Assume that a bond makes 10 equal annual payments of $1,000 starting one year from today. The bond will make an additional payment of $100,000 at the end of the last year, year 10. (This security is sometimes referred to as a coupon bond.) If the discount rate is 3.5$% per annum, what is the current price of the bond? (Hint: Recognize that this bond can be viewed as two cash flow streams: (1) a 10-year annuity with annual payments of $1,000, and (2) a single cash flow of $100,000 arriving 10 years from today. Apply the tools you've learned to value both cash flow streams separately and then add.)

Respuesta :

Answer:

$79,208.48

Explanation:

The computation of the current price of the bond is shown below:-

Number of    Cash flow    PV annuity factor    Discounted cash

years                                                                        flow

1 -10  years     $1,000                 8.3166                      $8,316.6

10 years        $100,000            0.7089188                $70,891.88

Current price of the bond                                        $79,208.48

Refer to the PV annuity factor so that we get to know the discounting factor value.

Based on the information given, the current price of the bond will be $71721.66

The current price of the bond is calculated thus:

  • Cash flow = $1000
  • Annuity factor = 0.83166
  • Discounted cash flow = $1000 × 0.83166 = $831.66

Also for 10 years, the discounted cash flow will be:

= $100000 × 0.7089 = $70890

The current bond price will be:

= $70890 + $831.66

= $71721.66

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