Ch 5 HW - FIN 370

A series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply. The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next five years: Annual Cash Flows Year 1 = $250,000 Year 2 = 20,000 Year 3 = $180,000 Year 4 = $450,000 Year 5 = $550,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$1,255,617 Excel: NPV 5 years = NPV(rate, value1, [value2], [value3], [value4], [value5]) = NPV(0.040, 250,000, 20,000, 180,000, 450,000, 550,000) = $1,255,617

An ordinary annuity selling at $4,947.11 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity's appropriate interest rate (I) remains at 6.50% during this time, the annual annuity payment (PMT) will be _________

$812.50 Excel: PMT = PMT(rate, nper, pv, [fv], [type]) =PMT(6.50,8,-4947.11,0,1) = $812.50

A table that reports the results of the disaggregation of each payment on an amortized loan, such as a mortgage, into its interest and loan repayment components

Annual percentage rate

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Simple interest?

FV = PV + (PV x I x N)

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest?

FV = PV x (1 + I) N (exponent N)

A process that involves calculating the current value of a future cash flow or series of cash flows based on a certain interest rate.

Future value

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows. An investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Nominal Rate = 4.4% Periodic Rate = 1.10% Effective Annual Rate = 4.47%

Investments and loans base their interest calculations on one of two possible methods: the __________ interest and the__________ interest methods. Both methods apply three variables—the amount of principal, the interest rate, and the investment or deposit period—to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.

Simple, Compound

The name given to the amount to which a cash flow, or a series of cash flows, will grow over a given period of time when compounded at a given rate of interest.

Time value of money

Which of the following is an example of an annuity? A. A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time B. An investment in a certificate of deposit (CD)

A. A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time

A 6% return that you could have earned if you had made a particular investment.

Annuity due

Which of the following statements is true—assuming that no additional deposits or withdrawals are made? A. An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time. B. An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time.

B. An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time. Excel: A. FV = FV(rate, nper, pmt, [pv], [type]) = FV(0.05, 5, 0, 50, 0) = $63.81 B. FV = FV(rate, nper, pmt, [pv], [type]) = FV(0.10, 5, 0, 25, 0) = $40.26

If a security currently worth $5,600 will be worth $8,228.24 five years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

8% Excel: Interest Rate= RATE(nper, pmt, pv, [fv], [type], [guess]) = RATE (5, 0, -5600, 8228.24, 0) = 8.00

Katie had a high monthly food bill before she decided to cook at home every day in order to reduce her expenses. She starts to save $1,060 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 14% annual interest. Katie's savings are an example of an annuity. If Katie decides to renovate her kitchen, how much would she have in her savings account at the end of seven years? If Katie deposits the money at the beginning of every year and everything else remains the same, she will save _________ by the end of seven years.

$11,374.32 Excel: FV = FV(rate, nper, pmt, [pv], [type]) = FV(14,7,-1060,0,1) = 11,374.32 $12,966.73 FVA Due = 11,374.32 * (1+0.140) = $12,966.73

Another bank is also offering favorable terms, so Rahul decides to take a loan of $12,000 from this bank. He signs the loan contract at 5% compounded daily for 12 months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$12,615.21 Excel: FV =FV(rate, nper, pmt, [pv], [type]) =FV(0.000136986, 365.0, 0, 12000, 0) =$12,615.21

Financial contracts involving investments, mortgages, loans, and so on are based on either a fixed or a variable interest rate. Assume that fixed interest rates are used throughout this question. Isabella deposited $1,400 in a savings account at her bank. Her account will earn an annual simple interest rate of 6.6%. If she makes no additional deposits or withdrawals, how much money will she have in her account in 13 years?

$2,601.20 Because Isabella earns simple interest on her savings account, interest will be earned on only the account's initial investment once every interest-earning period. Interest is not earned (or paid) on any previously-earned interest. Therefore, Isabella's $1,400 initial investment will earn interest of $1,201.20 ($1,400 x 6.6%) each year for the next 13 years. 1. Compute the future value (FV) of Isabella's investment in 13 years as follows: I=Interest Earned in One Year x Number of Years=(6.6% x $1,400.00) per year x 13 years=$1,201.20 FVn= Initial Investment (PV00) + Total Interest Earned (I) FV13=$1,400.00 + $1,201.20=$2,601.20

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in eight equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won_________ —assuming annual interest rate of 6.50%.

