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33:390:310 Lecture 6: Chapter 6 Multiple Cash Flows 9-19 Class notes

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rubysalmon273
29 Sep 2017
School
Rutgers University
Department
Finance
Course
33:390:310
Professor
Hoffman

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Document Summary

You think you will be able to deposit ,000 at the end of each of the next 3 years in a bank account paying 8% interest. Annuity: finite series of equal payments that occur at regular intervals. If the first payment occurs at the end of the period, its called an ordinary annuity. If the first payment occurs at the beginning of the period its called an annuity due: formula: c= [1-[1/(1+r)^t]] / r. Rule of 72: approximation of how long it will take our investment to double. A bond differs from a stock because a bond you give the money and get interest.

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Related Questions

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 ________.

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

zero
one
one hundred
none of the above

Question 2 5 pts

On a timeline, the space between date 0 and date 1 represents the _______ between dates. Let’s 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.

On a timeline, the space between date 0 and date 1 represents the _______ between dates. Let’s 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.

dollar amount
present value
time period
future value

Question 3 5 pts

As the interest rate __________, present value decreases.

As the interest rate __________, present value decreases.

decreases
increases
remains unchanged
is unrelated

Question 4 5 pts

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

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 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) __________.

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 6 5 pts

Edit this Question Delete this Question

0 multiple_choice_question 22047052

There are two basic types of annuities:

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.

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

consistent
dollar
annual
semi-annual

Question 8 5 pts

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

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

zero
one
100
none of the above

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 year’s 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; =

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 year’s 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 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.

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

1.

You have $49,061.69 in a brokerage account, and you plan todeposit an additional $5,000 at the end of every future year untilyour account totals $200,000. You expect to earn 9.1% annually onthe account. How many years will it take to reach your goal? Roundyour answer to the nearest whole number.

2.

Present and Future Value of an Uneven Cash Flow Stream

An investment will pay $100 at the end of each of the next 3years, $300 at the end of Year 4, $600 at the end of Year 5, and$800 at the end of Year 6. If other investments of equal risk earn11% annually, what is its present value? Round your answer to thenearest cent.
$

What is its future value? Round your answer to the nearestcent.
$

3.

You want to buy a car, and a local bank will lend you $20,000.The loan would be fully amortized over 3 years (36 months), and thenominal interest rate would be 12%, with interest paid monthly.What is the monthly loan payment? Round your answer to the nearestcent.
$

What is the loan's EFF%? Round your answer to two decimalplaces.
%

4.

  1. Find the present values of the following cash flow streams. Theappropriate interest rate is 5%. Round your answers to the nearestcent. (Hint: It is fairly easy to work this problemdealing with the individual cash flows. However, if you have afinancial calculator, read the section of the manual that describeshow to enter cash flows such as the ones in this problem. This willtake a little time, but the investment will pay huge dividendsthroughout the course. Note that, when working with thecalculator's cash flow register, you must enter CF0 = 0.Note also that it is quite easy to work the problem with Excel,using procedures described in the Chapter 4 Tool Kit.)
    Year Cash Stream A Cash Stream B
    1 $100 $300
    2 400 400
    3 400 400
    4 400 400
    5 300 100

    Stream A $
    Stream B $
  2. What is the value of each cash flow stream at a 0% interestrate? Round your answers to the nearest cent.
    Stream A $
    Stream B $

5.

Find the future values of the following ordinary annuities:

  1. FV of $200 paid each 6 months for 4 years at a nominal rate of12%, compounded semiannually. Round your answer to the nearestcent.
    $
  2. FV of $100 paid each 3 months for 4 years at a nominal rate of12%, compounded quarterly. Round your answer to the nearestcent.
    $
  3. The annuities described in parts a and b have the same amountof money paid into them during the 4-year period and both earninterest at the same nominal rate, yet the annuity in part b earnsmore than the one in part a over the 4 years. Why does thisoccur?
    -Select-The nominal deposits into the annuity in part (b) aregreater than the nominal deposits into the annuity in part (a). Theannuity in part (a) is compounded less frequently; therefore, moreinterest is earned on interest. The annuity in part (a) iscompounded more frequently; therefore, more interest is earned oninterest. The annuity in part (b) is compounded less frequently;therefore, more interest is earned on interest. The annuity in part(b) is compounded more frequently; therefore, more interest isearned on interest.

6.

To complete your last year in business school and then gothrough law school, you will need $25,000 per year for 4 years,starting next year (that is, you will need to withdraw the first$25,000 one year from today). Your uncle offers to put you throughschool, and he will deposit in a bank paying 9.57% interest a sumof money that is sufficient to provide the 4 payments of $25,000each. His deposit will be made today.

  1. How large must the deposit be? Round your answer to the nearestcent.
    $
  2. How much will be in the account immediately after you make thefirst withdrawal? Round your answer to the nearest cent.
    $

    How much will be in the account immediately after you make the lastwithdrawal? Round your answer to the nearest cent. Enter "0" ifrequired
    $

7.

