Question

1. If the interest rate is 5%, the net present value of a ten-year 20% coupon bond with a face value of $10,000 is:
   1. $30,000
   2. $21,583
   3. $16,145
   4. $12,583
2. If the interest rate is 10%, the net present value of a ten-year 20% coupon bond with a face value of $10,000 is:
3. 1. $30,000
   2. $21,583
   3. $16,145
   4. $12,583

Answer 1

Answer

1)

He is receiving 20% of 10,000 = 2000 annualy for 10 years and received 10,000 after 10th year.

Present value(PV) of Periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)n)

Present value of Amount after nth year is given by :

PV = A/(1 + r)n

where n = time period, r = interest rate = 5% = 0.05, P = Periodic payment = 2000 and A = 10,000

Thus Net Present value(PV) = (2000/0.05)(1 - 1/(1 + 0.05)10) + 10000/(1 + 0.05)10

=> PV = 21582.60 = $21,583(approx)

Hence the correct answer is (b) $21,583

2)

He is receiving 20% of 10,000 = 2000 annualy for 10 years and received 10,000 after 10th year.

Present value(PV) of Periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)n)

Present value of Amount after nth year is given by :

PV = A/(1 + r)n

where n = time period, r = interest rate = 10% = 0.10, P = Periodic payment = 2000 and A = 10,000

Thus Net Present value(PV) = (2000/0.10)(1 - 1/(1 + 0.10)10) + 10000/(1 + 0.10)10

=> PV = 16144.57 = $16,145(approx)

Hence the correct answer is (c) $16,145