FINM1001 Lecture Notes - Lecture 4: Interest Rate, Cash Flow, Dont

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30 May 2018

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FINM1001 Week 2 Lecture A

● Time Value of Money: Financial Maths

○ Future value -> is the value of a cash flow at some point in the future

○ Present Value -> value of a future cash flow in today’s dollars

○ Two types of interest:

■ Simple: Constant interest

■ Compound: Interest on top of interest

○ Single cash flows:

■ Present value: FV/(1+r)^n

■ Future value: f(1+r)^n

○ Multiple cash flows:

■ Future value of cash flows of different values or are not evenly

spaced in time, we consider each cash flow separately, and sun

● Annuity

○ The cash flow are all the same value

○ Cash flows are evenly spaced

○ Ordinary Annuity e.g. mortgage or some type of loan first payment doesn’t

occur until the first period

○ Annuities due e.g. rent make a payment at period 0

○ Deferred Annuity e.g. buy now pay later payments don’t start until

sometime in the future

○ Future value of ordinary annuities: FV = F[(1(r+1)n-1)/r]

● Present value of multiple cash flows

○ Formula used to calculate the present value of an annuity differs based on

the type of annuity being considered

○ Ordinary annuity: PV = F(1-(1+R)-n/R) = FA

○ Annuity Due: PV = F + F/(1+R) + F/(1+r)2 +....+ F/(1+r)n-1 = F + F(1-(1+r)-(n-

1)/r) = F + FAn-1

○ Deferred Annuity: PV= F[1-(1+R)-n/R] / (1+r)n-1

● Infinite cash flows

○ Evenly spaced

○ Same value of cash flows

○ Cash flows go forever -> perpetuities

○ Since PV = F(1-(1-r)-n/r) and let n approach infinity since a business can

stand infinitely thus Pv = F/r

● Perpetuities

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Document Summary

Future value -> is the value of a cash flow at some point in the future. Present value -> value of a future cash flow in today"s dollars. Future value of cash flows of different values or are not evenly spaced in time, we consider each cash flow separately, and sun. The cash flow are all the same value. Ordinary annuity e. g. mortgage or some type of loan first payment doesn"t occur until the first period. Annuities due e. g. rent make a payment at period 0. Deferred annuity e. g. buy now pay later payments don"t start until sometime in the future. Future value of ordinary annuities: fv = f[(1(r+1)n-1)/r] Formula used to calculate the present value of an annuity differs based on the type of annuity being considered. Ordinary annuity: pv = f(1-(1+r)-n/r) = fa. Annuity due: pv = f + f/(1+r) + f/(1+r)2 ++ f/(1+r)n-1 = f + f(1-(1+r)-(n-

Related Questions

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.

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

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FINM1001 Lecture Notes - Lecture 4: Interest Rate, Cash Flow, Dont

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