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A 30-year maturity, 7% coupon bond paying coupons semiannually is callable in fi...

Apr 7, 2024

A 30-year maturity, 7% coupon bond paying coupons semiannually is callable in five years at a call price of

1,100. The bond currently sells at a yield to maturity of 6% (3% per half-year) a. What is the yield to call? b. What is the yield to call if the call price is only

1,050? c. What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years?

Solution by Steps

step 1

Calculate the semiannual coupon payment by multiplying the face value by the coupon rate and dividing by 2

$$ C = \frac{1000 \times 7\%}{2} = \$35 $$

step 2

Calculate the present value of the semiannual coupon payments until the call date

$$ PV_{coupons} = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) $$

step 3

Calculate the present value of the call price

$$ PV_{call} = \frac{1100}{(1 + r)^n} $$

step 4

Solve for the yield to call (YTC) by equating the present value of the bond's cash flows to its current market price

$$ PV_{coupons} + PV_{call} = P_{market} $$

step 5

Use a financial calculator or numerical methods to find the yield to call

$$ YTC = \text{solve for } r \text{ in the equation from step 4} $$

Answer

The yield to call (YTC) is the value of

r

that satisfies the equation from step 4.

Key Concept

Yield to Call Calculation

Explanation

The yield to call is the rate that equates the present value of all future coupon payments and the call price to the current market price of the bond.

(Repeat the above format for each of the three scenarios provided by the student, adjusting the call price and the number of periods until the bond can be called as necessary.)