Question

1. Why does the right to collect a dollar in the future have a present value that is less than a dollar? If you could lend money at a nominal interest rate of 12% per year, and interest rates were expected to remain unchanged, what would be the present value of the right to collect $400, 4 years from now? What would be the present value of the right to collect $100 at the end of the year, for each of the next 4 years? 2. Suppose that you own a zero coupon bond that will mature in 10 years. The face value of the bond is $10,000. a. If the (nominal) interest rate is currently 5% and is expected to remain at 5% for the life of the bond, what should the bond's current price be? b. Assuming that you are right about future interest rates, what should the bond's price be in 5 years? C. Suppose, instead, that the (nominal) interest rate is currently 5%, but is expected to fall to 3% after 2 years and remain at 3% after that). What should the bond's current price be? d. Assuming that interest rates follow the expected pattern i.e. -5% per year for 2 years, then 3% per year), what should the bond's price be in 5 years? 3. Consider coupon bond with a $1000 face value, a 20% coupon rate, and a term to maturity of 4 years. Coupon payments will be made once each year, at the end of the year. a. If the (nominal) interest rate is 10% at the time the bond is issued and is expected to remain at 10% for the next 4 years, what should the bond's price be at the time it is issued? b. If the (nominal) interest rate is 10% at the time the bond is issued, but is expected to fall to 5% after 2 years (and remain there), what should the bond's price be at the time it is issued? 4. Describe the difference between coupon bonds and zero coupon bonds. Which type of bond tends to come with a term to maturity of 1 year or less? Why is that?

Answer 1

1)

Present value of $400 FVx(1:(1+r)^n) Here, 12% A Rate per annum B Number of years C Number of compoundings per per annum A:C Rate per period (r) BxC Number of periods (n) Future value (FV) 1 12% 400.00 Present value of $400 / $ 254.21 400x(1=(1+12%)^4)

Present value of $100 payments Px[1-(1=(1+r)^n)]=r Here, 12.00% A Interest rate per annum B Number of years c Number of compoundings per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 1 12.00% 100 Present value of $100 payments ments $ 303.73 100/(1-(1:(1+12%)^4)):12%

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