Financial Management: Theory and Practice

Eugene F. Brigham, Michael C. Ehrhardt

Chapter 2 Time Value of Money - all with Video Answers

Educators

Chapter Questions

01:23

Problem 1

An investor recently purchased a corporate bond which yields $9 \%$. The investor is in the $36 \%$ combined federal and state tax bracket. What is the bond's after-tax yield?

Jennifer Stoner

Numerade Educator

02:17

Problem 1

If you deposit $\$ 10,000$ in a bank account that pays $10 \%$ interest annually, how much will be in your account after 5 years?

Willis James

Numerade Educator

01:23

Problem 2

Corporate bonds issued by Johnson Corporation currently yield $8 \%$. Municipal bonds of equal risk currently yield $6 \% .$ At what tax rate would an investor be indifferent between these two bonds?

Jennifer Stoner

Numerade Educator

00:54

Problem 2

What is the present value of a security that will pay $\$ 5,000$ in 20 years if securities of equal risk pay $7 \%$ annually?

Subhadeepta Sahoo

Numerade Educator

00:40

Little Books Inc. recently reported $\$ 3$ million of net income. Its EBIT was $\$ 6 \mathrm{mil}$ lion, and its tax rate was $40 \% .$ What was its interest expense? [Hint: Write out the headings for an income statement and then fill in the known values. Then divide $\$ 3$ million net income by $(1-\mathrm{T})=0.6$ to find the pre-tax income. The difference between EBIT and taxable income must be the interest expense. Use this same procedure to work some of the other problems.

Emily Himsel

Numerade Educator

01:23

Problem 3

Your parents will retire in 18 years. They currently have $\$ 250,000$, and they think they will need $\$ 1,000,000$ at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?

Narayan Hari

Numerade Educator

02:07

Problem 4

If you deposit money today in an account that pays $6.5 \%$ annual interest, how long will it take to double your money?

Sanchit Jain

Numerade Educator

00:41

Problem 4

Pearsun Brothers recently reported an EBII DA of $\$ 7.5$ million and net income of $\$ 1.8$ million. It had $\$ 2.0$ million of interest expense, and its corporate tax rate was $40 \% .$ What was its charge fur depreciation and amortization?

Zach Steedman

Numerade Educator

00:40

Problem 5

Kendall Corners Inc. recently reported net income of $\$ 3.1$ million and depreciation of $\$ 500,000 .$ What was its net cash flow? Assume it had no amortization expense.

Emily Himsel

Numerade Educator

01:19

Problem 5

You have $\$ 42,180.53$ in a brokerage account, and you plan to deposit an additional $\$ 5,000$ at the end of every future year until your account totals $\$ 250,000 .$ You expect to earn $12 \%$ annually on the account. How many years will it take to reach your goal?

Kratika Bhadauria

Numerade Educator

05:42

Problem 6

In its most recent financial statements, Newhouse Inc. reported $\$ 50$ million of net income and $\$ 810$ million of retained earnings. The previous retained earnings were $\$ 780$ million. How much in dividends was paid to shareholders during the year?

Carson Merrill

Numerade Educator

02:03

Problem 6

What is the future value of a $7 \%, 5$ -year ordinary annuity that pays $\$ 300$ each year? If this were an annuity due, what would its future value be?

Julie Silva

Numerade Educator

01:32

Problem 7

The Talley Corporation had a taxable income of $\$ 365,000$ from operations after all operating costs but before (1) interest charges of $\$ 50,000,(2)$ dividends received of $\$ 15,000,(3)$ dividends paid of $\$ 25,000,$ and (4) income taxes. What are the firm's income tax liability and its after-tax income? What are the company's marginal and average tax rates on taxable income?

Oluwadamilola Ameobi

Numerade Educator

02:40

Problem 7

An investment will pay $\$ 100$ at the end of each of the next 3 years, $\$ 200$ at the end of Year $4, \$ 300$ at the end of Year $5,$ and $\$ 500$ at the end of Year $6 .$ If other investments of equal risk earn $8 \%$ annually, what is its present value? Its future value?

Narayan Hari

Numerade Educator

01:52

Problem 8

The Wendt Corporation had $\$ 10.5$ million of taxable income.
a. What is the company's federal income tax bill for the year?
b. Assume the firm receives an additional $\$ 1$ million of interest income from some bonds it owns. What is the tax on this interest income?
c. Now assume that Wendt does not receive the interest income but does receive an additional $\$ 1$ million as dividends on some stock it owns. What is the tax on this dividend income?

