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
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
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
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
. 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
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
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
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
Timelines, ii) Calculator TV Timelines and iii) formulae (of actuarial
equivalence) #3) You may have to convert the problem to an
algebraically simpler form. Conversions are a very important step in
solving complex problems #4) Typically there is a link b
constant means the same amount each year. English constant annual
effective interest rate i same each year payment period=1 year
compound not discount rate 3.3 Solution to Typical Problem Rule of 6
states that we should approach the problem solution in mu
some problems you must combine nominal-effective methods to get j
8.5 3 Basic Principles of Conversion Principle #1: Never use i (m) .
Always immediately replace i (m) with j = i (m) m j is interpreted as
the interest rate per m-th of a year Principle #2
end of every year I pay the lender iL L Notice that there are two
interest rates, iL and iSF Also notice that there are two payees: The
lender and the bank into which I sink money We use the same
example to illustrate Sinking fund as we did to illustrate
the end of 10 years, immediately after Bill receives the final coupon
payment and the redemption value of the bond, Bill has earned an
annual effective yield of 7% on his investment in the bond. Calculate i
12.5. SOLUTION - COUNT BANKS / INTEREST RATES 14
performance We use the letter C to denote either Deposits or
Withdrawals Here, C stands for Cash Flow, D stands for Deposits, and
W stands for Withdrawals Deposit Dk at time tk Ck = +Dk
Withdraw Wj at time tj Cj = Wj 3.5 EOV - Equation of Value An
import
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
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
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
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
. . 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
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)
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
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