Question

(Chapter 4): Solomon Brothers

You are working at the fixed-income sector of Solomon Brothers. You were asked to prepare a quiz for the new interns to assess their knowledge of bonds. To evaluate interns’ ability to apply their knowledge to real world, you would like to have the interns to analyze risk as well.

1. Please calculate the following bond values, Yield to Maturity, current yield and capital gains.

1. Value of 10-year, 10% coupon, semiannual bond if rd = 13%.
2. Value of 10-year, 10% coupon, semiannual bond if rd = 7%.
3. Value of 10-year, 10% coupon, semiannual bond if rd = 10%.
4. YTM on a 10-year, 9% semi-annual coupon, $1,000 par value bond selling for $887
5. Current yield and capital gains for case 4)
6. What is the relation between bond value and years remaining till maturity?
7. Calculate the yield to call a 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1,135.90 with an 8% yield to maturity. It can be called after 5 years at $1,050.
8. Please explain price/interest rate risk and reinvestment risk. What kind of bond has higher price risk? What kind of bond has higher reinvestment risk?

Answer 1

(a) Tenure = 10 years, Bond Face Value = $ 1000, rd (YTM) = 13 % and Coupon Rate = 10 % payable semi-annually

Semi-Annual Coupon Payment = 0.5 x 0.1 x 1000 = $ 50

Bond Value = Sum of Present Value of Bond Coupons + Present Value of Face Value = 50 x (1/0.065) x [1-{1/(1.065)^(20)}] + 1000 / (1.065)^(20) = $ 834.72

(b)

Tenure = 10 years, Bond Face Value = $ 1000, rd (YTM) = 7 % and Coupon Rate = 10 % payable semi-annually

Semi-Annual Coupon Payment = 0.5 x 0.1 x 1000 = $ 50

Bond Value = Sum of Present Value of Bond Coupons + Present Value of Face Value = 50 x (1/0.035) x [1-{1/(1.035)^(20)}] + 1000 / (1.035)^(20) = $ 1213.19

(c)

Tenure = 10 years, Bond Face Value = $ 1000, rd (YTM) = 10 % and Coupon Rate = 10 % payable semi-annually

Semi-Annual Coupon Payment = 0.5 x 0.1 x 1000 = $ 50

Bond Value = Sum of Present Value of Bond Coupons + Present Value of Face Value = 50 x (1/0.05) x [1-{1/(1.05)^(20)}] + 1000 / (1.05)^(20) = $ 1000

(d)

Tenure = 10 years or 20 half-years, Coupon Rate = 9 % payable semi-annually, Par Value = $ 1000 and Market Price = $ 887

Let the YTM be 2R

Semi-Annual Coupon = 0.5 x 0.045 x 1000 = $ 45

Therefore, 887 = 45 x (1/R) x [1-{1/(1+R)^(20)}] + 1000 / (1+R)^(20)

Using EXCEL's Goal Seek Function/ a financial calculator/ hit and trial method to solve the above equation we get:

R = 0.05441 or 5.441 %

Therefore, YTM = 2 x 5.441 = 10.882 %

NOTE: Please do raise separate queries for solutions to the remaining sub-parts, as one query is limited to the solution of only one complete question with a maximum of four sub-parts.