Question

Question 1 (25%) Lenguard Inc. is planning to issue a perpetual bond now. Based on the company credit rating, its borrowing rate is currently 8%. At the end of year 1, there is 35% chance that its borrowing rate will be 5% and 65% chance that it will be 10%. Then the company expects its borrowing rate will stay at that level forever. a. If coupon rate is 8% and the bond is non-callable, what is the price of the bond? b. If the bond is callable at its face value of $1,000 plus two additional coupon payments at the end of year 1, what is the price of this callable bond? C. If Lenguard wants to sell the callable bond in part b above at $1,000, what must be the coupon rate?

Answer 1

Sol:

a) Non callable bond are such which cannot be paid out before its maturity period. If paid out then penalties should be provided. So, the interest rate to be provided till its maturity period. Interest Rate is fixed for the investor regardless of volatlity or market movements.

The bond is a perpetual bond and it means interest are paid forever i.e upto the infinity period or we can called as irredeemable bond.

Therefore , value or the price of bond (B₀) = Annual Interest amount

RR(i.e discount rate)

Suppose , Face Value = $ 1000

given, coupon rate = 8%

Annual interest = 8% * 1000 = $ 80

Specifically discount rate is not given so we are using borrowing rate as discount rate i.e 8% (RR)

B₀ = $ 80

8%

= $ 1000

Hence , the price of bond is $ 1000.

b) Since the perpetual bonds have no maturity date fixed and issuer can structured such bond as callable bond after a set of certain period of time like 5-15 years.

Callable bonds are redeemable bond and such bonds can be paid prior to its maturity period.

In this the investors can reduce the interest rate if such rates falls.

In this the future interest payment can become lower which indicates higher risk for the investors.

In the case of callable bond investors can get the higher interest payment without being paid of premium on bond.

Given, Face value = $ 1000

Coupon rate at the end of year 1 = 0.35* 5 + 0.65*10 = 8.25 %

Annual interest = 8.25% * 1000 = $ 82.5

Discount rate is not provided so coupon rate = borrowing rate = discount rate = 8% pa.

Value of bond (B₀) = $ 82.5  

8%

= $ 1031.25

Hence, the price of callable bond (B₀) = $ 1031.25

c) If callable bonds want to be sold in part b above $ 1000 then coupon rate will be

coupon rate = $ 82.5 * 100

$1031.25

= 8 % pa.