Investing in Financial Assets
A truck has a useful life of 5 years. Maintenance cost s during
the first year is $1000. Maintenance cost s expected to increase at
a rate of $250 per year over the remaining life. Maintenance
account earns 12% annual interest. How much does the firm have to
deposit in the account now?Step 1Step 2
1
A young engineer deposits an annual bonus into a savings
accounts that pays 7% interest compounded annually. The size of the
bonuses increases by $2500 each year, and the initial bonus amount
was $12,000. Determine how much will be in the account immediately
after the fifth deposit.Linear gradient series future worth factor
(F/G,i,N)
P = A1 (F/A,7%,5) +
G(P/G,7%,5)(F/P,7%,5)12,000(5.7507)+2500(7.6467)(1.4026)
Airplane ticket price will increase 8% in each of the next four
years. The cost at the end of the first year will be $180. How much
should be put away now to cover a students travel home at the end
of each year for the next four years? Use an interest rate of 5%
per year.
Geometric gradient series present worth factor (P/A,g,i,N)
Engineers at Sea World have completed an innovation on an
existing water sports with a modifications costs only $80000 and is
expected to last 6 years with a $13000 salvage value. The
maintenance cost is expected to be high at $17000 the first year,
increasing by 11% per year thereafter. Determine the equivalent
resent worth of the modification and maintenance cost. Use the
interest rate of 5% per year.
Geometric gradient series present worth factor Pg =
(P/A,g,i,N).
Pt = -80000 Pg + 1300(P/F,8%,6)
= - 80000 17000 [1-(1.11/1.08)6]/[0.08-0.11]
+1300(P/F,0.08,6)
= -80000 17,000(5.9559) + 81926 = 173,058
4
Ah Long the loan shark lends money on the following terms. Yo,
If gua gib you 50 dolla on Wednesday, den lu guys owes me 60 dolla
da following Wednesday. 1. What is the effective rate, ia ?
Nominal int. rate = 20% a week x 52 weeks =1040% per
yearEffective interest rate =(1+r/m)mi = (1+10.4/52)52 = 13104 or
1,310,400%
Suppose Ah long can keep the $50, as well as all the money he
receives in payments, out in loans at all times? How much would Ah
Long have at the end of the year? F = P(1+i)n to get F = 50(1.2)52
$655,232Not bad but probably illegal
Ah Long the loan shark lends money on the following terms. Yo,
If gua gib you 50 dolla on Wednesday, den lu guys owes me 60 dolla
da following Wednesday. 1. What is the effective rate, ia ?
Suppose Ah long can keep the $50, as well as all the money he
receives in payments, out in loans at all times? How much would Ah
Long have at the end of the year?
A lender requires that monthly mortgage payments be no more than
25% of gross monthly income with a maximum term of 30 yrs. If you
can make 20% down payment, what is the minimum monthly income
needed to purchase a $325,000 link house when the interest rate is
6% compounded monthly.
$325,000 65000 = $260,000260000(A/P, 0.50%,360)260000(0.0060) =
15601560/0.25 = $6,240
Investing in Financial AssetsLecture No.11b
Ekonomi, Kewangan, & JuruteraKxex2162
8
A. Investment BasicsThe three basic investment objects are:
growth, income, and liquidity.Liquidity How accessible is your
money?Risk What is the safety involved?Return How much profit will
you be able to expect from your investment?The two greatest risks
investors face are inflation and market volatility.Contemporary
Engineering Economics, 5th edition, 2010
9
Contemporary Engineering Economics, 5th edition, 2010
Real Return2%Inflation 4%Risk premium 0%Total expected
return6%
Real Return2%Inflation 4%Risk premium 20%Total expected
return26%
Basic Concept - How to Determine Your Expected ReturnRisk-free
real returnInflationRiskpremiumU.S. Treasury BillsAn internet
stock
Very safeVery risky
10
Figuring Average Versus Compound Return
Contemporary Engineering Economics, 5th edition, 2010
0 1 2 35%10%12%Average rate of returnCompound Rate of Return
11
Contemporary Engineering Economics, 5th edition, 2010
Compound Versus Average Rate of ReturnInvestmentCase 1Case 2Case
3Case 4Case 5 Case 6Average
return9.00%9.00%9.00%9.00%9.00%9.00%Balance at the end of year
3$1,295$1,294$1,284$1,270$1,264$1,224Compound
return9.00%8.96%8.69%8.29%8.13%6.96%
Annual Investment Yield (Base investment of
$1,000)InvestmentCase 1Case 2Case 3Case 4Case 5 Case 6Year
19%5%0%0%-1%-5%Year 29%10%7%0%-1%-8%Year 39%12%20%27%29%40%
12
Risk refers to the chance that some unfavorable event will
occur.Volatility measures the deviation from the expected value, or
sudden swings in valuefrom high to low, or the reverse.Standard
deviation measures the degree of volatility when you have the
probabilistic information about the uncertain event.
