal rate of 8% with end-of-month payments. How much interest would you pay the 2nd month? a. $627.04 b. $652.90 c. $666.22 d. $614.50 e. $639.84

c. $666.22

What is the present value of the following uneven cash flow stream: $0 at t = 0, $200 at t = 1, $300 at t = 2, and $400 at t = 3 if the appropriate annual interest rate is 10%? a. $646.11 b. $673.03 c. $730.28 d. $701.07 e. $759.49

c. $730.28

Which of the following statements is TRUE? a. It would be better to both lend and borrow money at a rate of 6%, simple interest, rather than at a rate of 6%, compound interest. b. A deposit will grow faster if simple interest rather than compound interest is paid. c. Compound interest means that interest in future periods is earned on the interest earned in the past, whereas under simple interest, interest is earned only on the original investment.

c. Compound interest means that interest in future periods is earned on the interest earned in the past, whereas under simple interest, interest is earned only on the original investment.

Which of the following statements is FALSE? a. Time lines can show cash flows that occur over years, quarters, or any other periods. b. Time lines typically show dollars below the line and years above the line. c. Cash flows do not have to occur for every period shown on the time line. A lump sum cash flow can be depicted as easily as annuities on a time line. d. The FV as shown on a time line is always the cash flow at Time = 1. e. Time lines put verbal information into a diagram that is useful for seeing the cash flows that occur, when they occur, and the interest rate used in the analysis.

c. The FV as shown on a time line is always the cash flow at Time = 1.

Assume that you just received an ordinary annuity with 5 annual payments of $1,000 each. You plan to invest the payments at a 6% annual interest rate. What will the value of the first payment be at the end of the 5th year? a. $1,300.35 b. $1,224.61 c. $1,187.87 d. $1,262.48 e. $1,152.23

d. $1,262.48 FV formula with only 4 periods because 1st payment t = 1 =FV(0.06, 4, 0, 1000)

Suppose your rich uncle gave you $50,000, which you plan to use for graduate school. You will make the investment now, you expect to earn an annual return of 6%, and you will make 4 equal annual withdrawals, beginning 1 year from today. Under these conditions, how large would each withdrawal be so there would be no funds remaining in the account after the 4th withdrawal? a. $15,308.33 b. $14,068.83 c. $15,767.58 d. $14,429.57 e. $14,862.46

d. $14,429.57

Your father is now planning to retire, and his employer has promised him a guaranteed, but fixed, income of $50,000 per year for the rest of his life. If the rate of inflation is 5% per year, how much in current dollars will the payment at the end of 20th year be worth? a. $19,315.58 b. $19,798.47 c. $20,293.43 d. $18,844.47 e. $20,800.77

d. $18,844.47

Assume that you have $10,000 which you plan to invest for 3 years. How much more would you have if you invested the funds at 10% with annual compound interest versus 10% with simple interest? No funds will be paid until the end of the 3rd year. a. $297.72 b. $285.93 c. $303.80 d. $310.00 e. $291.77

d. $310.00

What's the present value of a 4-year ordinary annuity of $1,000 plus an additional $2,000 at the end of Year 4 if the annual interest rate is 10%? a. $4,626.61 b. $4,356.27 c. $4,445.17 d. $4,535.89 e. $4,719.14

d. $4,535.89

What is the PV of an ordinary annuity with 5 annual payments of $10,000 each if the appropriate annual interest rate is 6%? a. $43,825.44 b. $45,595.98 c. $42,966.11 d. $42,123.64 e. $44,701.94

d. $42,123.64

Suppose you bought a condo and took out a 30-year, $100,000 amortized loan at a nominal annual rate of 8% with annual end-of-year payments. How large would your annual payments be? a. $9,332.43 b. $7,929.38 c. $9,565.74 d. $8,882.74 e. $9,804.88

d. $8,882.74

Your uncle the banker offers to lend you $25,000 to start a new business. You will have to make a payment of $7,000 at the end of each of the next 3 years plus a final payment of $10,000 at the end of Year 4. What annual interest rate is built into this loan? a. 9.37% b. 9.74% c. 9.01% d. 8.66% e. 10.13%

d. 8.66%

The concept of opportunity cost is described in which of the following statements? a. The monetary value of an exchange of goods for services or the opportunity to do something b. The value of what certain resources could have produced had they been used in the best alternative way c. The cost of choosing between two alternatives d. Both B and C

d. Both B and C

Your younger sister is just starting high school, and 4 years from today she should be entering college. Your father plans to start a college fund for her, beginning today. He will invest $6,000 per year in a mutual fund, beginning today, and he expects to earn an annual return of 9%. What is the expected value of the college fund when your sister enters college? a. $29,160.55 b. $31,422.37 c. $30,655.97 d. $28,431.54 e. $29,908.26

e. $29,908.26

Suppose a U.S. government bond promises to pay $1,000 three years from now, with no payments until the end of the 3rd year. If the going annual interest rate on such bonds is 6%, how much is the bond worth today? a. $881.60 b. $797.64 c. $925.68 d. $971.97 e. $839.62

e. $839.62

Assume that you just received an ordinary annuity with 8 annual payments of $1,000 each. You plan to invest the payments at a 6% annual interest rate. How much would you have, in total, at the end of the 8th year? a. $10,095.42 b. $10,503.27 c. $10,297.33 d. $10,713.34 e. $ 9,897.47

e. $9,897.47 FV formula = FV(0.06,8,-1000,0)

Assuming that all interest payments are reinvested, how long would it take $5,000 to double if it were invested in a bank that pays 5% per year? a. 15.67 years b. 14.92 years c. 16.45 years d. 17.27 years e. 14.21 years

e. 14.21 years