School

York UniversityDepartment

Administrative StudiesCourse Code

ADMS 3530Professor

AlagurajahStudy Guide

FinalThis

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ADMS 3530 Final Exam Tutorial â€“ Notes & Practice Problems (Example)

TVM- Ch.5

PV & FV: SINGLE CASH FLOWS

Future Value: FV = PV Ã— (1 + r)n

Present Value: PV = Future Value

(1 + r)n

PV & FV: MULTIPLE CASH FLOWS

Example 1: Multiple Cash Flows

In two years from today, the following cash flows will have a future value

of $3032.32: $200 today, $Y at the end of one year, and $2,400 at the end of two

years. The annual interest rate is 4%. What is Y?

A) $330.00

B) $400.00

C) $416.00

D) $432.64

E) $167.55

PERPETUITIES & ANNUITIES

â€¢ Ordinary (regular) Annuity & Ordinary Perpetuity â€“ Cash flows start at end of first

time period

â€¢ Perpetuity Due & Annuity Due â€“ Cash Flows start immediately

PV Perpetuity (ordinary) = C

r

PV Perpetuity due = PV Ordinary Perpetuity x (1 +r)

Basic Annuity Formulas:

PVannuity = PVA = C x PVAF (note: C = PMT)

FV annuity = FVA = C x FVAF (future value annuity factor)

Annuity Due:

PV (Annuity Due) = PV(Simple Annuity) Ã— (1+r)

FV (Annuity Due) = FV (Simple Annuity) Ã— (1+r)

Example 2: Delayed Annuity

What is the present value of a four-year annuity of $100 per year

that begins two years from today if the discount rate is 9 percent?

A) $297.22

B) $323.86

C) $356.85

D) $388.97

E) $451.64

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EFFECTIVE ANNUAL INTEREST RATES (EAR) â€“ see Lecture 3 (TVM) Notes

Two Options:

EAR = Compounded rate

EAR = (1 + im)m -1

APR = Finding nominal rate using simple interest

APR = im x m

Note:

EAR = APR with annual compounding

EAR > APR when interest in calculated more than once/yr

Example 3: EAR

You are expected to pay $1,883.33 per month on a one-year loan with a

principal of $20,000. What is the EAR of this loan?

A) 13.00%

B) 13.80%

C) 23.19%

D) 25.82%

E) 16.55%

Example 4: Mortgages: You want to buy a house that costs $400,000. You make a 20% down

payment and finance the rest with a 25 year mortgage. The mortgage has a five year renewal

term for which the annual mortgage rate is 6.25% compounded semi-annually. What will the

remaining principal of the loan be at the end of the 5-year term?

A) $185,780.

B) $196,670.

C) $245,450.

D) $288,480.

E) $400,000

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BONDS

Terminology

â€¢ Par Value

â€¢ Maturity Date

â€¢ Coupons

â€¢ Discount Rate

Also referred to as market interest rate ,or the current interest rate that the market is

demanding of similar securities Also known as its yield to maturity.

* Do not mix-up COUPON RATE and MARKET INTEREST RATE

â€¢ They are usually different.

â€¢ If they are the same, (i.e. coupon rate = market interest rate), then bond will

sell at par value or $1000)

Valuation of Bonds

Current Price = PV bond payments = PV (Coupons) + PV (Face Value)

3 TYPES OF BOND PROBLEMS:

1. Pricing Problems:

2. Return Problems:

3. Combination Problems

First asked to find a bond price at a point in time and then calculate a return if you hold it to

maturity or another point in time.

Example 5: Bonds

You bought a bond with a 7% annual coupon rate at its par value of $1,000 three years ago.

The bond had an original maturity of 10 years. Today, the yield to maturity of the bond has

increased to 8% annually. The bond pays coupons semi-annually. Assume coupons are not

reinvested.

a) What is the current yield of the bond today?

A) 8.0%

B) 7.39%

C) 7.09%

D) 8.39%

E) 5.54%

5B. A government bond carries a 6% coupon rate, pays semi-annual coupons, and has

a $1,000 face value. If you purchase it today at $1,015 and expect to sell it 4 years from

now at $1,040, what would be your annual rate of return if the coupons are reinvested at

4% APR semi-annually compounded?

A)

3.1654%

B)

6.3309%

C)

6.9579%

D)

27.8314%

E)

16.5464%

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