Question

**Problem 6-17**

Interest Rate Premiums

A 5-year Treasury bond has a 4.65% yield. A 10-year Treasury
bond yields 6.1%, and a 10-year corporate bond yields 8.8%. The
market expects that inflation will average 2.85% over the next 10
years (IP_{10} = 2.85%). Assume that there is no maturity
risk premium (MRP = 0) and that the annual real risk-free rate, r*,
will remain constant over the next 10 years. (Hint: Remember that
the default risk premium and the liquidity premium are zero for
Treasury securities: DRP = LP = 0). A 5-year corporate bond has the
same default risk premium and liquidity premium as the 10-year
corporate bond described above. What is the yield on this 5-year
corporate bond? Round your answer to two decimal places.

Answer #1

**Yield of T year Corporate Bond**

= Risk free rate(T year TreasuryBond) + Market Risk Premium(MRP) + (Default Risk Premium(DRP) + Liquidity Risk Premium(LRP))

Acc. to question; MRP = 0;

DRP + LRP (5 year Corporate Bond) = DRP + LRP (10 year Corporate Bond)

So Yield of 10 year Corporate Bond = Risk free rate(10 year Treasury Bond) + Market Risk Premium (MRP) + (DRP + LRP (10 year Corporate Bond))

So DRP + LRP (10 year Corporate Bond) = 8.8% - 6.1% = 2.7% = DRP + LRP (5 year Corporate Bond)

So Yield of 5 year Corporate Bond,R = Risk free rate(5 year Treasury Bond) + Market Risk Premium (MRP) + (DRP + LRP (5 year Corporate Bond))

= 4.65% + 2.7% = 7.35%

Inflation Adjusted yield = {(1+R)/(1+Inflation Rate)} - 1

**So Inflation Adjusted yield of 5 year corporate bond =
1.0735/1.0285 - 1**

**= 4.38%**

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