estimating interest rate using risk premiums
MINICASE 1: ESTIMATING INTEREST RATE USING RISK PREMIUMS. [5 points]
(References: See essentially Schedule of Classes Units 1, 3 and 6)
 Preliminary Remarks:
 The MiniCase Assignment:
The purpose of this minicase is to demonstrate how the required rate of return on a fixedincome security can be determined, using the risk premium perspective. The minicase brings together in a simple model several of the various risks associated with fixedincome securities. From a corporation perspective, the nominal interest rate to be determined in this minicase can serve as a basis for the firmâ€™s beforetax cost of debt. At the issue of the security, if the nominal interest rate is set as the coupon rate that is equal to the yield to maturity (so that the price equals the par value), then the rate can also be interpreted as the discount rate. From the perspective of investors (buyers of the security), the rate could be interpreted as the investorâ€™s nominal required rate of return.
 Your company, Binghamton Truck, Inc., is about to offer a new issue of corporate bonds to the investing marketplace. You have been asked by your CFO to provide a reasonable estimate of the nominal interest rate (nominal yield), R_{d}, for a new issue of Aaarated bonds to be offered by Binghamton Truck.
 Some agreedupon procedures related to generating estimates for key variables in the relevant equation, R_{d} = R^{*}_{rf} + IRP + DRP + MP + LP, are as follows:
 The current (mid2008) financial market environment is considered representative of the prospective tone of the market near the time of offering the new bonds to the investing public. This means that current interest rates will be used as benchmarks for some of the variable estimates. All estimates will be rounded off to hundredths of a percent; thus, 6.288 becomes 6.29 percent.
 The real riskfree rate of interest, R^{*}_{rf}, is the difference between the calculated average yield on 3month Treasury bills and the inflation rate.
 The inflationrisk premium, IRP, is the rate of inflation expected to occur over the life of the bond under consideration.
 The defaultrisk premium, DRP, is estimated by the difference between the average yield on Aaarated bonds and 30year Treasury bonds.
 The maturity premium, MP, is estimated by the difference between the calculated average yield on 30year Treasury bonds and 3month Treasury bills.
 Binghamton Truckâ€™ bonds will be traded on the New York Exchange for Bonds, so the liquidity premium, LP, will be slight. It will be greater than zero; however, because the secondary market for the firmâ€™s bonds is more uncertain than that of some other truck producers, it is estimated at 3 basis points.
Note: A basis point is one onehundredth of 1 percent. (E.g., 1 basis point = 0.01%; 25 basis points = 0.25%)
 Based on your research, the mid2008 estimates of the representative interest and inflation rates are as follows: (1) 3Month TBills = 4.89%, (2) 30Year TBonds = 5.38% (use this as proxy for 20year TBonds), (3) AaaRated Corporate Bonds = 6.24%, and (4) Inflation Rate = 3.60%. Visit online Federal Reserve Bank of St. Louis (Google â€œFederal Reserve Bank of St. Louis FREDâ€) and update the above data with the most recently available rates for each of the above fixed income securities and for the inflation rate.
 Required Task: Complete the Solution Table below, which is presented in form of a formula required to determine R_{d}. Place your answers (values) in the cells below the variables in the second row, and show your calculations below the Table, where applicable, of how you obtained the value for each of the variables. Similarly, use your most recent collected rates to complete the third row of the worksheet below. Briefly comment on the differences between the two results (i.e. results obtained from above old data versus results obtained from recent data you collected).
Solution to MiniCase 1 (show your work below the table, as appropriate):
R*_{rf}_{}

+ IRP 
+ DRP 
+ MRP 
+ LRP 
= 
R_{d} 
Source of data for part II of MiniCase 1:
FRED â€“ ECONOMIC DATA, by The Federal Reserve Bank of St. Louis
https://fred.stlouisfed.org/categories
Look for the following data, under either â€œPricesâ€ or â€œInterest Ratesâ€:
Inflation Rate: PCETRIM12M159SFRBDAL
PCETRIM12M159SFRBDAL 
Trimmed Mean PCE Inflation Rate, Percent Change from Year Ago, Monthly, Seasonally Adjusted 
Adjusted 
Three (3)Month Treasury Bill
TB3MS 
3Month Treasury Bill: Secondary Market Rate, Percent, Monthly, Not Seasonally Adjusted 
30Year Treasury Constant Maturity Rate
DGS30 
30Year Treasury Constant Maturity Rate, Percent, Daily, Not Seasonally Adjusted 
20Year Treasury Constant Maturity Rate
DGS20 
20Year Treasury Constant Maturity Rate, Percent, Daily, Not Seasonally Adjusted 
Moodyâ€™s Seasoned Aaa Corporate Bond Yield
AAA 
Moody’s Seasoned Aaa Corporate Bond Yield, Percent, Monthly, Not Seasonally Adjusted 
MINICASE 2: BOOTSTRAPPING METHOD FOR ESTIMATING SPOT RATES. [5 points]
 Introduction: As discussed in the text and the PowerPoints, the Yield Curve should be constructed using theoretical rates, which represent the spot rates corresponding to each maturity. These rates and corresponding calculated prices are referred to as â€œSpot Ratesâ€ (or pure discount rate) and â€œImplied Zeroesâ€ (or zerocoupon prices). The purpose of this minicase is to illustrate how to calculate these implied prices and spot rates. Ideally, the calculated spot rates are the rates that should be used to discount the respective cash flows, instead of using for example a single yield to maturity when determining the value of a bond.
 The Problem: Consider the problem of finding the pure discount bond prices from the coupon prices that are available. Table 1 gives data for three bonds for a period of three years.
Table 1: Coupon Bond Prices and Coupon Payments. (Notice that the Cash Flows in years 1 through Year 3 already reflect the coupon payments and the par value at maturity.)
Bond 
Price 
Year 1 
Year 2 
Year 3 
1 2 3 
99.50 101.25 100.25 
105 6 7 
0 106 7 
0 0 107 
 Let Pi be the price of bond i (e.g., if i=1, then Pi=P1 for bond 1). Let ci denote the dollar coupon associated with bond i, and y1 as a oneyear spot rate of interest. Then, we can denote the price of the first bond as
 Required task: Use the above procedure, called â€œBootstrappingâ€ to complete Table 2 below for maturities 2 and 3.
Then, using known data, solve for y1.
Finally, we can solve for the oneyear implied zero price, z1, as follows:
Note: z1 is also referred to as the â€œdiscount factorâ€ or the present value of a $1 to be received at time t in the future. The two terms to the right of the z1 equation are equivalent ways of finding the answer. They should give the same answer.
Following the same procedure, we can solve iteratively for y2 and z2, etc â€¦.
Note that, after solving for yi in one step it becomes a known value in the next step. For example, when solving for y2 and z2, P1, P2 and y1 are known values that you can just plug in the formula for P2 to find y2 and then solve for z2.
(Note: I provided the answers for maturity 1, for illustration. However, show your work, i.e., show the steps you followed to reach the answers, including your work to verify the answers already provided).
Table 2: Implied Zeroes and Spot Rates. (Answers for maturity 1 are already given to you for illustration. This will not count in your grade.)
Maturity (Years) 
Implied Zero (zi) 
Spot Rate (yi) 
1 
z1 = 0.9476 
y1 = 5.53% 
2 
z2 = ? 
y2 = ? 
3 
z3 = ? 
Y3 = ? 