FIN 300 Lecture Notes - Lecture 5: Compound Interest, Cash Flow, Effective Interest Rate

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8 Oct 2015

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Fin300 - lecture #5: varying compound periods including continuous compounding, Annuity due: cash flow occurs at beginning of the period. if limited number of payments then it is annuity ex) lease. Example: what is the pv of a ,000 payment for 5 years at 6% starting immediately. Pv = ,000 + pv ordinary annuity for 4 periods. First compute value as measured at t= -1. Perpetuity: annuity in which the cash flows continue forever if unlimited number of payments, forever . Growing perpetuity: constant stream of cash flows without end that is expected to rise indefinitely, unlimited number of payments formula: Pv = [c (1 + r)] + [(c x (1+g)) (1 + r)^2] + [(c x (1+g)^2) (1 + r)^3] + [(c x (1+g)^(n-1)) (1. Interest rate, r, must be greater than growth rate, g. Assumes that cash flows are received/disbursed at regular/discrete times formula: Growing annuity: finite number of growing annual cash flows at constant rate. formula:

Related Questions

Question 1 of 25

You are planning to deposit $1,000 in a savings account. Account A compounds semiannually while account B compounds monthly. If both accounts have the same quoted annual rate of interest, you should choose _______________.

A. either account since both quote the same rate of interest

B. account A because it has a higher APR

C. account A because it has a higher EAR

D. account B because it is compounded more often

Question 2 of 25

You are evaluating two annuities. They are identical in every way, except that one is an ordinary annuity and the other is an annuity due. Which of the following is FALSE?

A. The ordinary annuity must have a lower future value than the annuity due.

B. The ordinary annuity must have a higher present value than the annuity due.

C. The two annuities will differ in present value by the amount (1+r).

D. The annuity due and the ordinary annuity will make the same number of total payments over time.

Question 3 of 25

What is the total present value of $80 received in one year, $300 received in two years, and $700 received in six years if the discount rate is 7%? Note: There is no direct formula for this kind of PV computation other than the basic equation, PV = FV/(1+r)t. 0 1 2 3 4 5 6 |-----------|----------|----------|----------|----------|---------| PV=? $80 $300 $700

A. $582.72

B. $681.68

C. $757.25

D. $803.24

Question 4 of 25

You need to borrow $23,000 to buy a car. The current loan rate is 7.9% APR compounded monthly and you want to pay the loan off in equal monthly payments over 5 years. What is the correct computation to find your monthly payment (C)?

A. C = $23,000 [PVIFA(7.9%/12, 60)]

B. $23,000 = C [1 - (1/1.0795)] / .079

C. $23,000 = C [1 - (1 /1.0065860)] / .00658

D. C = $23,000 [1 - (1/1.07960)] / .079

Question 5 of 25

The monthly mortgage payment on your house is $821.69. It is a 30-year mortgage at an APR of 6.5% compounded monthly. How much did you borrow? Note: PVIFA(r, t) = [1 â 1/(1+r)t] / r, and of course, you can use your calculator here.

A. $100,000

B. $115,000

C. $130,000

D. $140,000

Question 6 of 25

You just won the lottery and you are given two choices for your prize money: (1) A present lump sum of $20 million or (2) $1 million per year that you and your heirs will receive forever, beginning one year from now. If the appropriate interest rate is 5%, which should you choose and why? Note: PV of a perpetuity = C/r

A. Either, because both have the same present value.

B. (1) because it has a higher present value.

C. (2) because it has a higher present value.

D. (2) because it has a higher future value.

Question 7 of 25

What is the effective annual rate of 6% compounded quarterly? Note: EAR = (1 + APR/m)m â 1.0, where m is the number of compoundings in a year.

A. 6.00%

B. 6.14%

C. 7.50%

D. 24.00%

Question 8 of 25

At the end of each year for the next 8 years you will receive cash flows of $500. The initial investment is $2,500. Which of the following is the correct equation to find the rate of return (r) you are expecting from this investment?

