Assume that a bond makes 10 equal annual payments of $1,000 starting one year fr

Question

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.)

Explanation / Answer

As the bond will make payments starting one year from now, it’s same as annuity. So, the formula to calculate PV of annuity:

PV = Pmt x ((1-((1+r)-n )) / r)

Payment per period (PMT) = $1,000
Discount Rate per period= 3.5%
Number of periods (n) = 10

PV = $1,000 x ((1-((1+0.035)-10)) / 0.035) = $8,316.61

PV of lump-sum amount of $100,000 = $100,000/(1.035)10 = $70,891.88

So the current price of the bond = $8,316.61 + $70,891.88 = $79,208.49

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