Question

Discount Bonds

Discount bonds such as Treasury bills have no stated interest rate. They are sold at a discount from face value, F. The yield or nominal interest rate is the percentage increase above the purchase price, P. The yield, i, is found as

                i = ((F – P)/P) * 100

You multiply by 100 to convert the decimal to a percentage.

An example:

Assume F = 1000 and P = 950 for a 1-year discount bond. Its yield is

         ((1000-950)/950)*100

         = (50/950)* 100

         = (0.0526) * 100

         = 5.26%

1. For a 1-year discount bond, if F =1000 and P = 950, the yield is

___5.26%________?

2. For a 1-year discount bond, if F =2000 and P = 1950, the yield is

____2.56%________?

3. If a one-year $10,000 discount bond has a yield of 5%, its price is ___$95281_______?

(Hint, find the present value of the bond using its yield.)

4. If a two-year discount bond has a face value of $5000 and a yield of 3%, its price is __________?

Rate of Return

5. If a bond has a current yield of 4% and a capital gain of 3%, its rate of return is _______?

6. If a bond has a current yield of 6% and a rate of return of 4%, it has a _____ capital gain or loss.

7. If a bond has a 2% rate of return and a capital loss of 4%, its current yield is ________?

Real and Nominal Interest Rates

8. If the nominal interest rate is 3% and expected inflation is -1%, the real interest rate is ___________?

9. If the nominal interest rate is 6%, the expected rate of inflation is 5% and the actual rate of inflation is 3%, the ex post real interest rate is __________?

10. If the expected rate of inflation is 4% and the ex ante real interest rate is 4%, the nominal interest rate is _______?

Answer 1

Discount Rate:

(1) Bond Tenure = 1 year, F = $ 1000, P = $ 950

Therefore, Yield = [(1000/950)-1] = 0.05263 or 5.263 % ~ 5.26 %

(2)

Bond Tenure = 1 year, F = $ 2000, P = $ 1950

Therefore, Yield = [(2000/1950)-1] = 0.02564 or 2.56 %

(3) Face Value = $ 5000, Tenure = 2 years and Yield = 3 %

Let the bond price be $ p

Therefore, p = 5000 / (1.03)^(2) = $ 4712.98

Rate of Return

(1) Current Yield = 4 % and Capital Gains Yield = 3%, Rate of Return = Capital Gains Yield + Current Yield = 3+4 = 7%

(2) Current Yield = 6 % and Rate of Return = 4%

Therefore, Capital Gain/Loss = Rate of Return - Current Yield = 4 - 6 = - 2 %

(3) Rate of Return = 2% and Capital Loss = - 4%

Current Yield = Rate of Return + Capital Loss = 2 + 4 = 6 %

Real & Nominal Rate

(1) Nominal Interest Rate = 3% and Expected Inflation = - 1 %

Real Interest Rate + Inflation Rate ~ Nominal Interest Rate

Real Interest Rate ~ Nominal Rate - Inflation = 3 - (-1) = 4 %

(2) Nominal Interest Rate = 6%, Expected Inflation = 5% and Actual Inflation = 3%,

Ex Post Real Interest Rate = Nominal Rate - Actual Interest Rate = 6 - 3 = 3 %

(3)

Ex-Ante Real Rate = 4 %, Expected Inflation = 4%

Nominal Interest Rate = Ex-Ante Real Rate + Expected Inflation = 4 + 4 = 8 %