FIN 010 Lecture Notes - Lecture 5: Santa Barbara City College, Cash Flow

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9 Jan 2021

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If the first instalment of kate"s stream (paid annually) incurs now (i. e. annuity due). Multi steps single (lump sum) + multiple cash flows. Deferred annuity first payment made in period d (d>1) Kate decides to defer the collection of her retirement income stream. 20 annual payments, but the first payment will be received in year 5. If the first payment of ordinary annuity is paid in period d, the formula provide present value as of period (d-1) Amount of periodic payment (annuity) such as a mortgage. Notice that annuity" may not be received/paid annually. Steve has bought a house for ,000 with 20% cash down payment. The remaining balance is financed by a 30-year mortgage at 5. 25% per annum. The mortgage installments are paid monthly and first installment is due in one month. Pv = 800,000 (1-0. 2) = ,000 r = 0. 0525 / 12 = 0. 004375 (0. 4375%) n = 30 x 12 = 360.

Related Questions

CAN SOMEONE LET ME KNOW IF I DID THESE RIGHT?? PLEASE

1. What is the effective rate of interest for an investment paying 18% compounded monthly?

Effective rate of interest= (1+r)^n-1

r= 18% or .18; compounded monthly= 0.18/12

N= no of period ie 12

Effective rate r= (1+.18/12)^12-1

= 0.1956 ie 19.56%

2. If you want to buy a $25,000 car in 5 years, what single amount must you invest now at 10% compounded quarterly to have the money to pay cash?

Fv= PV(1+i)^n

Fv= 25,000 n=5 years so 5*4= 20 periods; r = 10% compounded quarterly ie .10/4

25,000=PV(1+.10/4)^20

25,000= PV (4.10/4)^20

PV= (25,000/1.025)^20

PV=$15,256.77

3. What is the present value of $50,000, 4 years from now at 12% interest compounded monthly?

Fv= Pv (1+r)^n

Fv=50,000; Pv?; n= 4 years compounded monthly ie 48; R= 12% compounded monthly ie .12/12

50,000= PV (1+.12/12)^48

PV=50,000/(1.01)^48

PV=$31,013.02

4. What is the future value of $5,000 in 15 years if you can earn 12% interest compounded semi-annually?

Fv=PV(1+i)^n

Fv=5,000; n=15 years semi annually= 30 periods; I=12% compounded semi annually=.12/2

5,000= PV (1+.12/2)^30

PV=5,000(1.06)^30

PV=$28,717.46

5. What is the future value of $800 deposited annually at 9% interest for 25 years if the deposits are made at the end of the period? And, if the deposits are made at the beginning of the period?

FV(end)= PMT[(1+i)^n-1)/i] (Ordinary annuity)

FV= $800; i=9% or .09; n=25 years

Fv+800[(1+0.09)^25-1)/0.09

FV=$67,760.72

FV=(beginning)= PMT[((1+i)^n-1)/i](1+r)

FV=$800; I=9% or 0.09; n=25 years

FV=800[(1+0.09)^25-1)/0.09)(1+0.09)

FV=$73,859.18

6. Using the information from the previous problem, how much more interest is earned from the annuity due than from the ordinary annuity?

Annuity due= annuity (beginning) - ordinary annuity

=$73,859.18-$67,760.72= $6,098.46

7. How much must be deposited now in order to withdraw $15,000 at the end of each year for 30 years, if interest is 11% compounded annually?

Annuity the end of each year= 15,000

N=30 years; r= 11% compounded annually

To find PV of an annuity of $15,000 @ the end of each of the year

PV= PMT [1-(I+i)^-n/i

PV=15,000[1-(I+0.11)^-30/0.11]

PV= PMT[1-(I+i)^-n/i

=$130,406.89

8. If you want $2,000,000 in your retirement fund in 45 years, and you can earn 14% compounded annually, what will be your annual contribution? How much interest will you earn?

FV= 2,000,000; N= 45 years; i= 14% compounded annually

We have the FV of an annuity â to find the annuity

FV= PMT [(I+i)^n-1)/i]

2,000,000=PMT [((1+0.14)^45-1)/(0.14]

2,000,000= PMT [2590.5648]

PMT=$772.03

9. If you retire with $1,375,000 in your retirement fund and plan to live for 20 years, how much can you withdraw every year if your investment earns 10%?

PV= 1,375,000 n=20 years i=10%

To find annuity given the PV

PV=PMT [1-(1+i)^-n/I]

1,375,000= PMT [1-(1+0.10)^-20/0.10)

PMT(yearly withdrawl) =$161,506.98

10. How much more interest is earned from ordinary annuity payments of $6,000 per year for 25 years if you can increase your rate of interest from 6% to 9%?

PMT=$6,000 per year; n=25 years; i=6% to 9%

Interest at 6%

FV= PMT [((1+r)^25-1)/0.06]

FV= 6,000[((1+0.06)^25-1)/0.06]

=$329,187.07

Interest at 9%

FV=6,000[(91+0.09)25-1)/0.09]

= $508,205.38

More earned interest 9%- 6% = $508,209.38 - $329,187.07 = $179,018.31

sapphiresnake702

The financial pages of the local newspaper helped Mary in identifying that she can buy a bond ($1,000 par) for $800. If the coupon rate is 10 percent, the annual interest payments equal $80

a true

b false

Assuming everything else equal, one of the concepts to consider to make sound financial decisions is that _____.

a the riskier assets always have lower market value

b the riskier assets are more valuable than (preferred to) less risky assets

c the sooner cash is received, the more valuable it is

d investors always achieve higher returns from less risky assets

Dwayne invests $4,700 in a savings account at the beginning of each of the next twelve years. If his opportunity cost rate is 7 percent compounded annually, how much will his investment be worth after the last annuity payment is made?

a $89,817.00

b $95,157.85

c $91,250.52

d $87,542.29

When the payment for an annuity is made at the end of each period, such an annuity is referred to as a(n) _____.

a ordinary annuity

b deferred annuity

c discounted annuity

d annuity due

The balance sheet is a financial statement measuring the flow of funds into and out of various accounts over time while the income statement measures the progress of the firm at a point in time.

true

false

Which of the following mathematical expressions computes earnings per share?

a Earnings per share = Net Income Ã· Number of outstanding shares of common stock

b Earnings per share = (Net Income + Dividend Paid) Ã· Number of outstanding shares of common stock

c Earnings per share = Net Income Ã Number of outstanding shares of common stock

Primary markets are markets _____.

a where loans are traded

b where financial assets that have previously been issued by various organizations are traded among investors

c in which various organizations raise funds by issuing new securities

d where the instruments traded have original maturities equal to one year or less

peachsardine11

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 010 Lecture Notes - Lecture 5: Santa Barbara City College, Cash Flow

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