FIN 300 Lecture Notes - Lecture 5: Preferred Stock, Annual Percentage Rate, Interest

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26 Dec 2016

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A dollar received today is worth more than a dollar received tomorrow. The value of cash flows received at different times can never be directly compared. Economic value of a dollar depends on the time at which it is received or disbursed. Time-value concept forms the basis for valuation. Compounding: translation of current dollars (pv) into economically equivalent future dollars (fv) Discounting: translation of future dollars (fv) into economically equivalent current dollars (pv) Future value: amount to which an investment will grow after earning interest. Simple: interest earned only on initial investment: formula: fv = pv x (1 + t x r) Compound: interest is earned on interest: formula: fv = px x (1 + r)t. Cash flows can be compared only at the same point in time thus we need to find pv of option 2. Annuity: equally spaced and a level stream of cash flows (finite periods) to link: fv = pv x (1 + r)t.

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QUESTION 1 The time value of money refers to the issue of: A. what the value of the stream of future cash flows is today. B. why a dollar received tomorrow is worth more than a dollar received today. C. what the time required to double an amount of money. D. why people prefer to consume things at some time in the future rather than today.

QUESTION 2 The process of converting an amount given at the present time into a future value is called: A. annualizing. B. discounting. C. compounding. D. capital budgeting. 2 points

QUESTION 3 Juan Vinson is planning to buy a house in five years. He is looking to invest $25,000 today in an index mutual fund that will provide him a return of 12 percent annually. How much will he have at the end of five years? (Round to the nearest dollar.) A. $45,000 B. $28,000 C. $44,059 D. $28,530 2 points

QUESTION 4 Which of the following statements is true with respect to the present value of a future amount? A. The higher the discount rate, the higher the present value of a single sum for a given time period. B. The relation between present value and time is exponential. C. The greater the time period, the higher the present value of a single sum for a given interest rate. D. The lower the discount rate, the lower the present value of a single sum for a given time period. 2 points

QUESTION 5 Which of the following statements is true of the rule of 72? A. It can be used to determine the amount of time it takes to double an investment. B. It is fairly accurate for interest rates between 25 and 50 percent. C. It states that the time to double your money (TDM) approximately equals 72/i, where i represents the years it takes to double your investment. D. It can be used to estimate approximate compound interest earned for a period of 72 days. 2 points

QUESTION 6 The present value of future cash flows are computed by multiplying future value with the: A. discounting factor. B. compound factor. C. interest rate. D. number of periods. 2 points

QUESTION 7 The present value of multiple cash flows is: A. greater than the sum of the cash flows. B. equal to the sum of all the cash flows. C. less than the sum of the cash flows. D. higher or lower than the cash flows depending on the interest rate. 2 points

QUESTION 8 Cash flows associated with annuities are considered to be: A. an uneven cash flow stream. B. a constant cash flow stream. C. a mix of constant and uneven cash flow streams. D. a cash flow stream with decreasing trend. 2 points

QUESTION 9 The annuity transformation method is used to transform: A. a present value annuity to a future value annuity. B. a present value annuity to an annuity due. C. an ordinary annuity to an annuity due. D. a perpetuity to an annuity. 2 points

QUESTION 10 The true cost of borrowing is the: A. annual percentage rate. B. effective annual rate. C. quoted interest rate. D. periodic rate.

Are my answers correct?

Suppose you invest $10,000 in a savings account earning 2% interest (compounded yearly) with no risk. After 7 years, how much will you have?

Principal = $10,000.00

Rate = 2.00%

Year = 7

Amount (Compound interest) = P x (1 + r/n) ^nt

Where P = Principal

r rate of interest

n = number of time interest is calculated in a year

t = time

Amount after 7 years = 10,000 x (1+0.02) ^7 = $11,486.86

Repeat Question #1, but this time there is an inflation rate of 4%. How does this change your overall return on investment? If you had a chance to invest in an account with a long-term expected rate of 5%, with a 50% chance of earning 0% nominal compound interest and a 50% chance of earning 10% nominal compound interest in each year, would you choose this account, or the savings account? Why?

Effects of inflation on PV = 10,000 x (1/(1+0.04)^7) = $7,599.18

FV Adjusted for inflation = 11,486.86 x (1/(1+0.04)^7) = $ 8,729.07

Overall return on investment will decrease by 1,270.93 = 10,000 â 8,729.07

Repeat #1 with inflation:

Amount after 7 years = 10,000 x ((1+0.02)/(1+0.04)) ^7

10,000 x (0.98) ^7 = $8,729.07.

Safe vs. Risky (not including inflation)

If I get 0%, the amount after 7 years = 10,000 x (1+0.00) ^7 = $10,000.00

If I get 10%, the amount after 7 years = 10,000 x (1+0.10) ^7 = $19,487.17

If I get 5% (expected), amount after 7 years = 10,000 x (1+0.05) ^7 = $14,071.00

I would choose the account with the 5% expected rate of return because it has higher effective annual return over the saving account. There is a higher return, but the risk is higher as compared to the savings account, which provides a certain return.

Suppose you will need $50,000 in 4 years to start up a new business you have planned. With a 5% real interest rate, how much do you have to invest now in order to achieve this goal?

This condition clearly says that we need to calculate the present value of the future earnings and it has to be the present value factor and not annuity.

Therefore, to get 50000 is the future value therefore present value of 50000

Amount to be invested today =PVF@5%,4 *Amount

= .82270 * 50000

= $ 41135.12

Repeat Problem #3, but assume you can contribute an equal amount on a yearly basis. How much would you need to put into the account each year?

Amount to invested each year = Amount /FVAF@5%,4 = 11,600.66

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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.

FIN 300 Lecture Notes - Lecture 5: Preferred Stock, Annual Percentage Rate, Interest

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