A firm issues 20-year bonds with a coupon rate of 4.4%, paid semiannually. The credit spread for this firm's 20-year debt is 1.2%. New 20-year Treasury notes are being issued at par with a coupon rate of 5.3%. What should the price of the firm's outstanding 20-year bonds be if their face value is $1000

$327.08

Explanation:

The following steps are followed:

Step 1: Calculation of the present value of the coupon (PVC) of cash flows

To achieve this, the formula for calculating the PV of an ordinary annuity is employed as below:

PVC = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PVC = Present value of the coupon (PVC) cash flow = ?

P = Semiannual coupon amount = $100 × (4.4% ÷ 2) = $2.2 0

r = Yield to maturity rate = 1.2% +5.3% annual = 6.5% annual = 6.5% ÷ 2 semiannually = 3.25% or 0.0325 semiannually

n = number of period = 20 years = 20 × 2 semiannual = 40 semiannual

Substituting the values into equation (1), we have:

PVC = 2.20 × [{1 - [1 ÷ (1+0.0325)]^40} ÷ 0.0325] = $48.86

Step 2: Calculation of the present value of the face value (PVFAV) of the bond

The following PV formula is used to calculated this:

PVFAV = FAV ÷ (1 + r)^n ……………………………………. (2)

Where;

PVFAC = Present value of the face value of the bond = ?

FAC = Face value of the bond = $1,000

r and n are as already described in step 1 above

Substituting the values into equation (2), we have:

PVFAV = $1,000 ÷ (1 + 0.0325)^40 = $278.23

Step 3: Calculation of the price of the firm's outstanding 20-year bonds

The price of a bond can be obtained by adding the PV of expected cash flows and PV of the face  value of the bond as follows:

Price of bond = PVC + PVFAC …………………………… (3)

Since PVC = $48.86  and PVFAV = $278.23, we have:

Price of bond = $48.86 + $278.23 = $327.08

Therefore, the price of the firm's outstanding 20-year bonds with face value of $1000 is $327.08 .

answer; limited pay life;