Question

Part E please

Floating Rate Note Practice Problem Let's denote today by t = 0. The term structure of interest rates (all rates stated at an annual rate) is given by: r(0,1)= 10.52% r(0,2) = 11.33% r(0,3) 11.96% r(0,4) = 12.47% DE a) Consider a floating rate note with a face value of $5,000. This floater pays a coupon at timet equal to r(t-1,t). The coupons are annual, and the reset dates for the floater are t = 1,2,3. The floater matures at t = 4. What is the value of this floater when it is issued at t = 0? b) Now assume today is 15 months from the original issue date of the floater. That is, today is 1.25 years from t = 0. In addition to the above information, you now know: r(1.25,2) = r(1.25,3) r(1.25,4) = 8.00% 19.10% 10.05% If this floater is sold on t = 1.25, assume the buyer of this floater receives the entire coupon paid at t = 2. How much is the buyer willing to pay for this floater? c) Today is t = 0. Consider a floater similar to the one described in part (a) above. However, the coupon rate for any year t is now equal to r(t = 1,t) + 2% (i.e. the spread is s = 2.0%). How much is this floater worth att = 0? d) Consider a floater similar to the one described in part (a) above. As in part (C), the coupon rate for year t (where t equals 2,3, or 4) is now equal to r(t - 1,0) +2%. However, the coupon rate for year 1 is equal to r(0,1) - 3%. When the early coupon rates have a negative spread, this is called a teaser rate. Given the specifications of this new floater how much is it worth att = 0? e) Today is t = 0. Reconsider the floater in part (d). While the spread for the coupon rates in years t = 2, t = 3, and t = 4 remains at 2%, the coupon rate for t = 1 is not the same as in part (d). Find the appropriate teaser rate for the first coupon for this new floater to sell for its face value at t = 0

Answer 1

E) The rates for coupon payments are as follows

r(0.1) = 10.52%

r(1,2) = (1+ r(0.2))^2 / (1+r(0,1)) -1 = 1.1133^2/1.1052 - 1 =0.121459 = 12.1459%

r(2,3) = (1+ r(0.3))^3 / (1+r(0,2)^2) -1 = 1.1196^3/1.1133^2 - 1 =0.132307 = 13.2307%

r(3,4) = (1+ r(0.4))^4 / (1+r(0,3)^3) -1 = 1.1247^4/1.1196^3 - 1 =0.14014 = 14.014%

Let the coupon Amount for year 1 be $A

Coupon rate for year 2 = r(1,2) +2% = 12.1459% + 2% =14.1459%,Coupon Amount = $5000*14.1459% = $707.2968

Coupon rate for year 3 = r(2,3) + 2% = 13.2307% + 2% =15.2307%,Coupon Amount = $5000*15.2307% = $761.5358

Coupon rate for year 4 = r(3,4) + 2% = 14.014% + 2% =16.014%,Coupon Amount = $5000*16.014% = $800.6991

So,

Value of bond at t= 0 is equal to face value = 5000

=> A/1.1052 + 707.2968/1.1133^2+ 761.5358/1.1196^3+ 800.6991/1.1247^4+ 5000/1.1247^4 = 5000

=> A/1.1052 +4738.50 =5000

=> A/1.1052 = 261.50

=> A = $289.009

So, teaser rate = 289.009/5000 = 0.0578019 =5.78%

So, teaser rate for year 1 = 5.78% = 10.52%- 4.74% = r(0,1) - 4.74%