5.a.In evaluating credit risk, discuss the statement: "An increase in collateral is a direct substitute for an increase in default risk."In your discussion, evaluate the credit risk premium on a one-year loan with and without collateral using the following formula and values:

Risk Premium with collateral:

where,k = required yield on a risky loan,

i = 0.04 (default risk free interest rate),

(1-p) = 0.1 (probability of default over the year), and

= 0.9 (the portion of the loan collateralized for certain).

5.b. Suppose the expected probability of survival in year 2 decreases from p1= 0.9 in year 1 to 0.80 in year 2 (p2).During the same period, the default risk free interest rate stays the same at 4 percent.What will be the risk premium for the second year, assuming the same collateral structure if the firm survives through year 1?What is the cumulative probability of default over the 2-year period? (HINT: Cp = 1 - (p₁)(p₂) ).

5.c.If the portion of the loan collateralized was not known for certain and could vary between =0.9 and =0.3, would the risk premium be higher than in 5.a. or 5.b.? The risk premium in this case is:

5.d.Given the information in 5.a. and 5.b. above, what should the interest rate be in the initial period for a two year default risky loan with the above default characteristics?(HINT: Use the unbiased expectations hypothesis as shown in Question 2 to compute the forward rate and this interest rate.)