Question

Bond M has face val of $40,000 & matures in 20 yrs, makes no pmts for 1st 6 yrs, then $1500 every 6 mths for 8 yrs, then pays $1800 evry 6 mths for last 6 yrs. Bond N has face val of $40,000 & maturity 20 yrs & makes no coupon paymts over the life of the bond. Req ret on both is 12% compounded semiannually what is the current price of each bond?

Answer 1

Bond M has face value of $40,000 & matures in 20 years, makes no payments for 1st 6 years, then $1500 every 6 months for 8 years, then pays $1800 every 6 months for last 6 years. Bond N has face value of $40,000 & maturity 20 years & makes no coupon payments over the life of the bond. Required rate on both is 12% compounded semiannually, what is the current price of each bond?

Solution.

Consider bond M. Discount rate is $\frac{0.12}{2} = 0.06$ for semi-annual and total numbers of periods is 20 years · 2 (per year) = 40.

So

Cash flows for periods 1-12: 0.

Cash flows for periods 13-28:

$$\frac{\$1500}{(1 + 0.06)^{13}} + \frac{\$1500}{(1 + 0.06)^{14}} + \cdots + \frac{\$1500}{(1 + 0.06)^{28}} = \sum_{i=13}^{28} \frac{\$1500}{(1 + 0.06)^{i}} = \$7533.48$$

Cash flows for periods 29-39:

$$\frac{\$1800}{(1 + 0.06)^{29}} + \frac{\$1800}{(1 + 0.06)^{30}} + \cdots + \frac{\$1800}{(1 + 0.06)^{39}} = \sum_{i=29}^{39} \frac{\$1800}{(1 + 0.06)^{i}} = \$2777.24$$

And final payment is par plus the last coupon payment:

$$\frac{\$40000 + \$1800}{1.06^{40}} = \$4063.89$$

Price is the sum of all the discounted cash flows:

$$PV_M = \$7533.48 + \$2777.24 + \$4063.89 = \$14374.61$$

Consider bond N. We have only one cash flow – at maturity.

So

$$PV_N = \frac{40000}{1.06^{40}} = \$3888.89$$

Answer: $PV_M = \$14374.61$; $PV_N = \$3888.89$.