109 110 CHAPTER 9. AMORTIZATION 9.3 I) Amortization Table Let us
begin with an example English You can pay back a loan of 10000 at 5
percent by paying 2820.12 at the end of each year for 4 years Formula
Ra4 0.05 = 10000 = R = 2820.12 Calculator: 4 5 10000
to CFo. 42 CHAPTER 3. IRR - INTERNAL RATE OF RETURN +1000, ENTER
Scroll to C01, -600, ENTER Scroll to F01, 1, ENTER F01 indicates
frequency. It will be 1 for now (Discuss later) e Scroll to c02, -550,
ENTER, F02,1, ENTER IRR CPT - Shows yield is 10% 3.12
need to buy milk at t = 1; it costs 1 at t = 0; inflation is 50% g = 0.50. i =
0.75. Compute 1+g 1+i = 1.50 1.75 = 0.857 Now solve 1 1+i 0 = 0.857
(Hint: Use 1 x key.) Obtain 1 + i 0 = 1.16666 = i 0 = 0.16666 7.10
Example Continued Original Timeline P V i
goals VIII, IX 10.2 I) Problem Solving Approach #1) a) Read problem
and identify the b) variables and the c) cells, that is the column and row
#2) Fill in cells you can see #3) Do not jump to abstraction; First do
3-4 examples. Examples are important #4)
. . n + n n 1 n 2 . . . 1 = 0 n + 1 n + 1 n + 1 . . . n + 1 (Da)n + (Ia)n = (n
+ 1)an Why? But we have formulae for (n + 1)an and (Da)n So we
can compute formula for (Ia)n (Ia)n = an nvn i (6.3) 6.25 Other
Formulae For the due version replace i in denomin
Overview We have 8 sub-goals to meet in this chapter I) Review of
Chapter 1 - single investments under compound interest II) Portfolios Multiple investments - Equation of Value - Equivalence Principle III)
IRR: Internal Rate of Return, calculator workshee
inflation increases geometrically You can recognize an Increasing
annuity because the amount increases Contrastively, inflation has an
increasing percent 7.14 VI) Model Example Q-IT#14 N01#5 is
illustrative We approach this problem with the Example method
annual effective interest rate of i, the present value of Annuity 2 is twice
the present value of Annuity 1 . Calculate the value of Annuity 1.
Timeline #1 X = (Da) 10 . . . 10 9 8 . . . 0 1 2 3 . . . For timeline #2 we
have two reasonable ways to break
the stream of payments P, P, P, P This stream of level payments, P, is
fictitious, it does not correspond to anything in the real world 3)
Compute the stream of P at rate i 0 as an annuity due Either Pan :i 0
or Pa :i 0 4) Then use a deferral factor v m i
example is approached using i) formalism (algebra), ii) graphs, iii)
numerics iv)verbal 32 CHAPTER 2. MONEY GROWTH 2.29 Rule of 4 in
Theory of Interest In interest theory, we will use algebraic formulas for
formalism (Functions are used in calculus) In in
k AX(5) 0 n Y A(0) = 1 d (2) = 0.08 AY (5) 0 n AX(5) = AY (5). 2.35
M01#45 - Equations Y How do I get an equation for Y? Answer:
Every topic has key formulae Use (?). AY (5) = 1 d (2)=.08 2 25
2.36 M01#45 - Equations X How do I get an equation for X? Answ
see the pattern? It = 6% 5000 = 300 for t = 0 through 9 OLBt =
5000 for t = 0 through 9 126 CHAPTER 10. AMORTIZATION PROBLEMS
Table 10.5: QIT#26 - Janices Approach P ERSON t R I P OLB Janice 0 0 0
0 5000 Janice 1 300 300 0 5000 Janice 2 300 300 0 5000 Jan
What is the present value of milk/oj/beer at t = 1 7.4 Solution to
Interest/Inflation Timeline 1 .50 inflation 1.50 P V .75 interest 1.50 P V
= 1.50 1.75 = .857 0 1 7.5 Formula for PV of Inflation Makes Sense
Suppose I have .857 at t = 0. Then at t = 1,
the first year of inflation (7.2) Compute PV as you ordinarily would with
an annuity due The deferral factor would be v m i where (m, m + 1) is
the first year of inflation The deferral factor uses i not i 0 (7.3) This
method avoids the need for Geometric
