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SMG FE 101 Lecture Notes - Lecture 4: Forklift

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greyox571
25 Feb 2016
School
Boston University
Department
Finance
Course
SMG FE 101
Professor
Fox

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Document Summary

A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever. An annuity is a stream of n equal cash flows paid at regular intervals. The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments. Ellen is 35 years old, saves 10,000 every year till 65. A growing annuity is a stream of n growing cash flows, paid at regular intervals. It is a growing perpetuity that eventually comes to an end. Solving for variables other than pv or fv. The rate of return is the rate at which the present value of the benefits exactly offsets the cost. Suppose you have an investment opportunity that requires a investment today and will pay in six years. Suppose your firm needs to purchase a new forklift. A price for the forklift if you pay cash (,000)

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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 – 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

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

Que: - (1)

Which one of the following statements is true about an amortized loan?

A.

With an amortized loan, a smaller proportion of each month’s payment goes toward interest in the early periods.

B.

With an amortized loan, a bigger proportion of each month’s payment goes toward interest in the later periods.

C.

With an amortized loan, a bigger proportion of each month’s payment goes toward interest in the early periods.

D.

With an amortized loan, the proportion of the loan that goes toward interest does not change at any point.

(2) Your investment in a small business venture will produce cash flows that increase by 15 percent every year for the next 25 years. This cash flow stream is called:

A.

an annuity due.

B.

a growing perpetuity.

C.

an ordinary annuity.

D.

a growing annuity.

(3)

If your investment pays the same amount at the end of each year forever, the cash flow stream is called:

A.

an ordinary annuity.

B.

a perpetuity.

C.

an annuity due.

D.

none of the above.

(4)

Use the following table to calculate the expected return for the asset.

Return

Probability

0.10

0.30

0.20

0.50

0.25

0.25

A.

15.0%

B.

17.5%

C.

18.75%

D.

19.25%

(5)

George purchased a stock for $45 one year ago. The stock is now worth $65. During the year, the stock paid a dividend of $2.50. What is the total return to George from owning the stock? (Round your answer to the nearest whole percent.)

A.

5%

B.

44%

C.

35%

D.

50%

(6)

Barbara purchased a piece of real estate last year for $85,000. The real estate is now worth $102,000. If Barbara needs to have a total return of 25 percent during the year, then what is the dollar amount of income that she needed to have to reach her objective?

A.

$3,750

B.

$4,250

C.

$4,750

D.

$5,250

(7)

The risk-free rate of return is currently 3 percent, whereas the market risk premium is 6 percent. If the beta of Lenz, Inc., stock is 1.8, then what is the expected return on Lenz?

A.

8.40%

B.

10.80%

C.

13.80%

D.

19.20%