A. $2,500 = $500 [1/(1+r)8 â 1] / r

B. $500 = $2,500 [PVIFA(r%,8)]

C. $500 = $2,500 [FVIFA(r%,8)]

D. $2,500 = $500 [1 â 1/(1+r)8] / r

Question 9 of 25

Consider the following cash flow stream. What is the correct way to find the present value of this cash flow stream at a 10% discount rate? 0 1 2 3 4 5 6 7 8 9 10 |----------|----------|----------|----------|----------|----------|---------|----------|----------|----------| PV=? $35 $35 $35 $35 $35 $35 $20 $20 $20 $20

A. PV = 35 [PVIFA(10%, 6)] + 20 [PVIFA(10%, 4)]

B. PV = 20 [PVIFA(10%, 10)] + 15 [PVIFA(10%, 6)]

C. PV = 35 [PVIFA(10%, 10)] â 15 [PVIFA(10%, 4)]

D. PV = 35 [PVIFA(10%, 6)]/(1.10)6 + 20 [PVIFA(10%, 4)]

Question 10 of 25

You plan to amortize your $10,000 loan by making five equal payments over the next 5 years. The interest rate is 5% compounded annually. What number should appear in (A) of your amortization table below? Note: PVIFA(5%, 5)=4.3295.

Beginning Ending Year Loan Balance Payment Interest Principal Loan Balance

----------------------------------------------------------------------------------------------

1 $10,000 xxxx xxx xxx xxxx

2 ( A ) xxxx xxx xxx xxxx

3 xxxx xxxx xxx xxx xxxx

4 xxxx xxxx xxx xxx xxxx

5 xxxx xxxx xxx xxx 0

A. $8,457.12

B. $8,190.26

C. $7,690.26

D. $6,809.74

Question 11 of 25

The rate of return required by investors for owning a bond to its maturity is called the

A. coupon rate.

B. current yield.

C. dividend yield.

D. yield to maturity.

Question 12 of 25

Which of the following statements regarding bond terminologies is INCORRECT?

A. The written, legally binding agreement between the corporate borrower and the lender detailing the terms of a bond issue is called the indenture.

B. The unsecured long-term debts of a firm are commonly called debentures.

C. An agreement giving the bond issuer the option to repurchase the bond at a specified price prior to maturity is called the zero provision.

D. A special account that sets aside periodic payments for bond redemption is called a sinking fund.

Question 13 of 25

Which of the following statements regarding bond trading is INCORRECT?

A. The long-term bonds issued by state and local governments in the United States are called municipal bonds.

B. The long-term bonds issued by the U.S. government are called Treasury Bills.

C. A bond that makes no coupon payments (and thus is initially priced at a deep discount) is called a zero coupon bond.

D. The price a dealer is willing to pay for a security is called the bid price.

Question 14 of 25

Which bond would most likely possess the least degree of interest rate risk?

A. 8% coupon rate, 12 years to maturity

B. 8% coupon rate, 15 years to maturity

C. 10% coupon rate, 10 years to maturity

D. 12% coupon rate, 8 years to maturity

Question 15 of 25

What is the value of a bond that will pay a total of 50 semiannual coupons of $80 each over the remainder of its life? The yield to maturity is 12%, p.a. Note: B = C [{1 â 1/(1+y)t}/y] + F /(1+y)t. Be careful about specifying t and y for this semiannual bond.

A. $ 734.86

B. $ 942.26

C. $1,135.90

D. $1,315.24

Question 16 of 25

Dizzy Corporationâs 10-year semiannual bond bearing a coupon rate of 12% is currently selling for $950. Given this information, which of the following is the correct valuation equation for this bond?

A. B = 120 [PVIFA(12%, 10)] + 1,000 [PVIF(12%, 10)]

B. $950 = 60 [PVIFA(r/2, 20)] + 1,000 [PVIF(r/2, 20)]

C. $950 = 120 [PVIFA(r, 10)] + 1,000 [PVIF(r, 10)]

D. B = 60 [PVIFA(6%, 20)] + 1,000 [PVIF(6%, 20)]

Question 17 of 25

To find the yield-to-maturity of the bond in Question #16 by trial and error, which number (as a semiannual YTM) should you pick as your first try?

