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

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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

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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

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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

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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

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Figuring Average Versus Compound Return

Contemporary Engineering Economics, 5th edition, 2010

0 1 2 35%10%12%Average rate of returnCompound Rate of Return

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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%

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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

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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

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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

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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

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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

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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

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Types of Bonds and How They are Issued in the Financial MarketContemporary Engineering Economics, 5th edition, 2010

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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

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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%

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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

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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):

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