FINA 2201 Lecture Notes - Lecture 5: Cash Flow, Compound Interest, Interest Rate

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orchidscorpion269

25 Feb 2016

School

Northeastern University

Department

Finance & Insurance

Course

FINA 2201

Professor

georgegray

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Document Summary

The first step in time value analysis is to set up a time line to help visualize what is happening in a particular problem. The process of going to future value (fv) from present value (pv) is called compounding. Pv = present value, or beginning amount. Fvn = future value, or ending amount of your account after n periods. After interest earned has been added to the account. Cft = cash flows: can be positive or negative, cf0 = pv = the cash flow at time 0, cf3 (for example) = the cash flow at the end of period 3. I = interest rate earned per year: usually expressed in decimals. Int = dollars of interest earned during year = beginning amount x interest. N = number of periods involved in the analysis. 4 methods to solve time value problems: step-by-step approach, formula approach.

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 ________.

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

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

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

salmonhound248

FINA 2201 Lecture Notes - Lecture 5: Cash Flow, Compound Interest, Interest Rate

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