A house is rented at $20,000 annually, paid at the start
of the year. The rent increases at 3% pa effective, and
interest rates are 4% pa effective. Calculate the present
value of the next 20 years rent.
Q3 2009 Final
On March 1, 2012 you buy $30,000 with
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer & Mathematical Sciences
December 2013 Final Examination
ACTB40 H3F
Fundamentals of Investment & Credit
Duration: 3 hours
Examination aids allowed: Non-programmable scientific calculator, formula
she
ACTB40
Fundamentals of
Investment & Credit
Lecture 9
1
Dividend Discount Model for
Stock Valuation
Consider buying stock of a company at an IPO.
You pay price which goes to the company, and
in exchange you get a stream of periodic
dividend payments.
Assum
ACTB40
Fundamentals of
Investment & Credit
Lecture 7
1
Annuity Due
Another standard form of annuity is one
where payments occur at the beginning of
each period. This is called an annuity-due:
1
1
1
1
1
1
1
0
1
2
n1
1
Annuity-Immediate
Annuity-Due
n
time
2
ACTB40
Fundamentals of
Investment & Credit
Lecture 4
1
Nominal Rates
In practice, many interest rates are quoted in
a format different than compound rates
E.g. Credit cards typically quote their APR (Annual
Percentage Rate) or Annual Interest Rate , which
ACTB40
Fundamentals of
Investment & Credit
Lecture 5
1
Inflation Rate
General increase in price of products &
services measured by annual inflation rate (r)
Calculated as annual rate of change of Consumer
Price Index (CPI), a specific collection of
consum
ACTB40
Fundamentals of
Investment & Credit
Lecture 6
1
Annuity Decomposition
We can break down annuity into 2 or more
smaller components (annuities) and combine
them to get an equivalent accumulation
Ann. A:
Ann. B:
1
1
1
A=B + C
1
n1
1
1
1
1
1
Ann. C:
0
ACTB40
Fundamentals of
Investment & Credit
Lecture 3
1
Dated Cash Flows
Many financial investments/transactions
involve cash-flows (CF) at different times
E.g. (Simple pension) Pay $5 now & $10 in 1 year
and in return receive $X in 5 years
Out-flows ():
5
ACTB40
Fundamentals of
Investment & Credit
Lecture 2
1
Accumulated Amount Function
Simple Interest: A(t ) A(0) (1 i t )
Compound Interest: A(t ) A(0) (1 i )t
Time t measured in multiples of interest period
E.g. 1 year w/ annual rate i t = 1
1 year w/ mont
ACTB40
Fundamentals of
Investment & Credit
Lecture 1
1
Administrivia
Instructor: Sotirios Damouras
Contact Info:
Pronounced So-tee-ree-os or Sam
email: sdamouras@utsc.utoronto.ca
Office hours: IC456 every MO & WE 11am-1pm,
or by appointment (email)
Course
1. You joyfully burn your mortgage documents just after making the last (end-of) monthly
payment, the 300th. The interest rate had been fixed for the whole 25 year period. That last
payment consisted of $2,000 of principal and $20 of interest. Calculate t
1. (Assignment Sept 21, 2009;) Mike receives cash flows of 100 today, 200 in one year, and 100
in two years. The present value of these cash flows is 383.48 at an annual effective rate of interest
i.
Calculate i.
(A) Less than 0.03000
(B) 0.03000 but less
Mathematics of Investment and Credit 5-th Ed
Errata List, by S. Broverman Updated September 23, 2011
Table of Contents, page vii, bottom line should be 1.10 Exercises 52
Page 146, Exercise 2.1.15 should read
, find the present value on June 1, 2007 of al
ACTB40: Fundamentals of Investment & Credit
Assignment 11
1.
2.
3.
4.
5.
Exercise 5.1.2 on p. 291
Exercise 5.1.4 on p. 291
Exercise 5.1.5 on p. 292
Exercise 5.1.7 on p. 293
Exercise 5.1.8 on p. 294
ACTB40: Fundamentals of Investment & Credit
Assignment 10
1.
2.
3.
4.
5.
6.
7.
