# Fixed Income Question

Can somone explain to me how to answer this question? I am having troubl solving and I dont have the explanation to the solution. R.T. Farris purchased a 5-year, \$100,000 parvalue, 8% annual coupon bond at a 8.4% yield to maturity. In order to realize a compound return of 7.9%, the amountFarris will have to earn in reinvestment income over the bond’s life is closest to: Thanks!

I don’t have my calculator here, so I’ll just say how I would proceed for that Purchase price = PV at inception = FV = 100 000 Period N = 5 * 2 = 10 (semi annual) Total Coupon payments = 8%/2 * 100 000 * 10 = 40 000 Capital gain = Purchase Price – FV = 0 Calculate the FV with a YTM of 7.9% Total return = FV calculated at 7.9% - purchase price Then Reinvestment income = Total return – Total coupon payment – Capital Gain

But what I don’t get is the first YTM of 8.4%. If the investor bought the bond at par, then the coupon rate should equal the YTM. Why do we have a YTM of more than the coupon as for a discount ? Also does it make sense for this investor to require a return of 7.9% then ?

Miss Yiota, I agree with your solution. The question does not mean that the bond was bought at par, it just says 100.000 par value, and the YTM is provided for calculating the price of the bond, and because it’s a discount bond (YTM > coupon rate), the price calculated inevitably is less than the par value. 7.9% is the realized return, which is the final return, the return when the investor actually close out his position, it’s may differ from the the require return. Because the market is uncertain, it does make sense.

oh yes, sorry i read he purchased it at par…hope my eyes won’t read like that in june Then 1st step will be to calculate the PV at YTM of 8.4 % and then use this PV moving forward

This didn’t give me the correct answer and the question states that the coupon pays annually not semiannually. Can anyone else work through this problem? Thanks!

kasinkei Wrote: ------------------------------------------------------- > Can somone explain to me how to answer this > question? I am having troubl solving and I dont > have the explanation to the solution. > > R.T. Farris purchased a 5-year, \$100,000 parvalue, > 8% annual coupon bond at a 8.4% > yield to maturity. In order to realize a compound > return of 7.9%, the amountFarris will > have to earn in reinvestment income over the > bond’s life is closest to: > > Thanks! The PV of the bond is \$98,419, which is the original investment. To realize a 7.9% annualized return over 5 years, the investor would need to receive total cash payments of \$98,419 x 1.079^5 = \$143,942 at the end of 5 years. The total inflows in the 5 years would be the \$100,000 par value at maturity + \$40,000 (5x\$8,000) of coupon payments, totaling \$140,000. Therefore, reinvestment income required to realize a 7.9% annual return is \$143,942 - 140,000 = \$3,942.

My calculation is \$1980.72 Is that a correct number?

thisisbrianly Wrote: – > The total inflows in the 5 years would be the > \$100,000 par value at maturity + \$40,000 > (5x\$8,000) of coupon payments, totaling \$140,000. > Therefore, reinvestment income required to realize > a 7.9% annual return is \$143,942 - 140,000 = > \$3,942. Your logic seems reasonable, but my humble opinion is, you are comparing the Future value , or present value at the end of year 5: total cash payments of \$98,419 x 1.079^5 = \$143,942 at the end of 5 years with the cashflow of coupon payments at each year’s end ( they will have different present value), I dont think we should sum them up to have 140k. Its like comparing orange and apple. How do you think?

maxmeomeo Wrote: ------------------------------------------------------- > thisisbrianly Wrote: > – > > The total inflows in the 5 years would be the > > \$100,000 par value at maturity + \$40,000 > > (5x\$8,000) of coupon payments, totaling > \$140,000. > > Therefore, reinvestment income required to > realize > > a 7.9% annual return is \$143,942 - 140,000 = > > \$3,942. > > > Your logic seems reasonable, but my humble opinion > is, you are comparing the Future value , or > present value at the end of year 5: > > total cash payments of \$98,419 x 1.079^5 = > \$143,942 at the end of 5 years > > with the cashflow of coupon payments at each > year’s end ( they will have different present > value), I dont think we should sum them up to have > 140k. > > Its like comparing orange and apple. > > How do you think? Not exactly following your question…but if you look at the example in the Fixed Income chapter (there is an example identical to this question), the process is pretty clear. I think its in chap. 66.

Thanks brianly! Your answer was correct according to the key, (closet to \$3950)

Booyah…going to celebrate and eat a slim jim.

Sorry I still dont get the logic behind. So you guys OMIT the present value factor when comparing these two cash flows? The present value of principal and coupon is not 140k . Can you explain why we compare this 140k and 146k? At what point of time we are evaluating these 2 cash flows?