Question

Problem 5 What is the market value of each of the following bond issues? $1,000,000 face value; 8% stated interest rate; 10-year life; interest paid semi-annually; 6% effective interest rate. $1,000,000 face value; 8% stated interest rate; 10-year life; interest paid semi-annually; 8% effective interest rate. $1,000,000 face value; 8% stated interest rate; 10-year life; interest paid semi-annually; 10% effective interest rate.

Answer 1

The market price of the bond is calculated by calculating the present value of all the coupon payments and redemption value at the end of maturity using the effective interest rate as discount rate.

Coupon payments are calculated using the stated interest rate.

Case 1:

Stated interest rate = 8%. Coupons are paid semi-annually. So coupon rate = 8%/2 = 4%. Coupon periods = 10*2 = 20. Effective interest rate = 6%. Effective rate for discounting = 6%/2 = 3%

Formula for discounting factor = 1/(1+r)^n

where r = rate of interest and n = period

Coupon amount = 1,000,000*4% = $40,000

Period Cash flow DF @ 3% 40000 0.970874 40000 0.942596 40000 0.915142 40000 0.888487 40000 0.862609 40000 0.837484 40000 0.813092 40000 0.789409 40000 0.766417 40000 0.744094 40000 0.722421 40000 0.70138 40000 0.680951 40000 0.661118 15 40000 0.641862 40000 0.623167 40000 0.605016 40000 0.587395 40000 0.570286 1040000 0.553676 Market value of the bond Present value 38,834.95 37,703.84 36,605.67 35,539.48 34,504.35 33,499.37 32,523.66 31,576.37 30,656.67 29,763.76 28,896.85 28,055.20 27,238.05 26,444.71 25,674.48 24,926.68 24,200.66 23,495.78 22,811.44 5,75,822.78 11,48,774.75 117

Case 2

Stated interest rate = 8%. Coupons are paid semi-annually. So coupon rate = 8%/2 = 4%. Coupon periods = 10*2 = 20. Effective interest rate = 8%. Effective rate for discounting = 8%/2 = 4%

Formula for discounting factor = 1/(1+r)^n

where r = rate of interest and n = period

Coupon amount = 1,000,000*4% = $40,000

9/ Period Cash flow DF @ 4% Present value 40000 0.961538 38,461.54 40000 0.924556 36,982.25 40000 0.888996 35,559.85 40000 0.854804 34,192.17 40000 0.821927 32,877.08 40000 0.790315 31,612.58 40000 0.759918 30,396.71 40000 0.73069 29,227.61 40000 0.702587 28,103.47 101 40000 0.675564 27,022.57 40000 0.649581) 25,983.24 12 40000 0.624597 24,983.88 13 40000 0.600574 24,022.96 40000 0.577475 23,099.00 15 40000 0.555265 22,210.58 161 40000 0.533908 21,356.33 17 40000 0.513373 20,534.93 40000 0.493628 1 9,745.12 19 40000 0.474642 18,985.70 20 1040000 0.456387 4,74,642.42 Market value of the bond 10,00,000.00

Case 3

Stated interest rate = 8%. Coupons are paid semi-annually. So coupon rate = 8%/2 = 4%. Coupon periods = 10*2 = 20. Effective interest rate = 10%. Effective rate for discounting = 10%/2 = 5%

Formula for discounting factor = 1/(1+r)^n

where r = rate of interest and n = period

Coupon amount = 1,000,000*4% = $40,000

21 3 Period Cash flow DF @ 5% 40000 0.952381 40000 0.907029 40000 0.863838 41 40000 0.822702 51 40000 0.783526 61 40000 0.746215 40000 0.710681 8 40000 0.676839 91 40000 0.644609 101 40000 0.613913 40000 0.584679 12 40000 0.556837 131 40000 0.530321 141 40000 0.505068 40000 0.481017 40000 0.458112 17 40000 0.436297 40000 0.415521 19) 40000 0.395734 20 1040000 0.376889 Market value of the bond Present value 38,095.24 36,281.18 34,553.50 32,908.10 31,341.05 29,848.62 28,427.25 27,073.57 25,784.36 24,556.53 23,387.17 22,273.50 21,212.85 20,202.72 1 9,240.68 18,324.46 1 7,451.87 16,620.83 15,829.36 3,91,965.06 8,75,377.90 11 15 16 18