Beta measures how closely a funds performance correlates with
broader stock market movement.Alpha shows whether a fund is
producing better or worse returns than expected, given the risk it
takes.Contemporary Engineering Economics, 5th edition, 2010 How to
Determine Expected Financial Risk
13
B. Investment StrategiesTrade-Off between Risk and RewardCash:
the least risky with the lowest returnsDebt: moderately risky with
moderate returnsEquities: the most risky but offering the greatest
payoffDollar-cost averaging concept - a planned transfer, over a
period, of equal amounts from one asset to another.Broader
diversification reduces risk - by combining assets with different
patterns of return, it is possible to achieve a higher rate of
return without increasing significant risk.Broader diversification
increase expected returnPortfolios with long-term horizons need
equities to offset inflation while short time frames requires debt
and/or cash investments to reduce volatility
Contemporary Engineering Economics, 5th edition, 2010
14
Contemporary Engineering Economics, 5th edition, 2010Dollar-Cost
Averaging ConceptTimingAmount InvestedFund Unit PriceNo. of Units
PurchasedEnding Fund BalanceMonth 1$1,000$5.00200$1,000Month
2$1,000$4.00250$1,800Month 3$1,000$2.50400$2,125Month
4$1,000$3.75267$4,189Month
5$1,000$5.00200$6,585Totals$5,0001,317
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Contemporary Engineering Economics, 5th edition, 2010Broader
Diversification Increases ReturnAmountInvestmentExpected
Return$2,000Buying lottery tickets-100% (?)$2,000Under the
mattress0%$2,000Term deposit (CD)5%$2,000Corporate
bond10%$2,000Mutual fund (stocks)15%
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Expected Value in 25 Years Option 1: Invest $10,000 in one asset
category (say, bond with 7% interest ) Option 2: Invest $10,000 in
five different classes of assets.Contemporary Engineering
Economics, 5th edition, 2010
17
C. Investing in StocksInvesting in stocks and bonds is one of
the most common investment activities among the American
investors.Stocks: Ownership in a corporationOwnership: If a company
issues 1M shares, and you buy 10,000 shares, you own a 10% of the
company.Valuation: (1) cash dividend and (2) share appreciation at
the time of saleContemporary Engineering Economics, 5th edition,
2010
18
Conceptual Stock Valuation
Given: Stock price as of May 1 , 2010: $72/shareEarnings growth
for next 5 years: 8%Expected cash dividend in 2010:
$2.00/shareExpected stock price in 3 years: $95/shareRequired
return on your investment: 10%Find: Current value of stock
Valuation:Contemporary Engineering Economics, 5th edition,
2010
$95$2$2$20123
19
D. Investing in BondBonds: Loans that investors make to
corporations and governments.Face (par) value: Principal amount
(typically $1,000 or $10,000)Coupon rate: Nominal interest rate
quoted on par valueMaturity: the length of the loan
Contemporary Engineering Economics, 5th edition, 2010
20
Types of Bonds and How They are Issued in the Financial
MarketContemporary Engineering Economics, 5th edition, 2010
21
Bond Price Notation Used in Financial MarketsContemporary
Engineering Economics, 5th edition, 2010Corporate BondsTreasury
Bonds1/8=$1.255/8=$6.251/32=$0.31252/32=$0.6250
3/32=$0.93754/32=$1.2517/32=$5.312518/32=$5.625019/32=$5.937520/32=$6.251/4=$2.503/4=$7.506/32=$1.56257/32=$1.87507/32=$2.18758/32=$2.5021/32=$6.562522/32=$6.875023/32=$7.187524/32=$7.503/8=$3.75
9/32=$2.812510/32=$3.1250 11/32=$3.4375
12/32=$3.7525/32=$7.812526/32=$8.125027/32=$8.437528/32=$8.751/8=$5.001=$1013/32=$4.062514/32=$4.37515/32=$4.687516/32=$5.0029/32=$9.062530/32=$9.375031/32=$9.687532/32=$10
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How To Read a Bond NotationContemporary Engineering Economics,
5th edition, 2010
Coupon rateMaturity date2020No meaning,Spacing
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How Do Prices and Yields Work?Yield to Maturity: The actual
interest earned from a bond over the holding periodP = A(P/A,i , n)
+P(P/F,i, n)Current Yield: The annual interest earned as a
percentage of the current market priceNominal current Yield = A/Pi
= (1 + A)nContemporary Engineering Economics, 5th edition, 2010
24
Bond QuotesContemporary Engineering Economics, 5th edition,
2010
AT&T 7s20 6.5% 5 million 108 1/4Coupon rate of 7%Maturity
(2020)Current yieldTrading volumeClosingMarket price
$1,082.50$70/108.25= 6.47%
25
Example 4.20 Yield to Maturity and Current Yield Given: Initial
purchase price = $996.25, coupon rate = 9.625% per year paid
semi-annually, and 10-year maturity with a par value of $1,000
Find: (a) Yield to maturity and (b) current yield Solution:(a)
Yield to maturity
i = 4.8422% per semi-annual(b) Current yield Contemporary
Engineering Economics, 5th edition, 2010Cash Flow Transaction
Associated with Investing in Delta Corporate Bond
26
Bond Value Over TimeMr. Gonzalez wishes to sell a bond that has
a face value of $1,000. The bond bears an interest rate of 8% with
bond interests payable semiannually. Four years ago, $920 was paid
for the bond. At least a 9% return (yield) in investment is
desired. What must be the minimum selling price?
Solution:Semiannual interest payment = $40Required semiannual
return = 4.5%Desired selling price of the bond (F):
Contemporary Engineering Economics, 5th edition, 2010
27