$28,369,774.00 PV = PV(rate, nper, pmt, [fv], [type]) =PV(6.50,8,4375000,0,1) = -28,369,774.00

Now, assume that Isabella's savings institution modifies the terms of her account and agrees to pay 6.6% in compound interest on her $1,400 balance. All other things being equal, how much money will Isabella have in her account in 13 years?

$3,213.45 Excel may also be used to solve the problem, and the Excel inputs are as follows: FV = FV(rate, nper, pmt, [pv], [type]) = FV(6.6%, 13, 0, -1,400, 0) = $3,213.45 4

Suppose Isabella had deposited another $1,400 into a savings account at a second bank at the same time. The second bank also pays a nominal (or stated) interest rate of 6.6% but with quarterly compounding. Keeping everything else constant, how much money will Isabella have in her account at this bank in 13 years?

$3,278.78 In this case, the compounding period changed from annually to quarterly. Using the first technique, in 13 years, there are 52 quarters (13 years x 4 quarters per year), which represents the number of interest-earning periods (N = 52) for this problem. The periodic interest rate, or the interest rate paid per interest-earning period, is 1.6500% (6.6% / 4), and the initial investment is still $1,400 (PV = -1,400). Remember, there is no intermediate payment (PMT = 0). Excel: P/Y = 1 N = 52 I = 1.6500 PV = -1,400 PMT = 0 FV = $3,278.78

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding bimonthly (every two months). What is the effective interest rate that Rahul would pay for the loan?

4. 067% EFF%=[1+(II / M)]M−1[1+II / M]M−1 =[1+(0.04000 / 6)]6−1 =0.04067 =4.067%

If an investment of $40,000 is earning an interest rate of 12.00%, compounded annually, then it will take ________ years for this investment to reach a value of $66,610.25—assuming that no additional deposits or withdrawals are made during this time.

4.50 Years Excel: N =NPER(rate, pmt, pv, [fv], [type]) =NPER(0.1200, 0, -40000, 66610.25, 0) = 4.50 years Payment at the beginning of the period = 1; payment at the end of the period = 0

Jacob needed money for some unexpected expenses, so he borrowed $2,138.41 from a friend and agreed to repay the loan in three equal installments of $800 at the end of each year. The agreement is offering an implied interest rate of __________

6.00% Excel: Interest Rate = RATE(nper, pmt, pv, [fv], [type]) = RATE(3, 800, -2138.41, 0, 0) = 6.00%

Jacob's friend, Devan, wants to go to business school. While his father will share some of the expenses, Devan still needs to put in the rest on his own. But Devan has no money saved for it yet. According to his calculations, it will cost him $31,897 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $3,800 at the end of every year in a mutual fund, from which he expects to earn a fixed 6% rate of return. It will take approximately__________ years for Devan to save enough money to go to business school.

7 Years Years = NPER(rate, pmt, pv, [fv], [type]) = NPER(0.06, -3800, 0, 31897, 0) = 7.00

A. A local bank's advertising reads: "Give us $45,000 today, and we'll pay you $800 every year forever." If you plan to live forever, what annual interest rate will you earn on your deposit? B. Oops! When you went in to make your deposit, the bank representative said the amount of required deposit reported in the advertisement was incorrect and should have read $67,500. This revision, which will______ the interest rate earned on your deposited funds, will adjust your earned interest rate to_________ .

A. 1.78% PVBank Deposit = Payment/Interest Rate Interest Rate = 800/45,000 = 0.0178 or 1.78% B. Reduce, 1.19% Revised Interest Rate = 800/67,500 = 0.0119 or 1.19%

Perpetuities are also called annuities with an extended or unlimited life. Based on your understanding of perpetuities, answer the following questions. Which of the following are characteristics of a perpetuity? A. A perpetuity is a stream of regularly timed, equal cash flows that continues forever. B. The value of a perpetuity cannot be determined. C. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows. D. A perpetuity is a stream of unequal cash flows.

