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  • Time Value of Money
    • Compound Interest
    • Present Values
    • Future Values
    • Annuity

  • Project Evaluation
    • Net Present Value (NPV)
    • Internal Rate of Return (IRR)
    • Payback Period
    • Mutually Exclusive Projects

  • Capital Asset Pricing Model (CAPM) Model
    • Risk Free
    • Market Return
    • Betas
    • Portfolio Return and Risk

  • Corporate Finance
    • Dividends
    • Preferred Stock
    • Bonds
    • Capital Financing
    • Sustainable Growth

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Problem: What are financial markets? What function do they perform? How would an economy be worse off without them?

Solution: Financial markets are where buyers and sellers trade assets. For example, these assets could be equities, bonds, currencies, and derivatives. The marketplace has typically has transparent prices, regulations on trade, costs and fees and market forces that will be a determining factor for prices of the securities. The New York Stock Exchange is one of the largest trading markets in USA. However, trade markets can be found all over the world. The financial market functions are to trade and there may be heavy trade at one period as well as low level of demands at other periods. Downturns can cause the prices to fall because of low level in demand or other forces like tax rates, production, and or employment levels.

The financial market may consist of money markets which are short-term debt instruments, or capital markets which are long-term debt and equity instruments. What the financial market does is exchange capital and credit in the economy and this can be seen in stock, bond, commodities, and foreign exchange markets.

If there was no financial market then the economy could become stagnant. Business growth may not occur, unemployment could rise, interest rate would fluctuate probably at a high rate, production would probably decrease, and multiple other concerns could arise. The financial market allows businesses to move their dollars around for growth, etc.

Question: Present and Future Values

A. You will receive 100 payoff in terms of today’s dollars?

(iii) What is the real interest rate?

(iv) Show that the real payoff from the bond (from part (ii)) discounted at the real interest

rate (from part (iii)) gives the same present value for the bond as you found in part (I).

B. In order to live comfortably in retirement, Madonna will need to have saved $2,000,000 by the time she retires in 40 years. If the interest rate she earns on her savings is 5 percent per year, what fixed amount must she save each year to meet her retirement goal?

Solution: (A) (i) The present value is


(ii) In this case we have that the real payoff is $86.74.

(iii) The real interest rate is 8% - 5% = 3%.

(iv) Notice that

\[$PV*=\frac{86.74}{\left( 1+0.08-0.05 \right)}=\$79.38\]

(B) We assume that Madonna makes a payment of \(A\) at the end of the year. We need to solve

\[FV=A{{\left( 1+r \right)}^{0}}+A{{\left( 1+r \right)}^{1}}+...+A{{\left( 1+r \right)}^{n-1}} = 2,000,0000\]

\[\Rightarrow \,\,\,A\left( 1+1.05+...+{{1.05}^{39}} \right)=2,000,0000\]

\[\Rightarrow \,\,\,A\left( \frac{{{1.05}^{40}}-1}{0.05} \right)=2,000,0000\]

\[\Rightarrow \,\,\,120.799774A=2,000,0000\,\,\,\,\Rightarrow \,\,\,A=\frac{2,000,0000}{120.799774}=\$165,563.22\]

Finance Help Blog

A Case study of comparing two projects using time value of money.