ADMS 3530 Lecture 3: Week 3 - Lecture 3 (TVM) Supplementary Notes

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fuchsiaeel885

19 Oct 2015

School

York University

Department

Administrative Studies

Course

ADMS 3530

Professor

Samuel Benchimol

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Document Summary

Annuities: ordinary (regular) annuity cash flows start at end of first time period, annuity due cash flows start immediately. You can either use your calculator so solve annuity due problems by using the bgn button (see your manual) or you can remember this relationship. Pmtannuity due = pmtannuity / (1+r) when dealing with pv. Pmtannuity due = pmtannuity x (1+r) when dealing with fv. Example 1: a perpetuity of per year beginning at the end of year 1 is said to offer a 15% annual rate. Pv perpetuity = c / r = 5000 / . 15 = ,333,33. A perpetuity of per year beginning today is said to offer a 15% annual rate. Pv perpetuity due = c + c / r. There is an easy way to solve problems that involve cash flows which are not the same amount but which grow at a constant rate.

Related Questions

4.3	Need help with 4.4 a and b at bottom. 4.3 is required to answerthis. Calculate the following values, assuming a discount rate of8%:
	a.	present value of a perpetuity (also called a perpetual annuity)of $50 received each year at the end of each year
	b.	present value of an annuity of $50 received at the end of eachyear for 5 years
	c.	present value of an annuity of $50 received at the end of eachyear for 10 years, with the first payment to be received at the endof the 6^th year
	d.	present value of a perpetuity of $50, with the first paymentreceived at the end of the 16^th year. *ANSWER:* a. PV of perpetuity = A/i where A is annual payment &i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 504.3295 = $216.48 c. This has 2 parts. First Find the PV of Annuity at 6 yrs &then find the PV of that amount at T0. Here it is PV of annuity for n=10 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,10). From PV of annuity Table, we get (PVIFA8%,5) = 6.7101 So PVA = 506.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^6 = $211.43 d. This has 2 parts. First Find the PV of Perpetuity at 16 yrs& then find the PV of that amount at T0. PV of Perpetuity = A/i = 50/8% = $625 Now PV of this amount PV = 625/(1+8%)^16 = $182.43
4.4	a.	Show (with a time line, for example) that the perpetuity in4.3a. is exactly the same as the sum of the annuities andperpetuities in 4.3b. to 4.3d.
	b.	Show that their present values add up to the same amount.

violetpig294

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

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

ADMS 3530 Lecture 3: Week 3 - Lecture 3 (TVM) Supplementary Notes

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