Question

Write down the equation for each of the following, and then find the price of the following assets. Assume an interest rate of 6%.                                                                           

An asset paying $200 for three years, beginning in one year.

1. A coupon bond with a coupon rate of 8.5 percent, a face value of $1,000, and three years to maturity.
2. A twenty-five year zero coupon bond with face value of $10,000
3. A perpetuity with a coupon of $10,000.

Answer 1

Interest Rate = r = 6%

Asset paying P = $200 for 3 years
Present Value = P/(1+r) + P/(1+r)² + P/(1+r)³ = 200/(1+0.06) + 200/(1+0.6)² + 200/(1+0.06)³ = $534.60

(a) Coupon rate =P = 8.5% of $1000 = $85
Face Value = FV = 1000
Number of years to maturity = n = 3
Present Value of the bond = P/(1+r) + P/(1+r)² + P/(1+r)³ + FV/(1+r)³
= 85/(1+0.06) + 85/(1+0.06)² + 85/(1+0.06)³ + 1000/(1+0.06)³
= $1066.83

(b) Face Value = FV = $10000
Number of years to maturity = n = 25
Present Value = FV/(1+r)²⁵ = 10000/(1+0.06)²⁵ = $2329.99

(c) Perpetuity = P = $10000
Present Value of perpetuity = P/r = 10000/0.06 = $166666.67