Problem Review Set Time Value of Money

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1.)

Suppose an investor plans to invest a given sum of money. She can earn an effective annual rate of 5% on Security A, while Security B will provide an effective annual rate of 12%. Within 11 years’ time, the compounded value of Security B will be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

a.

True

b.

False

2.)

The present value of a future sum decreases as either the discount rate or the number of periods per year increases.

a.

True

b.

False

3.)

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage declines in the loan’s later years.

a.

True

b.

False

4.)

Midway through the life of an amortized loan, the percentage of the payment that represents interest is equal to the percentage that represents principal repayment. This is true regardless of the original life of the loan.

a.

True

b.

False

5.)

You are analyzing the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

a.

The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.

b.

The discount rate increases.

c.

The riskiness of the investment’s cash flows decreases.

d.

The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.

e.

The discount rate decreases.

6.)

Which of the following statements is CORRECT?

a.

If you have a series of cash flows, all of which are positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.

b.

If you have a series of cash flows, and CF0 is negative but all of the other CFs are positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.

c.

To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise.

d.

If you solve for I and get a negative number, then you must have made a mistake.

e.

If CF0 is positive and all the other CFs are negative, then you cannot solve for I.

7.)

Which of the following bank accounts has the highest effective annual return?

a.

An account that pays 8% nominal interest with monthly compounding.

b.

An account that pays 8% nominal interest with annual compounding.

c.

An account that pays 7% nominal interest with daily (365-day) compounding.

d.

An account that pays 7% nominal interest with monthly compounding.

e.

An account that pays 8% nominal interest with daily (365-day) compounding.

8.)

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

a.

The annual payments would be larger if the interest rate were lower.

b.

If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.

c.

The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.

d.

The last payment would have a higher proportion of interest than the first payment.

e.

The proportion of interest versus principal repayment would be the same for each of the 7 payments.

9.)

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

a.

The monthly payments will decline over time.

b.

A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.

c.

The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.

d.

The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.

e.

Exactly 10% of the first monthly payment represents interest.

10.)

Which of the following statements is CORRECT, assuming positive interest rates and other things held constant?

a.

A 5-year, $250 annuity due will have a lower present value than a similar ordinary annuity.

b.

A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.

c.

A typical investment’s nominal interest rate will always be equal to or less than its effective annual rate.

d.

If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.

e.

Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will have the higher future value if you leave the funds on deposit.

11.)

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

a.

The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.

b.

The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.

c.

The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.

d.

The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.

e.

If the going rate of interest decreases, say from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.

12.)

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

a.

Bank 1; 6.1% with annual compounding.

b.

Bank 2; 6.0% with monthly compounding.

c.

Bank 3; 6.0% with annual compounding.

d.

Bank 4; 6.0% with quarterly compounding.

e.

Bank 5; 6.0% with daily (365-day) compounding.

13.)

Last year Toto Corporation’s sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

a.

$271.74

b.

$286.05

c.

$301.10

d.

$316.16

e.

$331.96

14.)

Suppose a U.S. government bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

a.

$765.13

b.

$803.39

c.

$843.56

d.

$885.74

e.

$930.03

15.)

Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

a.

4.37%

b.

4.86%

c.

5.40%

d.

6.00%

e.

6.60%

16.)

Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin’s earnings per share (EPS) over the 10-year period?

a.

15.17%

b.

15.97%

c.

16.77%

d.

17.61%

e.

18.49%

17.)

You have a chance to buy an annuity that pays $1,200 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

a.

$2,636.98

b.

$2,775.77

c.

$2,921.86

d.

$3,075.64

e.

$3,237.52

18.)

You own an oil well that will pay you $30,000 per year for 10 years, with the first payment being made today. If you think a fair return on the well is 8.5%, how much should you ask for if you decide to sell it?

a.

$202,893

b.

$213,572

c.

$224,250

d.

$235,463

e.

$247,236

19.)

What’s the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

a.

$8,508.74

b.

$8,956.56

c.

$9,427.96

d.

$9,924.17

e.

$10,446.50

20.)

An investment promises the following cash flow stream: $750 at Time 0; $2,450 at the end of Year 1 (or at t = 1); $3,175 at the end of Year 2; and $4,400 at the end of Year 3. At a discount rate of 8.0%, what is the present value of the cash flow stream?

a.

$7,916.51

b.

$8,333.17

c.

$8,771.76

d.

$9,233.43

e.

$9,695.10

21.)

What’s the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

a.

$1,819.33

b.

$1,915.08

c.

$2,015.87

d.

$2,116.67

e.

$2,222.50

22.)

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

a.

14.21

b.

14.96

c.

15.71

d.

16.49

e.

17.32

23.)

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

a.

7.62%

b.

8.00%

c.

8.40%

d.

8.82%

e.

9.26%

24.)

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years, then an additional lump sum payment of $1,000 at the end of the 5th year. What is the expected rate of return on this investment?

a.

6.77%

b.

7.13%

c.

7.50%

d.

7.88%

e.

8.27%

25.)

What’s the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded monthly?

a.

$1,922.11

b.

$2,023.28

c.

$2,124.44

d.

$2,230.66

e.

$2,342.19

26.)

East Coast Bank offers to lend you $25,000 at a nominal rate of 7.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $25,000, but it will charge an annual rate of 8.3%, with no interest due until the end of the year. What is the difference in the effective annual rates charged by the two banks?

a.

0.93%

b.

0.77%

c.

0.64%

d.

0.54%

e.

0.43%

27.)

You plan to make annual deposits into a bank account that pays a 5.00% nominal annual rate. You think inflation will amount to 2.50% per year. What is the expected annual real rate at which your money will grow?

a.

1.98%

b.

2.20%

c.

2.44%

d.

2.68%

e.

2.95%

28.)

You are considering investing in a bank account that pays a nominal annual rate of 6%, compounded monthly. If you invest $5,000 at the end of each month, how many months will it take for your account to grow to $200,000? Round fractional years up.

a.

33

b.

37

c.

41

d.

45

e.

49

29.)

Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?

a.

12.31%

b.

12.96%

c.

13.64%

d.

14.36%

e.

15.08%

30.)

Merchants Bank offers to lend you $30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the $30,000, but it will charge 7.0%, simple interest, with interest paid at the end of the year. What’s the difference in the effective annual rates charged by the two banks?

a.

1.49%

b.

1.24%

c.

1.04%

d.

0.86%

e.

0.69%

31.)

Your sister turned 35 today, and she is planning to save $5,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that will provide a return of 8% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

a.

$47,888

b.

$50,408

c.

$53,061

d.

$55,714

e.

$58,500

32.)

Your father now has $1,000,000 invested in an account that pays 9.00%. He expects inflation to average 3%, and he wants to make annual constant dollar (real) end-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year. How large will his initial withdrawal (and thus constant dollar (real) withdrawals) be?

a.

$68,139.22

b.

$71,725.49

c.

$75,500.52

d.

$79,474.23

e.

$83,657.08

33.)

You anticipate that you will need $1,500,000 when you retire 30 years from now. You plan to make 30 deposits, beginning today, in a bank account that will pay 6% interest, compounded annually. You expect to receive annual raises of 4%, so you will increase the amount you deposit each year by 4%. (That is, your 2nd deposit will be 4% greater than your first, the 3rd will be 4% greater than the 2nd, etc.) How much must your 1st deposit be if you are to meet your goal?

a.

$10,216.60

b.

$10,754.31

c.

$11,320.33

d.

$11,886.35

e.

$12,480.66