A. 5%

B. 6%

C. 7%

D. Any number (like one of your favorite lotto numbers).

Question 18 of 25

George bought an investment one year ago and just calculated his return on investment. He found that his purchasing power has increased by 15% as a result of his investment. If the inflation over the period was 4%, his _______________. Note: (1+R) = (1+r)(1+h), but you donât need calculation here.

A. real return on investment is more than 15%

B. nominal return on investment is more than 15%

C. nominal return on investment is 11%

D. real return on investment is equal to 4%

Question 19 of 25

Which statement is INCORRECT given the following Treasury quotes? Maturity Coupon Bid Ask(ed) Chg Ask(ed) Yld ---------------------------------------------------------------------------------------- 5/15/2030 6.250 150.7188 150.7500 .8906 2.713

A. The amount of each coupon on this bond is $31.25.

B. The ask(ed) price is $1,507.50.

C. The dealer is willing to sell this bond to you for 150.7188% of par.

D. This bondâs ask(ed) price rose by $8.906 (i.e., eight dollars and 90+ cents) from the previous trading day.

Question 20 of 25

Which of the following statements regarding stock trading is INCORRECT?

A. Stock that has priority for dividends and bankruptcy liquidation is called priority equity.

B. The short alphabetic abbreviation for an exchange-listed stock by which the issue is identified in the market is called the stock's ticker symbol.

C. Capital gains yield is the rate of return based on the stock price increase.

D. Proxy voting is the voting procedure where shareholders grant authority to another individual to vote their shares.

Question 21 of 25

What would you pay for a share of ABC Corporation stock today if the next dividend will be $3 per share, your required return on equity investments is 15%, and the stock is expected to be worth $90 one year from now? (Remember the stock price today is the PV of its future cash flows, i.e., dividends and the future stock price, properly discounted)

A. $75.00

B. $78.26

C. $80.87

D. $90.00

Question 22 of 25

A preferred stock that pays a constant dividend of $1.50 currently sells for $10.71. What is the required rate of return? Note: P0 = D/R for a preferred stock.

A. 14%

B. 13%

C. 12%

D. 10%

Question 23 of 25

A stock with a constant dividend growth rate of 5% is expected to make a $2 dividend in one year. If you require a 12% return on your investment, which of the following statements is INCORRECT? Note: P0 = D1/(Râg) or R = (D1/P0) + g.

A. The current stock price is $28.57.

B. The dividend yield is 7%.

C. The capital gains yield is 12%.

D. The stock price will grow at an annual 5%.

Question 24 of 25

McIver, Inc. currently pays a $2 annual dividend. Investors believe that dividends will grow at 20% next year, 12% for the following year, and 6% annually thereafter. The required return is 10%. What is the current price of the stock?

A. $63.27

B. $60.80

C. $58.71

D. $54.90

Question 25 of 25

Which statement is INCORRECT given the following stock quotes? Prev Close 44.34 Dayâs Range 43.45 â 44.37 Bid 44.01 x 1,200 Volume 908,587 Ask 44.02 x 400 P/E 17.26 Beta 2.4 EPS 2.55 Market Cap 10.11B Div & Yield 0.50 (1.10%)

A. At this point someone was willing to buy 1,200 shares of this stock for $44.01 a share.

B. The yield-to-maturity for this stock is 1.1%.

C. On this trading day so far 908,587 shares changed hands.

D. The total value of this companyâs stock is (about) $10,110 million.

Show ALL work

It will help to use the timeline to outline the following problems.

1. You decide to begin saving for a new car to purchase in five years. If you put $1,000 at the end
of each of the next 5 years in a savings account paying 6% compounded annually, how much will you accumulate after 5 years?

2. James Smith has a 4-year ordinary annuity that pays $1,000 per year and has an interest rate of 6%. a. Calculate the future value of this ordinary annuity.

b. Assuming this was an annuity due, calculate the future value of this annuity.

