Question

The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 4% per year for each of the next four years and 3% thereafter. 

The maturity risk premium (MRP) is determined from the formula: 0.1(t-1)%, where is the security's maturity. The liquidity premium (LP) on all Berth Construction Inc.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): 

Berth Construction Inc. Issues 13-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross product terms; that is, if averaging is required, use the arithmetic average. 

• 9.16% 

• 8.11% 

• 7.96% 

• 5.85% 

Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? 

• Higher inflation expectations increase the nominal interest rate demanded by investors. 

• A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond. 
  

Answer 1

The nominal interest rates for the first four years = real rate+ inflation rate = 2.8%+4% =6.8%

The nominal interest rates for the next nine years = real rate+ inflation rate = 2.8%+3% =5.8%

So, the average nominal rate for the 13 year period = (4*6.8%+9*5.8%)/13 = 6.11%

The premiums for the bond yield are =

Maturity risk premium + liquidity risk premium + default risk premium (AA bonds)

=0.1*(13-1)% + 1.05%+ 0.80%

=3.05%

So, the required yield is = 6.11%+3.05% = 9.16% (first option)

if everything else remains constant, a higher expected inflation rate increases the nominal rate of interest demanded by the Investors . This is a true statement as the real rates demanded by investors generally remains constant, so if inflation increases, nominal rates also increase to keep the real rates constant

The second statement is clearly false as a BBB rated bond bears a higher default risk than a AAA rated bond and hence it carries a higher default risk premium (also clear from the data provided in the question)

Answer 2

Gauge Imports Inc. issues nine-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average.