Answer:
The answer is: $655.20 (rounded to 2 decimal places)
Step-by-step 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.