You need to accumulate $10,000. To do so, you plan to makedeposits of $1,450 per year - with the first payment being made ayear from today - into a bank account that pays 10.24% annualinterest. Your last deposit will be less than $1,450 if less isneeded to round out to $10,000. How many years will it take you toreach your $10,000 goal? Round your answer up to the nearest wholenumber.
year(s)

How large will the last deposit be? Round your answer to thenearest cent.
$

8.

  1. It is now January 1. You plan to make a total of 5 deposits of$300 each, one every 6 months, with the first payment being madetoday. The bank pays a nominal interest rate of 10% butuses semiannual compounding. You plan to leave the moneyin the bank for 10 years. How much will be in your account after 10years? Round your answer to the nearest cent.
    $
  2. You must make a payment of $1,788.84 in 10 years. To get themoney for this payment, you will make 5 equal deposits, beginningtoday and for the following 4 quarters, in a bank that pays anominal interest rate of 8% with quarterly compounding.How large must each of the 5 payments be? Round your answer to thenearest cent.
    $

Assume that you are nearing graduation and that you have appliedfor a job with a local bank. As part of the bank’s evaluationprocess, you have been asked to take an examination that coversseveral financial analysis techniques. The first section of thetest addresses time value of money analysis. See how you would doby answering the following questions:

a. Drawcash flow time lines for (1) a $100 lump-sum cash flow at the endof Year 2, (2) an ordinary annuity of $100 per year for threeyears, (3) an uneven cash flow stream of $50, $100, $75, and $50 atthe end of Years 0 through 3.

b. (1)What is the future value of an initial $100 after three years if itis invested in an account paying 10%annual interest?

(2) What is the present value of $100 to bereceived in three years if the appropriate interest rate is10%?

c. Wesometimes need to find how long it will take a sum of money (oranything else) to grow to some specified amount. For example, if acompany’s sales are growing at a rate of 20%per year, approximatelyhow long will it take sales to triple?

d. Whatis the difference between an ordinary annuity and an annuity due?What type of annuity is shown in the following cash flow time line?How would you change it to the other type of annuity?

0 1 2 3

100 100 100

e. (1)What is the future value of a 3-year ordinary annuity of $100 ifthe appropriate interest rate is 10%?

(2) What is the present value of the annuity?

(3) What would the future and present values be ifthe annuity were an annuity due?

f. What is the present value of the following uneven cash flow stream?The appropriate interest rate is 10%, compounded annually.

0 1 2 3 4

100 300 300 150

g. Whatannual interest rate will cause $100 to grow to $125.97 in 3years?

h. (1)Will the future value be larger or smaller if we compound aninitial amount more often than annually—for example, every 6months, or semiannually—holding the stated interest rateconstant? Why?

(2) Define the stated, or quoted, or simple, rate,(rSIMPLE), annual percentage rate (APR), the periodicrate (rPER), and the effective annual rate(rEAR).

(3) What is the effective annual rate for a simplerate of 10%, compounded semiannually? Compounded quarterly?Compounded daily?

(4) What is the future value of $100 after threeyears under 10%semiannual compounding? Quarterly compounding?

i. Will the effective annual rate ever be equal to the simple (quoted)rate? Explain.

j. (1) What is the value at the end of Year 3 of thefollowing cash flow stream if the quoted interest rate is 10%,compounded semiannually?

0 1 2 3

100 100 100

(2) What is the PV of the same stream?

(3) Is the stream an annuity?

(4) An important rule is that you should nevershow a simple rate on a time line or use it in calculations unlesswhat condition holds? (Hint: Think of annual compounding,when rSIMPLE = rEAR = rPER.) Whatwould be wrong with your answer to parts (1) and (2) if you usedthe simple rate 10%rather than the periodic raterSIMPLE/2 = 10%/2 = 5%?

k. (1)Construct an amortization schedule for a $1,000 loan that has a10%annual interest rate that is repaid in three equalinstallments.

(2) What is the annual interest expense for theborrower, and the annual interest income for the lender, duringYear 2?

l. Suppose on January 1 you deposit $100 in an account that pays asimple, or quoted, interest rate of 11.33463%, with interest added(compounded) daily. How much will you have in your account onOctober 1, or after 9 months?

m. Now suppose youleave your money in the bank for 21 months. Thus, on January 1 youdeposit $100 in an account that pays a 11.33463%compounded daily.How much will be in your account on October 1 of the followingyear?

n. Suppose someone offered to sell you a note that calls for a $1,000payment 15 months from today. The person offers to sell the notefor $850. You have $850 in a bank time deposit (savings instrument)that pays a 6.76649%simple rate with daily compounding, which is a7%effective annual interest rate; and you plan to leave this moneyin the bank unless you buy the note. The note is not risky—that is,you are sure it will be paid on schedule. Should you buy the note?Check the decision in three ways: (1) by comparing your futurevalue if you buy the note versus leaving your money in the bank,(2) by comparing the PV of the note with your current bankinvestment, and (3) by comparing the rEAR on the notewith that of the bank investment.

o. Suppose the note discussed in part n, above, costs $850, but callsfor five quarterly payments of $190 each, with the first paymentdue in 3 months rather than $1,000 at the end of 15 months. Wouldit be a good investment?