Mitchell Cutler

Numerade Educator

03:28

Problem 8

You want to buy a car, and a local bank will lend you $\$ 20,000$. The loan would be fully amortized over 5 years $(60$ months), and the nominal interest rate would be $12 \%,$ with interest paid monthly. What would be the monthly loan payment? What would be the loan's EAR?

Willis James

Numerade Educator

03:59

Problem 9

The Shrieves Corporation has $\$ 10,000$ that it plans to invest in marketable securities. It is choosing among AT\&T bonds, which yield $7.5 \%$, state of Florida muni bonds, which yield $5 \%$, and AT\&T preferred stock, with a dividend yield of $6 \%$. Shrieves's corporate tax rate is $35 \%$, and $70 \%$ of the dividends received are tax exempt. Find the after-tax returns on both securities.

Sirat Shah

Numerade Educator

17:09

Problem 9

Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and $\mathrm{d}$, and in many other situations, to see how changes in input variables affect the output variable.)
a. An initial $\$ 500$ compounded for 1 year at $6 \%$.
b. An initial $\$ 500$ compounded for 2 years at $6 \%$.
c. The present value of $\$ 500$ due in 1 year at a discount rate of $6 \%$.
d. The present value of $\$ 500$ due in 2 years at a discount rate of $6 \%$.

Sreeraj P

Numerade Educator

01:32

Problem 10

The Moore Corporation has operating income (EBIT) of $\$ 750,000$. The company's depreciation expense is $\$ 200,000 .$ Moore is $100 \%$ equity financed, and it faces a $40 \%$ tax rate. What is the company's net income? What is its net cash flow?

Oluwadamilola Ameobi

Numerade Educator

03:09

Problem 10

Use equations and a financial calculator to find the following values. See the hint for Problem $2-9$.
a. An initial $\$ 500$ compounded for 10 years at $6 \%$.
b. An initial $\$ 500$ compounded for 10 years at $12 \%$.
c. The present value of $\$ 500$ due in 10 years at a $6 \%$ discount rate.
d. The present value of $\$ 500$ due in 10 years at a $12 \%$ discount rate.

Allison Knapp

Numerade Educator

04:25

Problem 11

To the closest year, how long will it take $\$ 200$ to double if it is deposited and earns the following rates? [Notes: (1) See the hint for Problem 2-9. (2) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV $-200,\mathrm{PMT}-0, \mathrm{PV}-400,$ and $1-7$ in an $\mathrm{HP} 2 \mathrm{C},$ and then press the $\mathrm{N}$ key, you will get 11 years for part a. The correct answer is 10.2448 years, which rounds to $10,$ but the calculator rounds up. However, the HP-10B gives the correct answer.
a. $7 \%$
b. $10 \%$
c. $18 \%$
d. $100 \%$

Himanshu Kushwaha

Numerade Educator

02:46

Problem 11

The Berndt Corporation expects to have sales of $\$ 12$ million. costs other than depreciation are expected to be $75 \%$ of sales, and depreciation is expected to be $\$ 1.5$ million. All sales revenues will be collected in cash, and costs other than depreciation must be paid for during the year. Berndt's federal-plus-state tax rate is $40 \%$.
Berndt has no debt.
a. Set up an income statement. What is Berndt's expected net cash flow?
b. Suppose Congress changed the tax laws so that Berndt's depreciation expenses doubled. No changes in operations occurred. What would happen to reported profit and to net cash flow?
c. Now suppose that Congress, instead of doubling Berndt's depreciation, reduced it by $50 \% .$ How would profit and net cash flow be affected?
d. If this were your company, would you prefer Congress to cause your depreciation expense to be doubled or halved? Why?

