The intrinsic value of a bond is the present value of all future cash flows discounted at the required rate of return.
Step 1: Calculate the annual coupon payment:
Coupon Rate = 4.5%
Face Value = $1,000
Annual Coupon Payment = 0.045 * $1,000 = $45
Step 2: Determine the number of periods remaining until maturity:
Bonds were issued on January 1, 2004 and mature on January 1, 2014. As of January 1, 2008, there are 6 years remaining until maturity. Since the coupon payments are semiannual, there are 12 periods remaining until maturity.
Step 3: Determine the required rate of return:
Required Rate of Return = 6% or 0.06 annually
Step 4: Calculate the present value of the annual coupon payments:
PMT = $45
n = 12
i = 0.03 (6% semiannually)
Using the PV of a regular annuity formula:
PV = PMT * [(1 - (1 + i)^-n) / i]
PV = $45 * [(1 - (1 + 0.03)^-12) / 0.03]
PV = $45 * [9.7153]
PV = $436.69
Step 5: Calculate the present value of the face value at maturity:
FV = $1,000
n = 12
i = 0.03
Using the PV formula:
PV = FV / (1 + i)^n
PV = $1,000 / (1 + 0.03)^12
PV = $1,000 / 1.425761
PV = $701.46
Step 6: Add the present values of the coupon payments and face value to get the intrinsic value of the bond:
Intrinsic Value = $436.69 + $701.46
Intrinsic Value = $1,138.15
Therefore, the intrinsic value of an SWH Corporation bond on January 1, 2008 to an investor with a required return of 6% is approximately $1,138, which is closest to option d. $888.