Question

Your client has been offered a 5-year, $1,000 par value bond with a 10 percent coupon. Interest on this bond is paid quarterly. If your client is to earn a simple rate of return of 12 percent, compounded quarterly, how much should she pay for the bond

Answer 1

$906.18

Step-by-step explanation:

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

The formula for calculating the PV of an ordinary annuity is used as follows:

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

Where;

PVC = Present value of the coupon (PVC) payment =?

P = Quarterly coupon amount = $1,000 × (10%/4) = $25

r = interest rate = 12% annual = 12% ÷ 4 quarterly = 3% or 0.03 quarterly

n = number of period = 5 years = 7 × 4 quarters = 28 quarters

Substitute the values into equation (1) to have:

PVC = 25 × [{1 - [1 ÷ (1+0.03)]^28} ÷ 0.03] = $469.10

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

The simple PV formula is used as follows:

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 given in step 1 above

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

PVFAV = FAV ÷ (1 + 0.03)^28 = $437.08

Step 3: Calculation of the market price of the bond

Market price of the bond = PVC + PVFAC …………………………… (3)

From step 1, PVC is $469.10, and PVFAC is $437.08 from Step 2. We can them substitute for them in equation (3) and have:

Market price of the bond = $469.10 + $437.08 = $906.18

Conclusion

Therefore, she should pay $906.18 for the bond.