Kratika Bhadauria

Numerade Educator

14:25

Problem 12

You have just obtained financial information fur the past 2 years for Bridgewater Equine Corporation. Answer the following questions.
a. What is the net operating profit after taxes (NUPAT) for $2007 ?$
b. What are the amounts of net operating working capital for both years?
c. What are the amounts of total net operating capital for both years?
d. What is the free cash flow for $2007 ?$
e. How can you explain the large increase in dividends in $2007 ?$

Oluwadamilola Ameobi

Numerade Educator

01:57

Problem 12

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year $1 ;$ that is, they are ordinary annuities. (Notes: See the hint to Problem $2-9 .$ Also, note that you can leave values in the TVM register, switch to "BEG," press FV, and find the FV of the annuity due.)
a. $\$ 400$ per year for 10 years at $10 \%$
b. $\$ 200$ per year for 5 years at $5 \%$
c. $\$ 400$ per year for 5 years at $0 \%$
d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Julie Silva

Numerade Educator

02:07

Problem 13

Find the present value of the following ordinary annuities (see note to Problem 2-9):
a. $\$ 400$ per year for 10 years at $10 \%$
b. $\$ 200$ per year for 5 years at $5 \%$
c. $\\$ 400$ per year for 5 years at $0 \%$
d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Breanna Ollech

Numerade Educator

02:50

Problem 13

The Bookbinder Company has made $\$ 150,000$ before taxes during each of the last 15 years, and it expects to make $\$ 150,000$ a year before taxes in the future. However, in 2007 the firm incurred a loss of $\$ 650,000 .$ The firm will claim a tax credit at the time it files its 2007 income tax return, and it will receive a check from the U.S. Treasury. Show how it calculates this credit, and then indicate the firm's tax liability for each of the next 5 years. Assume a $40 \%$ tax rate on all income to ease the calculations.

Coach Rye

Numerade Educator

09:36

Problem 14

Start with the partial model in the file FM12 Ch 03 P14 Build a Model.xls at the textbook's Web site. Cumberland Industries' most recent balance sheets (in thousands of dollars) are shown below and in the partial model in the file:
a. The company's sales for 2007 were $\$ 455,150,000$, and EBITDA was $15 \%$ of sales. Furthermore, depreciation amounted to $11 \%$ of net fixed assets, interest charges were $\$ 8,575,000,$ the state-plus-federal corporate tax rate was $40 \%$, and Cumberland pays $40 \%$ of its net income out in dividends. Given this information, construct Cumberland's 2007 income statement. (Hint: Start with the partial mudel in the file.
b. Next, construct the firm's statement of retained earnings for the year ending December 31,2007 , and then its 2007 statement of cash flows.
c. Calculate net operating working capital, total net operating capital, net operating profit after taxes, and free cash flow for 2007
d. Calculate the firm's EVA and MVA for 2007 . Assume that Cumberland had 10 million shares outstanding, that the year-end closing stock price was $\$ 17.25$ per share, and its after-tax cost of capital (WACC) was $12 \%$.

Omer Ceyhan

Numerade Educator

01:31

Problem 14

a. Find the present values of the following cash flow streams. The appropriate interest rate is $8 \%$. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note, if you do work with the cash flow register, then you must enter $\mathrm{CF}_{0}=0 .$)
b. What is the value of each cash flow stream at a $0 \%$ interest rate?

Nick Johnson

Numerade Educator

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Problem 15

Find the interest rates, or rates of return, on each of the following:
a. You borrow $\$ 700$ and promise to pay back $\$ 749$ at the end of 1 year.
b. You lend $\$ 700$ and receive a promise to be paid $\$ 749$ at the end of 1 year.
c. You borrow $\$ 85,000$ and promise to pay back $\$ 201,229$ at the end of 10 years.
d. You borrow $\$ 9,000$ and promise to make payments of $\$ 2,684.80$ per year for 5 years.

Taylor Jordan

Numerade Educator

02:04

Problem 16

Find the amount to which $\$ 500$ will grow under each of the following conditions:
a. $12 \%$ compounded annually for 5 years.
b. $12 \%$ compounded semiannually for 5 years.
c. $12 \%$ compounded quarterly for 5 years.
d. $12 \%$ compounded monthly for 5 years.

Ankit Gupta

Numerade Educator

02:04

Problem 17

Find the present value of $\$ 500$ due in the future under each of the following conditions:
a. $12 \%$ nominal rate, semiannual compounding, discounted back 5 years.
b. $12 \%$ nominal rate, quarterly compounding, discounted back 5 years.
c. $12 \%$ nominal rate, monthly compounding, discounted back 1 year.