unique to interest theory Verbal-Algebraic Dictionary The idea of
verbal is that each English phrase has a specific algebraic correlate We
will indicate these correlates with parenthesis using equal signs How
much (= A(t) is an initial 1000 deposit (= A(0
= F r = Cg Prospective Formulaii) OLBt = F rant i + Cvnt = C + C(g
i)ant i iii) Retrospective formula complicated because of coupons and
is therefore omitted iv) Pt = C(g i)v n+1t v) The formula for It is
derived from the formula for Pt (just given) and
is nvn , part of the Increasing annuity formula Calculator: n 100i CPT
1 n N I/Y PV PMT FV WARNING: Only use -1 for payments. Do not
use -2 or -3 (Multiply afterwards). Why? Display window now gives
you an nvn , #4: RCL i = #5: 100 = Chapter 7 Inflation
problem - a) loan with pay back or b) buy bond and get redemption
But then reinvest say coupons in a different bank, different rates A
typical problem may have 2-3 banks (2-3 investment rates) You may
be asked to find overall yield 12.3 II) Solution meth
10 Fourth: Use deferral factor v 5 where (5,6) is first year of inflation.
Year 5 10 10 10 . . . 5 6 7 . . . We next compute present value of
this equivalent timeline using the rule of 3. 7.21. APPLICATION OF RULE
OF 3 93 7.21 Application of Rule of 3 An
. F r 0 1 2 . . . n To apply the TV line we need to use all 5 calculator
keys since there is a balloon payment Remember the rule: balloon
payment goes to FV while periodic payment goes to PMT Calculator
TV Line: n 100i P F r C N I/Y PV PMT FV 132 CHAPTER
Same argument (write it out!) gives OLB2 = 95%2L And then the
same argument gives OLB3 = 95%3L 10.8 Recognize Pattern Do you
see the pattern? We can infer OLB10 = 95%10L If you didnt see
pattern you would have to do all 10 rows You could still solve the
p
bond pays 8% coupons seminannually. The bond is priced at 118.20 to
yield an annual nominal rate of 6% convertible semiannually. Calculate
the redemption value of the bond. In performing the solution we use
four steps . . . 11.11 Four steps of the problem
present two solutions, both based on the 8 Bond Formulae In this
slide we present the 1st solution Want interest portion in 7th
payment How do you compute this? How do you approach this? You
must review the 8 formulae Which of 8 formula talks about It Aha
Approach A: (Ia) 10 + v 1011a = 2(Da)10 Which approach right?
Both! Use the approach where the algebra simplifies! For a HW
exercise: Repeat the above set up of 2 approaches using timelines
Give two more approaches using Increasing Annuity Due Try solvin
bank gives me (n 1)i because of n 1 left at time t = 1. Timeline
i(Da)n ni (n 1)i (n 2)i . . . i 0 1 2 3 . . . n 1 So bank spends i(Da)n
6.21 Formulae: Decreasing Annuity Equivalence principle: My total
payments = Banks total payments. i(Da)n = n an (6.1)
coupons, monetary payments, periodically That way you dont have to
wait to maturity to profit The coupon amount equals F r where F is
the face amount of the bond and r is the coupon rate The sole/only
purpose of F and r is to obtain the coupon amount (Spo
subgoal of total payments We now do QIT#26 Please read it This
problem naturally breaks itself up into 3 subproblems We will name
the 3 subproblems by the people involved 10.11 Lori Lori repays her
loan with 10 level payments at the end of every sixmonth
800 158.42 = 641.58 Note that F r = Cg r = g This is true in
general whenever C = F 140 CHAPTER 11. BONDS Chapter 12
Reinvestment 12.1 Overview We have one main goal for today:
Reinvestment problems Although the SOA has eliminated
Replacement of Capital f