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ADM 2350 Lecture Notes - Lecture 3: Microsoft Powerpoint, 2016 Nfl Season

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roseskunk973
30 Jan 2017
School
University of Ottawa
Department
Administration
Course
ADM 2350
Professor
Anna Dodonova

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Document Summary

As we continue to talk about the time value of money we continue doing examples of problems in class. Now you should start reading ch 4 power point slides (posted on blackboard) From last week we need to remember formula. Example 1: you invested at an annual interest rate of x% and in 5 years you find that you have accumulated . Interest is annual, period of investment is five years, so, in five years you will get (1+x)5= in five. To solve this equation note that (1+x)5=4. 5 or (1+x) = Assume that the investment period was n months then: Assume that the investment period was n months then and interest rate per month is. And we can write (1+0. 001)n= or (1+x)n= 2. Taking ln of both sides of it we"ll get ln ((1+x)n)= ln(2) or n ln (1+0. 001)= ln(2) and, finally, n= Solution: let"s compare pvtoday of options (i) and (ii)

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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

Are my answers correct?

Suppose you invest $10,000 in a savings account earning 2% interest (compounded yearly) with no risk. After 7 years, how much will you have?

Principal = $10,000.00

Rate = 2.00%

Year = 7

Amount (Compound interest) = P x (1 + r/n) ^nt

Where P = Principal

r rate of interest

n = number of time interest is calculated in a year

t = time

Amount after 7 years = 10,000 x (1+0.02) ^7 = $11,486.86

Repeat Question #1, but this time there is an inflation rate of 4%. How does this change your overall return on investment? If you had a chance to invest in an account with a long-term expected rate of 5%, with a 50% chance of earning 0% nominal compound interest and a 50% chance of earning 10% nominal compound interest in each year, would you choose this account, or the savings account? Why?

Effects of inflation on PV = 10,000 x (1/(1+0.04)^7) = $7,599.18

FV Adjusted for inflation = 11,486.86 x (1/(1+0.04)^7) = $ 8,729.07

Overall return on investment will decrease by 1,270.93 = 10,000 – 8,729.07

Repeat #1 with inflation:

Amount after 7 years = 10,000 x ((1+0.02)/(1+0.04)) ^7

10,000 x (0.98) ^7 = $8,729.07.

Safe vs. Risky (not including inflation)

If I get 0%, the amount after 7 years = 10,000 x (1+0.00) ^7 = $10,000.00

If I get 10%, the amount after 7 years = 10,000 x (1+0.10) ^7 = $19,487.17

If I get 5% (expected), amount after 7 years = 10,000 x (1+0.05) ^7 = $14,071.00

I would choose the account with the 5% expected rate of return because it has higher effective annual return over the saving account. There is a higher return, but the risk is higher as compared to the savings account, which provides a certain return.

Suppose you will need $50,000 in 4 years to start up a new business you have planned. With a 5% real interest rate, how much do you have to invest now in order to achieve this goal?

This condition clearly says that we need to calculate the present value of the future earnings and it has to be the present value factor and not annuity.

Therefore, to get 50000 is the future value therefore present value of 50000

Amount to be invested today =PVF@5%,4 *Amount

= .82270 * 50000

= $ 41135.12

Repeat Problem #3, but assume you can contribute an equal amount on a yearly basis. How much would you need to put into the account each year?

Amount to invested each year = Amount /FVAF@5%,4 = 11,600.66

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?