Ankit Gupta

Numerade Educator

04:04

Problem 18

Find the future values of the following ordinary annuities:
a. FV of $\$ 400$ each 6 months for 5 years at a nominal rate of $12 \%,$ compounded semiannually.
b. FV of $\$ 200$ each 3 months for 5 years at a nominal rate of $12 \%$, compounded quarterly.
c. The annuities described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, yet the annuity in part b earns $\$ 101.75$ more than the one in part a over the 5 years. Why does this occur?

Niamat Khuda

Numerade Educator

02:26

Problem 19

Universal Bank pays $7 \%$ interest, compounded annually, on time deposits. Regional Bank pays $6 \%$ interest, compounded quarterly.
a. Based on effective interest rates, in which bank would you prefer to deposit your money?
b. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during the entire compounding period in order for you to receive any interest.

Priyanka Sadarangani

Numerade Educator

04:15

Problem 20

a. Set up an amortization schedule for a $\$ 25,000$ loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is $10 \%$
b. How large must each annual payment be if the loan is for $\$ 50,000 ?$ Assume that the interest rate remains at $10 \%$ and that the loan is paid off over 5 years.
c. How large must each payment be if the loan is for $\$ 50,000$, the interest rate is $10 \%,$ and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part $b$, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?

Ivan Kochetkov

Numerade Educator

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Problem 21

Hanebury Corporation's current sales were $\$ 12$ million. Sales were $\$ 6$ million 5 years earlier.
a. To the nearest percentage point, at what rate have sales been growing?
b. Suppose someone calculated the sales growth for Hanebury Corporation in part a as follows: "Sales doubled in 5 years. This represents a growth of $100 \%$ in 5 years, so, dividing $100 \%$ by $5,$ we find the growth rate to be $20 \%$ per year." Explain what is wrong with this calculation.

Jason Gerber

Numerade Educator

02:48

Problem 22

Washington-Pacific invests $\$ 4$ million to clear a tract of land and to set out some young pine trees. The trees will mature in 10 years, at which time Washington-Pacific plans to sell the forest at an expected price of $\$ 8$ million. What is Washington-Pacific's expected rate of return?

David Mccaslin

Numerade Educator

04:17

Problem 23

A mortgage company offers to lend you $\$ 85,000 ;$ the loan calls for payments of $\$ 8,273.59$ per year for 30 years. What interest rate is the mortgage company charging you?

Willis James

Numerade Educator

05:43

Problem 24

To complete your last year in business school and then go through law school, you will need $\$ 10,000$ per year fur 4 years, starting next year (that is, you will need to withdraw the first $\$ 10,000$ one year from today, Your rich uncle offers to put you through school, and he will deposit in a bank paying $7 \%$ interest a sum of money that is sufficient to provide the 4 payments of $\$ 10,000$ each. His deposit will be made today.
a. How large must the deposit be?
b. How much will be in the account immediately after you make the first withdrawal? After the last withdrawal?

Oluwadamilola Ameobi

Numerade Educator

05:46

Problem 25

While Mary Corens was a student at the University of Tennessee, she borrowed $\$ 12,000$ in student loans at an annual interest rate of $9 \% .$ If Mary repays $\$ 1,500$ per year, how long, to the nearest year, will it take her to repay the loan?

Tp Sarathy

Numerade Educator

01:19

Problem 26

You need to accumulate $\$ 10,000 .$ To do so, you plan to make deposits of $\$ 1,250$ per year, with the first payment being made a year from today, in a bank account that pays $12 \%$ annual interest. Your last deposit will be less than $\$ 1,250$ if less is needed to round out to $\$ 10,000 .$ How many years will it take you to reach your $\$ 10,000$ goal, and how large will the last deposit be?

Kratika Bhadauria

Numerade Educator

01:45

Problem 27

What is the present value of a perpetuity of $\$ 100$ per year if the appropriate discount rate is $7 \% ?$ If interest rates in general were to double and the appropriate discount rate rose to $14 \%$, what would happen to the present value of the perpetuity?

Kaylee Mcclellan

Numerade Educator

02:40

Problem 28

Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for 4 payments, $\$ 50$ at the end of each of the next 3 years, plus a payment of $\$ 1,050$ at the end of Year $4 .$ Your friend says she can get you some of these securities at a cost of $\$ 900$ each. Your money is now invested in a bank that pays an $8 \%$ nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?

Sheryl Ezze

Numerade Educator

03:02

Problem 29

Assume that your aunt sold her house on December 31 and that she took a mortgage in the amount of $\$ 10,000$ as part of the payment. The mortgage has a quoted (or nominal) interest rate of $10 \%$, but it calls for payments every 6 months, beginning on June 30 , and the mortgage is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house of the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?

