A few years ago, Super Tech Inc. issued a bond that has a face value equal to $1,000 and pays investors $20 interest every six months. The bond has eight years remaining until maturity. If you require an 8 percent rate of return to invest in this bond, what is the maximum price you should be willing to pay to purchase the bond

The answer is: $655.20 (rounded to 2 decimal places)

Explanation:

A bond is a contractual agreement between the issuer and the holder which specifies the face value of the bond upon issuance as well as the interest (coupon) which the issuer must pay the holder in fixed instalments within a specified period. A bond's valuation is the determination of a fair market value for a bond given the required rate of return and period of repayment. The computation of such valuation is done by discounting future cash flows at the required rate of return. Given:

The coupon payments (C): $20

The required return (r): 8%

Face Value: $1, 000

The present values associated with the cash flows from each year are calculated as follows: C/(1 + r)^t where t is time period

Year 1: $20/(1+ 0.08)^1  = 18.51851852

Year 2: $20/(1+ 0.08)^2 = 17.14677641

Year 3: $20/(1+ 0.08)^3 = 15.87664482

Year 4: $20/(1+ 0.08)^4 = 14.70059706

Year 5: $20/(1+ 0.08)^5 = 13.61166394

Year 6: $20/(1+ 0.08)^6 = 12.60339254

Year 7: $20/(1+ 0.08)^7 = 11.66980791

Year 8: $(1000+20)/(1+ 0.08)^8 = 551.0742622

Present value of the bond is the sum of all the present values calculated above:$655.2016634 . This is the maximum amount the holder must be willing to pay. Note: at year 8, the issuer must repay the face value plus coupon.

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