ADM 2350 Lecture Notes - Lecture 5: Fair Deal, Annuity

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13 May 2017

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> growing annuity is a series of nite cash ows that grow at a xed rate. > growing perpetuity is a constant stream of cash ows without end that is expected to rise inde nitely. > note: grow does not necessary means increase : the growth rate can be positive or negative e. g, assume your starting salary after graduation is ,000 and it expects to grow at 10% annually until you retire. What is the pv of all your future expected salary if you will be in employed for 40 years ant the interest rate is 6% I=0. 06 = interest rate g=0. 1 = growth rate c=,000 = cash payment at the rst period. I=0. 12 = interest rate g=0. 04 = growth rate c=,000 = cash payment at the rst period. > note: we must have r>g in order to have the nite value of a perpetuity.

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.

Question 1 5 pts

0 multiple_choice_question 22046808

The internal rate of return (IRR) is the interest rate that sets the net present value of the future cash flows equal to ________.

Question 2 5 pts

On a timeline, the space between date 0 and date 1 represents the _______ between dates. Letâs assume it is the first year of the loan. Date 0 is the beginning of the first year, and date 1 is the end of the first year.

Question 3 5 pts

As the interest rate __________, present value decreases.

Question 4 5 pts

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

Question 5 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) __________.

Question 6 5 pts

Edit this Question Delete this Question

0 multiple_choice_question 22047052

There are two basic types of annuities:

Discounted and compounded annuities

Ordinary annuities and annuities due.

Future value and present value annuities

None of the above

Question 7 5 pts

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

Question 8 5 pts

The Net Present Value rule implies that we should compare a projectâs net present value (NPV) to ________

Question 9 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; =

Question 10 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

limemacaw827

1. The 2013 balance sheet of Bear Inc., showed long-term debt of $1.45 million, and the 2014 balance sheet showed long-term debt of $1.52 million. The 2014 income statement showed an interest expense of $127,000. What was the firmâs cash flow to creditors during 2014?
2. The 2013 balance sheet of Bear Inc., showed $490,000 in the common stock account and $3.4 million in the capital surplus account. The 2014 balance sheet showed $525,000 and $3.7 million in the same two accounts, respectively. If the company paid out $275,000 in the cash dividends during 2014, what was the cash flow to stockholders for the year?
3. Given the information for Bear Inc. in the previous two questions, suppose you also know that the firmâs net capital spending for 2014 was $945,000 and that the firm reduced its net working capital by $87,000. What was the firmâs 2014 operating cash flow?
4. Brooks Corp. shows the following information on its 2014 income statement: sales=$185,000; costs=$98,000; other expense=$6,700; depreciation=$16,500; interest expense=$9,000; taxes=$19,180; dividends=$9,500. In addition, you are told that the firm issued $7,550 in new equity during 2014 and redeemed $7,100 in outstanding long-term debt. 1) What is the average tax rate? (Hint: Following the income statement in the notes to find the pretax income in order to calculate tax rate) 2) What is the 2014 operating cash flow? 3) What is the 2014 cash flow to creditors?
4) What is the 2014 cash flow to stockholders? 5) If net fixed assets increased by $26,100 during the year, what was the change to net working capital?
5. An investment offers $4,900 per year for 15 years, with the first payment occurring one year from now. If the required return is 8%, what is the present value of the investment? What would be the value if the payments occurred for 40 years? Forever?
6. Find the EAR in each of the following cases:
APR Compounding period EAR 7% Quarterly 16% Monthly 11% Daily (365 days in a year)
7. Joey Has just arranged to purchase a $550,000 home with a 20% down payment. The mortgage has a 6.1% stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. After the down payment, his first monthly payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8. How much is the balloon payment in 8 years?
8. Given an interest rate of 6.1% per year, what is the value at Date t=7 of a perpetual stream of $2,500 annual payments that begins at Date t=15?
9. You want to buy a new car for $73,000. The contract is in the form of a 60month annuity due at a 6.45% APR. What is your monthly payment?

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ADM 2350 Lecture Notes - Lecture 5: Fair Deal, Annuity

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