Question

On the first day of your summer internship, you've been assigned to work with the Chief Financial Officer (CFO) of SanBlas Jewels Inc. Not knowing how well trained you are, the CFO has decided to test your understanding of interest rates. Specifically, she asks you to provide a reasonable estimate of the nominal interest rate for a new issue of Aaa-rated bonds to be offered by SanBlas Jewels Inc. The final format that the chief financial officer of SanBlas Jewels has requested is that of equation (2-1) in the text.

Nominal interest rate = real risk free rate + inflation premium + default risk premium + maturity risk premium + liquidity risk premium

Some agreed - upon procedures related to generating estimates for key variables in equation (2-1) follow

a. The current 3-month treasury bill rate is 2.98 percent, the 30-year treasury bond rate is 5.26 percent, the 30-year Aaa-rated corporate bond rate is 6.62 percent, and the inflation rate is 2.32 percent.

b. The real risk-free rate of interest is the difference between the calculated average yield on 3 month. Treasury bills and the inflation rate

c. The default risk premium is estimated by the difference between the average yields on Aaa-rated bonds and 30-year Treasury bonds

d. The maturity risk premium is estimated by the difference between the average yields on 30 year treasury bonds and 3-month treasury bills

e. SanBlas Jewels' bonds will be traded on the New York Bond Exchange, so the liquidity-risk premium will be slight. It will be greater than zero, because the secondary market for the firms' bond is more uncertain than that of some other jewellery sellers. It is estimated at 6 basis points. A basis point is one one-hundredth of 1 percent.

Now place your output into the format of equation (2-1) so that the nominal interest rate can be estimated and the size of each variable can also be inspected for reasonableness and discussion with the CFO

Question

a. What is the real risk free interest rate?

b. What is the inflation premium?

c. What is the default risk premium?

d. What is the maturity risk premium?

e. What is the liquidity risk premium?

f. What is the nominal interest rate?

Answer 1

Firstly, let's get clear with what all information do we have:

current 3-month treasury bill rate is 2.98 percent

30-year treasury bond rate is 5.26 percent

30-year Aaa-rated corporate bond rate is 6.62 percent

Inflation rate is 2.32 percent.

a. As mentioned in the question itself, the real risk free interest rate is the difference between the average yield of the current 3-month T-Bill and the inflation rate.

So, Real risk free interest rate = 2.98% - 2.32% = 0.66%

b. Since T-Bills rates are considered as the risk free rate of return, the Nominal interest rate of a T-Bill = real risk free rate of return + inflation premium. Upon observation, we will come to the conclusion that the inflation premium is equal to the inflation rate of the period i.e. 2.32% (2.98 = 0.66 + inflation premium)

c. Default risk premium = 30-year AAA rated Corporate Bond - 30 year Treasury Bond= 6.62 - 5.26 = 1.36%

d. Maturity Risk premium = 30-year Treasury Bond - 3 month T-Bill = 5.26% - 2.98% = 2.28%

e. The liquidity risk in this case has been mentioned already in the question as 6bps or 0.06%

f. Plugging in the figures, we derived out of the question into the Nominal Interest Rate equation provided, we get

Nominal Interest Rate = Real Risk Free Rate + Inflation Premium + Default Risk Premium + Maturity Risk Premium + Liquidity Risk Premium = 0.66% + 2.32% + 1.36% + 2.28% + 0.06% = 6.68%