Wachowicz Corporation issued 15-year, noncallable, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 14 years to maturity?
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To determine the current price of the bonds, we can use the present value formula. The formula is:
\[ PV = \frac{C}{(1+r)^n} + \frac{C}{(1+r)^{n-1}} + ... + \frac{C}{(1+r)^2} + \frac{C}{(1+r)^1} + \frac{C+M}{(1+r)^n} \]
Where:
PV = Present value (current price)
C = Annual coupon payment
r = Market interest rate
n = Number of periods (years to maturity)
In this case, the annual coupon payment is $1,000 * 7.5% = $75. The market interest rate is 5.5% and the number of periods is 14 years.
Using this information, we can calculate the present value:
\[ PV = \frac{75}{(1+0.055)^1} + \frac{75}{(1+0.055)^2} + ... + \frac{75}{(1+0.055)^13} + \frac{75}{(1+0.055)^14} + \frac{75+1000}{(1+0.055)^{14}} \]
Calculating this equation will give us the current price of the bonds.
To calculate the current price of the bonds, we need to use the present value formula for a bond. The formula is as follows:
Current Price = Sum of Present Value of all Future Cash Flows
In this case, the future cash flows are the coupon payments and the face value of the bond. The coupon payments are fixed at 7.5% of the $1,000 face value, or $75 per year. The face value is $1,000.
To determine the present value of each future cash flow, we need to discount them by the market interest rate. The discount rate is 5.5%, and we have 14 years remaining until maturity.
To calculate the present value of the coupon payments, we need to discount each cash flow by the market interest rate. The formula for present value is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = interest rate
n = number of periods
Using this formula, we can calculate the present value of the coupon payments:
PV_coupon1 = $75 / (1 + 0.055)^1 = $71.43
PV_coupon2 = $75 / (1 + 0.055)^2 = $67.97
PV_coupon3 = $75 / (1 + 0.055)^3 = $64.70
...
PV_coupon14 = $75 / (1 + 0.055)^14 = $30.51
Since the bond is noncallable, the face value will also be paid at maturity. We can calculate the present value of the face value using the same formula:
PV_face_value = $1,000 / (1 + 0.055)^14 = $559.95
Finally, we sum up all the present values of the coupon payments and the present value of the face value to find the current price of the bonds:
Current Price = PV_coupon1 + PV_coupon2 + PV_coupon3 + ... + PV_coupon14 + PV_face_value
= $71.43 + $67.97 + $64.70 + ... + $30.51 + $559.95
By summing up all the present values, we can find the current price of the bonds with 14 years to maturity.
Bond Yield Example Data
A B
1 FV 1000
2 Annual Coupon Rate 7.5%
3 Annual Return 5.5%
4 Years to Maturity 14
5 Years 1
6 Payment Frequency 1
7 Value of Bond 1191.79
PUT THIS IN EXCEL AND YOU HAVE A CALCULATOR
VALUE OF BOND=
=-PV(B4/B7,B5*B7,B3/B7*B2,B2)