3. You have contacted a number of car dealerships to determine the best interest rate on a new automobile loan. A Ford dealership has quoted you a 5-year, 10% loan in the amount of $35,000 that will require monthly payments.

a. What is the monthly loan payment?

b. What will be the loanâs effective annual interest rate (EAR)?

4. Marcus has won the grand prize in a lottery and must choose between the following three options: a. Receive a lump sum payment of $9,000,000.

b. Receive annual end of the year payments of $1,000,000 for the next 12 years.
c. Receive annual end of the year payments of $1,500,000 for the next 8 years.
a. Which option should Marcus choose based on an annual investment rate of 8%?

5. How much money does Kristi need to have in her retirement savings account today if she wishes to withdraw $25,000 per year for 30 years? She expects to earn an average rate of 8%.

decide to begin saving towards the purchase of a new car in 5 years. If you put $1,000 at the end

6. What is the future value of $4,900 invested for 8 years at 7 percent compounded semiannually?

7. In 2005, soccer player David Beckham signed a contract reported to be worth $51 million. The contract called for $2 million immediately and $10 million in 2006. The remaining $39 million was to be paid as $9 million in 2007, $7 million in 2008, $6 million in 2009, $5 million in 2010, $4 million in 2011 and in 2012, $2 million in 2013, and $1 million in 2014 and 2015. Assuming all the payments, except the first $2 million are paid at the end of each year and the discount rate is 9%, what kind of deal did the soccer player snag?

8. What is the present value of the following set of cash flows at a 10% discount rate? Year 1 2 3 4
Cash Flow $600 â$600 $600 â$600

9. What is the future value of the set of cash flows (from the previous problem) 4 years from now? Assume an interest rate of 10%.

10. Starting today, George is going to contribute $300 on the first of each month to his retirement account. His employer will contribute an additional 50% of the amount George contributes. If both George and his employer continue to do this and he can earn a monthly rate of .68%, how much will George have in his retirement account 35 years from now?

turquoisemole375

Amongst corporations, sole proprietorships and partnerships, approximately what percentage of revenues are generated by corporations?

50%

42%

33%

82%

Question 2

What should be the financial goal of any firm?

attracting and acquiring capital and investing it

maximization of the ownersâ wealth

offering quality products at fair prices

quality customer service

Question 3
4 pts
Which of the following statement(s) is \ are true regarding the corporate management team?

In a corporation, ownership and direct control are typically separate.

Board of Directors is elected by shareholders and has ultimate decision-making authority

The Chief Executive Officer (CEO) â the Board typically delegates day-to-day decision making to the CEO.

All of the above

Question 4
4 pts
When calculating the present value of either a future single sum or a future annuity, it involves a process called discounting. The applicable interest rate to perform the discounting function is usually called the

yield to maturity

compound interest rate

discount rate

none of the above

Question 5
4 pts
_________________ are used to present additional information about items included in the financial statements and to present additional financial information.

stock certificates

Notes to financial statements

Preferred stocks

Convertible securities
Question 6
4 pts
What should be the financial goal of any firm?

maximization of the ownersâ wealth

attracting and acquiring capital and investing it

offering quality products at fair prices

quality customer service

Question 7
4 pts
A competitive market is one in which a _____ numbers of producers compete with each other to satisfy the wants and needs of a _____ number of consumers.

Large, small

Small, small

Large, large

Small, large

Question 8
4 pts
The Valuation Principle is an analysis between the value of the ______ of a financial alternative and the value of its ______.

revenues, income

benefits, costs

expenses, costs

Question 9
4 pts
The Net Present Value rule implies that we should compare a projectâs net present value (NPV) to___________. (zero \ future value \ the past).

