swh corporation issued bonds on january 1, 2004. The bonds had a coupon rate of 4.5%, with interest paid semiannually. The face of the bonds is $1000 and the bonds mature on January 1, 2014. What is the instrinsic value (to the nearest dollar) of an swh corporation bond on january 1, 2008 to an investor with a required return of 6%?
To calculate the intrinsic value of the SWH Corporation bond on January 1, 2008, we need to calculate the present value of the future cash flows the bond generates.
Step 1: Determine the number of periods until maturity
Since the bond was issued on January 1, 2004, and matures on January 1, 2014, there are 10 years until maturity. However, we need the number of periods in which the coupon payments are made, which is double that because the interest is paid semiannually. Therefore, there are 20 periods until maturity.
Step 2: Calculate the coupon payment
The coupon rate is given as 4.5%, and the face value is $1000. Since the coupon payments are made semiannually, the annual coupon payment is calculated as 4.5% * $1000 = $45. However, it needs to be divided by 2 since the payments are made semiannually. The semiannual coupon payment is $45 / 2 = $22.50.
Step 3: Determine the required discount rate
The investor in this case has a required return of 6%. This is the rate of return the investor expects to earn on this type of investment.
Step 4: Calculate the present value of future cash flows
To calculate the present value of the coupon payments and the final principal payment, we need to discount them using the required return of 6% and the number of periods remaining until each cash flow is received.
The present value of the coupon payments can be calculated using the formula:
PV = Coupon Payment / (1 + r)^n
Where PV is the present value, r is the required return, and n is the number of periods until each cash flow is received.
For the coupon payments in periods 1-19 (since the last coupon payment is received in period 20), we can calculate the present value of each payment and sum them up:
PV_coupon_payments = ∑ [Coupon Payment / (1 + r)^n]
Where ∑ denotes summation, n ranges from 1 to 19, and r is 6%.
For the final principal payment in period 20, the present value is simply the face value of $1000 divided by (1 + r)^n, where r is 6% and n is 20.
Step 5: Calculate the intrinsic value
The intrinsic value of the bond is the present value of the coupon payments plus the present value of the final principal payment.
Intrinsic Value = PV_coupon_payments + PV_final_principal_payment
Calculating all these values will give us the intrinsic value of the bond on January 1, 2008, to an investor with a required return of 6%.