Final Answer:
The market value of the Home and Hardware, Inc. bond today is approximately $1,824.47.
Step-by-step explanation:
Home and Hardware, Inc. recently issued a bond with a $2,000 par value, a five-year maturity, and a 6% annual coupon rate. To calculate the market value of the bond, we can use the present value of future cash flows. The bond pays interest annually, so the annual coupon payment is calculated as 6% of the par value, which is $2,000 x 6% = $120.
Now, we need to discount these future cash flows back to their present value using the required return on the market, which is 8%. The bond has a five-year life, so we discount the annual coupon payments and the face value using the formula for present value:
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PV=
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C
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Where:
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PV is the present value,
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C is the annual coupon payment,
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r is the required return on the market (in decimal form),
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t is the time to maturity in years, and
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F is the face value of the bond.
Plugging in the values, we get:
PV = \dfrac{$120} {(1+0.08)^1} + \dfrac{$2,000} {(1+0.08)^5}
Solving this equation gives the present value of the bond, which is approximately $1,824.47.
In summary, the market value of the Home and Hardware, Inc. bond today is calculated by discounting the future cash flows (coupon payments and face value) to their present value using the required return on the market. The result, $1,824.47, represents the fair market value of the bond given the specified parameters