A. A perpetuity is a stream of regularly timed, equal cash flows that continues forever C. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

Which of the following statements about annuities are true? Check all that apply. A. Annuities are structured to provide fixed payments for a fixed period of time. B. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due. C. When equal payments are made at the beginning of each period for a certain time period, they are treated as ordinary annuities. D. An ordinary annuity of equal time earns less interest than an annuity due.

A. Annuities are structured to provide fixed payments for a fixed period of time. B. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due. D. An ordinary annuity of equal time earns less interest than an annuity due.

Which of the following investments that pay will $17,500 in 8 years will have a lower price today? A. The security that earns an interest rate of 6.00%. B. The security that earns an interest rate of 4.00%.

A. The security that earns an interest rate of 6.00%. Excel: PV4.00%%= PV(rate, nper, pmt, [fv], [type]) = PV(0.04, 8, 0, -17500) = $12,787.08 PV6.00%% = PV(0.06, 8, 0, -17500) = $10,979.72

A cash flow stream that is created by an investment or loan that requires its cash flows to take place on the last day of each quarter and requires that it last for 10 years.

Amortization schedule

An interest rate that reflects the return required by a lender and paid by a borrower, expressed as a percentage of the principal borrowed.

Amortized loan

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: You recently moved to a new apartment and signed a contract to pay monthly rent to your landlord for a year.

Annuity Payments

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: You have committed to deposit $600 in a fixed interest-bearing account every quarter for four years.

Annuity Payments

Which of the following equations can be used to solve for the present value of an ordinary annuity? A. PMT x {[(1 + r)nn - 1]/r} x (1 + r) B. PMT x {1 - [1/(1 + r)nn]}/r C. PMT x {[(1 + r)nn - 1]/r} D. PMT/r

B. PMT x {1 - [1/(1 + r)nn]}/r

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? A. An investment that matures in four years B. An investment that matures in five years

B. An investment that matures in five years Excel: PV 4 Years = PV(rate, nper, pmt, [fv], [type]) = PV(0.054, 4, 0, -1000) = $810.284 PV5.40%= PV(0.054, 5, 0, -1000) = $768.77

Which of the following is true about present value calculations? A. Other things remaining equal, the present value of a future cash flow increases if the investment time period increases. B. Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases.

B. Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases.

The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value. The process for converting present values into future values is called ______________ . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables? A. The interest rate (I) that could be earned by invested funds B. The present value (PV) of the amount invested C. The inflation rate indicating the change in average prices D. The duration of the investment (N)

Compounding C. The inflation rate indicating the change in average prices

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. A. An annuity that pays $500 at the end of every six months B. An annuity that pays $500 at the beginning of every six months C. An annuity that pays $1,000 at the end of each year D. An annuity that pays $1,000 at the beginning of each year

D. An annuity that pays $1,000 at the beginning of each year

A cash flow stream that is generated by a share of preferred stock that is expected to pay dividends every quarter indefinitely.

Discounting

_________ is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.

Discounting

Identify whether the following statements about the simple and compound interest methods are true or false: After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.

False

Heather is willing to invest $30,000 for six years, and is an economically rational investor. She has identified three investment alternatives (L, M, and P) that vary in their method of calculating interest and in the annual interest rate offered. Since she can only make one investment during the six-year investment period, complete the following table and indicate whether Heather should invest in each of the investments.

Investment L: - 5% compound interest rate - expected Future Value = $40,203 -Make this investment? : No Investment M: - 4% simple interest rate - expected Future Value = $37,200 -Make this investment? : No Investment P: - 7% compound interest rate - expected Future Value = $45,022 -Make this investment? : Yes

A concept that maintains that the owner of a cash flow will value it differently, depending on when it occurs.

Opportunity cost of funds

A cash flow stream that is created by a lease that requires the payment to be paid on the first of each month and a lease period of three years.

Ordinary annuity

Identify whether the following statements about the simple and compound interest methods are true or false: All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.

True

Identify whether the following statements about the simple and compound interest methods are true or false: Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest.

True

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: Franklinia Venture Capital (FVC) invested in a budding entrepreneur's restaurant. The restaurant owner promises to pay FVC 10% of the profit each month for the next 10 years.

Uneven Cash Flows

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: SOE Corp. hires an average of 10 people every year and matches the contribution of each employee toward his or her retirement fund.

Uneven Cash Flows