The Garcia company's bond have a face value of 1000, will mature in 10 years and carry a coupon rate of 16 percent. Assume interest payments are made semi annually. Determine the present value of the bonds cash flow if the required rate of return is 16.64 percent
To determine the present value of the bonds' cash flow, we need to calculate the present value of each of the bond's future cash flows and then sum them up.
Step 1: Calculate the number of periods:
Since the bond pays interest semi-annually, and it matures in 10 years, there will be a total of 20 periods (10 years x 2).
Step 2: Calculate the periodic interest rate:
The annual coupon rate is 16 percent, which is divided by 2 since the bond pays interest semi-annually. Therefore, the periodic interest rate is 8 percent (16 percent / 2).
Step 3: Calculate the present value of each cash flow:
The bond's cash flow consists of periodic interest payments and the face value (maturity value) paid at the end.
To calculate the present value of the coupon payments, we can use the formula of an ordinary annuity:
PV = C × (1 - (1 + r)^(-n)) / r
Where:
PV is the present value of the cash flow
C is the periodic coupon payment
r is the periodic interest rate
n is the number of periods
Putting the values given in the question:
C = (Coupon Rate / 2) × Face Value
C = (16% / 2) × $1000
C = $80
r = Required Rate of Return / 2
r = 16.64% / 2 = 8.32%
n = Number of periods = 20
Calculate present value of coupon payments:
PV_coupon = $80 × (1 - (1 + 0.0832)^(-20)) / 0.0832
To calculate the present value of the face value, we can use the formula for a lump sum payment:
PV = F / (1 + r)^n
Where:
PV is the present value of the cash flow
F is the face value (maturity value)
r is the periodic interest rate
n is the number of periods
Calculate present value of face value:
PV_face = $1000 / (1 + 0.0832)^20
Step 4: Calculate the total present value of the cash flow:
Total present value = PV_coupon + PV_face
By substituting the calculated values into the formulas and performing the calculations, you can determine the present value of the bond's cash flow using the given information.