# FIN 720 Module 1.docx - Chapter 720-1 Some Basic Algebra 1...

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Chapter 720-1Some Basic Algebra1.To solve for a variable in a linear equationGive the following linear equation, solve for the variable X:Y=a+bXSubtracting afrom both sides of the equation:Ya=bXDividing both sides by bto obtain X:Yab=XExample:Given Y=.15a=.04b=.10for the following linear equation:Y=a+bXWhat is X?.15=.04+.10XSubtracting .04 from both sides of the equation:.15.04=.10XDividing both sides by .10 to obtain X:.15.04.10=1.1=XExample:
Given Y=.15a=.04X=1.1for the following linear equation:Y=a+bXWhat is b?.15=.04+b(1.1)Subtracting .04 from both sides of the equation:.15.04=b(1.1)Dividing both sides by 1.1 to obtain b:.15.041.1=b=.102.To solve for the variable gin the following equation:a(1+g)b+g=cSubtracting gfrom both sides:a(1+g)b=cgMultiplying both sides by b:a(1+g)=b(cg)Thus, a+ag=bcbgRearranging the equation, we obtain:ag+bg=bca
Then,(a+b)g=bcaThus,g=bcaa+bExample:Solve for the variable gin the following equation:4(1+g)70+g=.15Subtracting gfrom both sides:4(1+g)70=.15gMultiplying both sides by 70:4(1+g)=70(.15g)Thus, 4+4g=10.570gRearranging the equation, we obtain:4g+70g=10.54Then,74g=6.5Thus,g=6.574=.0878Problems:
1.Given Y=.22a=.07b=.12for the following linear equation:Y=a+bXWhat is X?.22=.07+.12XSubtracting .07 from both sides of the equation:.22.07=.12XDividing both sides by .12 to obtain X:.22.07.12=1.25=X2.Given Y=.22a=.07X=1.25for the following linear equation:Y=a+bXWhat is b?.22=.07+b(1.25)Subtracting .07 from both sides of the equation:.22.07=b(1.25)Dividing both sides by 1.25 to obtain b:.22.071.25=b=.12
3.Solve for the variable gin the following equation:3.5(1+g)46+g=.13Subtracting gfrom both sides:3.5(1+g)46=.13gMultiplying both sides by 46:3.5(1+g)=46(.13g)Thus, 3.5+3.5g=5.9846gRearranging the equation, we obtain:3.5g+46g=5.983.5Then,49.5g=2.48Thus,g=2.4849.5=.05
Chapter 720-2Risk and Return in the Context of Market EquilibriumFinancial assets vs. real assets:Financial assets:Securities: stocks, bonds, preferred stocks, etc. Contracts: options contracts, forward contracts, futures contracts, etc. Real assets: materials, machines, equipment, properties, etc. These items can be organized into a production line. A production line is also a real asset. If the production line is large, it may be called a division; for example, the Ford Motors has a division to manufacture the Mustangs. A production line is also called a project. A portfolio comprised of single assets is also an asset.Every asset, financial or real or a portfolio, has a market value. The market value changes overtime. The future value of the asset is uncertain; therefore, there is risk. Definition of key symbols:E(R):Expected rate of return of an assetR:Required rate of return of an assetσ2(R):Variance of an assetσ(R):Standard deviation of an assetρ(RA ,RB): Correlation coefficient between two assets A and B β: Market risk index of an assetEx-ante: before the fact; that is, the outcome of the event will occur in the future and is unknown at the present time.
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