Exercise 4.3.1 on p. 260
Exercise 4.3.2 on p. 260
Exercise 4.3.3 on p. 260
Exercise 4.3.4 on p. 260
Exercise 5.1.1 on p. 291
Exercise 5.1.3 on p. 291
Exercise 5.1.4 on p. 291;
ACTB40
Fundamentals of
Investment & Credit
Lecture 8
1
Perpetuity Due
A perpetuity-due is an infinite stream of
payments at the beginning of each period
1
1
Perpetuity-Immediate
1
1
1
Perpetuity-Due
0
1
2
Imm
Due
PV: a i
1
1
1 v v
1 v d
1 1
(1 i )a i (
ACTB40
Fundamentals of
Investment & Credit
Lecture 13
1
Bonds
Bond is interest-bearing certificate of public
(governments) or private (corporate) debt
Governments / corporations issue & sell bonds to
collect capital for their investments or expenses
Bonds
ACTB40
Fundamentals of
Investment & Credit
Lecture 22
1
Fixed-Income Prices
Consider fixed-income security: investment
whose future cashflows (time & amounts) are
known in advance; e.g. bonds
Given current term structure, can find current
fair price (i.e.
ACTB40
Fundamentals of
Investment & Credit
Lecture 23
1
Duration & Term Structure
D/DM measures price sensitivity w.r.t. YTM
In general, however, fixed-income prices
depend on every spot rate until their maturity
So prices change w.r.t. every spot rate ch
ACTB40
Fundamentals of
Investment & Credit
Lecture 20
1
Example
Assume term structure (normal):
Maturity
1yr
1 yr
2yr
Spot Rate
yr
8%
9%
10%
11%
Find prices of 2-yr bonds with coupon rates of 5%
& 10% (all rates nominal, comp. semi-annually)
2
Example
As
ACTB40
Fundamentals of
Investment & Credit
Lecture 21
1
Arbitrage
Arbitrage is a transaction that has only
positive cashflows (requires no money)
E.g.
0
1
2
3
Arbitrage
cashflows:
0
0
+C
+C
0
0
0
+C
0
0
+C
0
OR
OR
(C>0)
Arbitrage are the equivalent of a f
ACTB40
Fundamentals of
Investment & Credit
Lecture 18
1
Internal Rate of Return
For the 3 examples without a unique,
valid IRR, we had: C 1.33 (A)
2
C0 1, C1 2.3, & C2 1.32 (B)
C 1.2825 (C)
2
Even though we cannot compare IRRs, one
of these transactions
ACTB40
Fundamentals of
Investment & Credit
Lecture 19
1
Term Structure of Interest
Rates
Cashflows:
(P)
F
Consider ZCB w/ maturity t,
time 0
t
face value F, and price P:
ZCB yield at maturity t is called the spot rate
of interest for t, and is denoted by
ACTB40
Fundamentals of
Investment & Credit
Lecture 17
1
Comparing Investments
Consider an investment, represented by a
stream of (+ve or ve) cashflows C0,C1,Cn
C0
C1
C2
Cn1
Cn
0
Cashflow:
1
2
n1
n
time
Investment appraisal (Capital Budgeting) :
process of
ACTB40
Fundamentals of
Investment & Credit
Lecture 16
1
Callable Bond
Issuer can redeem bond (pay back face value
& stop coupons) at anyone of a range of predetermined dates
Choice of redemption date is up to the issuer
Buyer of callable bond is at a disa
ACTB40
Fundamentals of
Investment & Credit
Lecture 16
1
Callable Bond
Issuer can redeem bond (pay back face value
& stop coupons) at anyone of a range of predetermined dates
Choice of redemption date is up to the issuer
Buyer of callable bond is at a disa
ACTB40
Fundamentals of
Investment & Credit
Lecture 15
1
Amortization of Bonds
For taxation & other accounting purposes, it
is necessary to determine the amount of
interest received and principal returned in
bond coupons / redemption payment
E.g. When buyi
ACTB40
Fundamentals of
Investment & Credit
Lecture 14
1
Bonds
Bond: Debt certificates paying principal
amount at some future date (maturity), and
periodic payments (coupons)
F : face value (aka par value) of bond
n : number of coupon periods until maturit
ACTB40
Fundamentals of
Investment & Credit
Lecture 12
1
Prospective Form of
Outstanding Balance
(L)
Kt
Kt+1
Kt+2
Kn1
Kn
0
1
t
t+1
t+2
n1
n
vKt+1
v2Kt+2
vn1tKn1
vntKn
K1
Kt+1
time
Kt+2
Kn1
Kn
Outstanding Balance at time t = present
value at time t of futu
ACTB40
Fundamentals of
Investment & Credit
Lecture 11
1
Midterm 1 Marks
0.25
0.15
0.1
0.05
Marks (/50)
50
45
40
35
30
25
20
15
10
0
5
Frequency
0.2
2
Amortization of Loan with
Level Payments
Consider loan with level periodic payments of
K throughout and l