Question

Bond Problem:
Formulas: current yield = Dollar income Capital gains = Ending value – Beg. Value
Beginning value Beginning value
Bond yield = current yield + capital gains yield
Suppose that one year ago Cisco Systems sold a 15-year bond issue that had a $1,000 par value and a 7 percent coupon rate. Interest is paid semiannually.
a. If the bond sold at $1,000 initially, what was the market interest rate when it was sold?
b. If the going rate interest rate has risen to 10 percent, at what price would the bonds be selling today?
c. What would be the current yield and the capital gains yield for the year of this change to 10%?
Cisco continued.
d. Suppose that the interest rate remained at 10 percent for the next 10 years. What would happen to the price of the Cisco Systems bond over time?
e. Explain a scenario that would cause Cisco to call their 15 year bond.
f. What are the cash flows that we are discounting to determine the price of Cisco’s bond?

Answer 1

a. As the bond was sold at its par value, the market interest rate at that time must be same as the coupon rate i.e. 7%.

b. The price of a bond whose par value is $1,000 is equivalent to all the future cash flows associated with it. It can be calculated as:

Where C is the coupon rate; r is the market interest rate and n is no. of years to maturity.

Therefore, for C= 7% of 1000 = 70; r=10% (or 0.1), and n=14 years (as 1 year has already passed), the price of the bond can be calculated as:

c.

Current yield = Annual Cash flows/ Market Price = (70/395.07)*100 = 17.72%

Bond yield = current yield + capital gains yield = [(70/395.72) + (395 – 1000)/1000]*100 = -42.8%

d.

If the interest rate remain at 10% (which is higher than the coupon rate of 7%) the market price of the bond will keep on reducing (as other bonds of similar features are earning more)> Moreover, if we apply the formula of Price, with only 4 years remaining to maturity (after 10 years from now) the cash flows receivables will only be 8 coupon payments (of $35 each) and the par value of 1000, which when discounted @10% will give the price of around $88.

e.

As the bond price is continuously falling (due to higher market interest rate), the Cisco should be calling off the bond, because investors would be well-off in selling the bond in secondary market and investing the proceeds at higher interest rate.

f.

We are discount all future coupon payments ($35 received semi-annually) receivable from the bond and also the par value of $1000 that will be received at the time of maturity.