Charles Carter

Numerade Educator

01:55

Problem 30

Your company is planning to borrow $\$ 1,000,000$ on a 5 -year, $15 \%$, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal?

Zach Steedman

Numerade Educator

02:35

Problem 31

a. It is now January $1 .$ You plan to make 5 deposits of $\$ 100$ each, one every 6 months, with the first payment being made today. If the bank pays a nominal interest rate of $12 \%$ but uses semiannual compounding, how much will be in your account after 10 years?
b. You must make a payment of $\$ 1,432.0210$ years from today. To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quarters, in a bank that pays a nominal interest rate of $12 \%,$ quarterly compounding. How large must each of the 5 payments be?

Nick Johnson

Numerade Educator

01:54

Problem 32

Anne Lockwood, manager of Oaks Mall Jewelry, wants to sell on credit, giving customers 3 months in which to pay. However, Anne will have to borrow from her bank to carry the accounts payable. The bank will charge a nominal $15 \%$, but with monthly compounding. Anne wants to quote a nominal rate to her customers (all) of whom are expected to pay on time) that will exactly cover her financing costs. What nominal annual rate should she quote to her credit customers?

Kayleah Tsai

Numerade Educator

01:47

Problem 33

Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is $85 .$ He wants his first retirement payment to have the same purchasing power at the time he retires as $\$ 40,000$ has today. He wants all his subsequent retirement payments to be equal to his first retirement payment (do not let the retirement payments grow with inflation: he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be $5 \%$ per year from today forward; he currently has $\$ 100,000$ saved up; and he expects to earn a return on his savings of $8 \%$ per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year) to meet his retirement goal? (Hint: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.)

Kratika Bhadauria

Numerade Educator

05:49

Problem 34

You wish to accumulate $\$ 1$ million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays $8 \%$ interest, compounded annually. You expect to get an annual raise of $3 \%,$ so you will let the amount you deposit each year also grow by $3 \%$ (i.e., your second deposit will be $3 \%$ greater than your first, the third will be $3 \%$ greater than the second, etc.). How much must your first deposit be to meet your goal?

Matt Bremer

Numerade Educator

06:13

Problem 35

Start with the partial model in the file $F M 12$ Ch 02 P35 Build a Model.xls from the textbook's Website. Answer the following questions, using a spreadsheet model to do the calculations.
a. Find the FV of $\$ 1,000$ invested to earn $10 \%$ after 5 years. Answer this question by using a math formula and also by using the Excel function wizard.
b. Now create a table that shows the FV at $0 \%, 5 \%$, and $20 \%$ for $0,1,2,3,4,$ and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results.
c. Find the PV of $\$ 1,000$ due in 5 years if the discount rate is $10 \% .$ Again, work the problem with a formula and also by using the function wizard.
d. A security has a cost of $\$ 1,000$ and will return $\$ 2,000$ after 5 years. What rate of return does the security provide?
e. Suppose California's population is 30 million people, and its population is expected to grow by $2 \%$ per year. How long would it take for the population to double?
f. Find the $P V$ of an annuity that pays $\$ 1,000$ at the end of each of the next 5 years if the interest rate is $15 \%$. Then find the FV of that same annuity.
g. How would the $P V$ and $F V$ of the annuity change if it were an annuity due rather than an ordinary annuity?
h. What would the FV and $\mathrm{PV}$ for parts a and $\mathrm{c}$ be if the interest rate were $10 \%$ with semiannual compounding rather than $10 \%$ with annual compounding?
i. Find the $P V$ and $F V$ of an investment that makes the following end-of-year payments. The interest rate is $8 \%$
j. Suppose you bought a house and took out a mortgage for $\$ 50,000$. The interest rate is $8 \%$, and you must amortize the loan over 10 years with equal end-of-year payments. Set up an amortization schedule that shows the annual payments and the amount of each payment that goes to pay off the principal and the amount that constitutes interest expense to the borrower and interest income to the lender.
(1) Create a graph that shows how the payments are divided between interest and principal repayment over time.
(2) Suppose the loan called for 10 years of monthly payments, with the same original amount and the same nominal interest rate. What would the amortization schedule show now?

Ankit Gupta

Numerade Educator