Zero

Future Value

The Past

An Estimate

Question 10
4 pts
The internal rate of return (IRR) rule will _______ agree with the Net Present Value rule on a given investment project.

always

never

sometimes

none of the above

Question 11
5 pts
The law of one price exists due to arbitrage opportunities. If the price of a security, commodity or asset is different in two different markets, then an arbitrageur will ______ the asset in the more expensive market and ________ it where prices are lower.

sell, purchase

purchase, sell

purchase, purchase

sell, sell

Question 12
5 pts
Approaching every problem using a timeline is a(n) ________ idea because timelines identify events in a transaction or investment which might otherwise be easily overlooked.

good

bad

indifferent

unrealistic

Question 13
5 pts
The present value (PV) of a stream of cash flows is the _______ the present values of each individual cash flow

difference between

product of

sum of

same as

Question 14
5 pts
As the number of periods increases, present value (increases\decreases\stays the same).

increases

decreases

stays the same

is unrelated

Question 15
5 pts
When a constant cash flow will occur at regular intervals for a finite number of periods of time, it is called a(n) __________.

annuity

perpetuity

interest payment

principle payment

Question 16
5 pts
When a constant cash flow will occur at regular intervals forever, it is called a(n) ___________.

annuity

perpetuity

interest payment

principle payment

Question 17
5 pts
The NPV measures the ______ change in shareholder wealth that arises from undertaking a project.

consistent

dollar

annual

semi-annual

Question 18
5 pts
When calculating the present value of either a future single sum or a future annuity, the applicable interest rate is usually called the _______ rate

compounding

inverted

market

discount

Question 19
5 pts
To endow a perpetuity is the same as calculating the present value (PV) of a perpetuity. Say you want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one yearâs time, how much will you need to donate to endow the party?
The formula for PV of a perpetuity = C\r; = $30,000 \ 0.08; =

$3,750

$37,500

$375,000

$3,750,000

Question 20
5 pts
With an Ordinary Annuity, payments are required at the ________ of each period. An example of this is bonds which usually pay coupon payments at the end of every six months until the bond's maturity date.

beginning

middle

end

payments are not required

Question 21
5 pts
Sales of securities that the seller does not own is called a:

stop-loss order

short sale

limit order

maintenance margin

Question 22
5 pts
What is the name of the market where money market securities, bonds, and mortgages are originated and traded?

debt securities market

foreign exchange market

derivative securities market

equity securities market

Question 23
5 pts
If an investor feels the price of a stock will decline in the future, which trade should the investor undertake?

market order

buy on margin

limit order

short sale

Question 24
5 pts
For risk averse investors, how much return is expected for taking on more risk?

lower

equal

zero

higher

Question 25
5 pts
A ___________________ is a highly regulated document which details the issuers operations and finances and must be provided to each buyer of a newly issued security.

Prospectus

An underwriting agreement

A best efforts agreement

none of the above

Question 26
5 pts
Which of the following statements about liquidity ratios is true?

The lower the quick ratio relative to the current ratio, the safer a firm is in terms of liquidity.

The higher the current ratio, the more likely a firm is able to pay its short-term obligations.

The quick ratio is always between 0 and 1.

All the above statements are true.

Question 27
5 pts
The ability of a firm to meet its short-term debt obligations as they come due is indicated by which of the following ratios:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 28
5 pts
Which one of the following financial statements reports a firmâs assets and the claims on assets?

balance sheet

income statement

statement of changes in financial position

cash flow statement

Question 29
5 pts
The extent to which assets are used to support sales is indicated by which of the following ratios:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 30
5 pts
The extent to which assets are financed by borrowed funds and other liabilities is indicated by:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 31
5 pts
The basic price that equates the demand for and supply of loanable funds in the financial markets is the __________:

interest rate

yield curve

term structure

cash price

none of the above

Question 32
5 pts
Federal obligations usually issued for maturities of two to ten years are called:

Treasury bonds

Treasury notes

Treasury bills

Agency issues

Question 33
5 pts
An increase in the demand for loan-able funds, holding supply constant, will cause interest rates to:

increase

decrease

stay the same

none of the above

Question 34
5 pts
As interest rates rise, the prices of existing bonds will:

rise

stay the same

fall

either a or b

Question 35
5 pts
In an inflationary period, interest rates have a tendency to:

rise

fall

stay the same

act erratically

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FIN 300 Lecture Notes - Lecture 5: Compound Interest, Cash Flow, Effective Interest Rate

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