- Exactly one year ago, an investor purchased a $1,000 face value, zerocoupon bond with 11 years remaining to maturity. The YTM was 8.0%. Now, one year later, with market rates unchanged, an investor purchases an annuity that pays $40 every six months for 10 years. The combined value of the two investments based on the 8% BEY is approximately: A. $966. B. $1,000. C. $1,007. D. $1,456. answer given is B. can anyone explain why? i thought it was D. Thanks.
Bond: FV =1,000 PMT = 0 N = 20 i = 4 PV = 456.38 Annuity: PMT = 40 N = 20 i = 4 PV = 543.62 Sum = 1,000!
The zero coupon is worth 456, the annuity is worth 543 and change. 1000/1.04^20 = 456 for the zero coupon. To get the annuity value, N = 20 (2 paymts ./ yr * 10) I = 4 or 8/2 PMT=40 FV=0 CPT PV = 543.61 Add them up you get a G. The key is remembering to calculate the zero coupon at N=20 payments left, not 22 since a year has passed.
An easier way is to think of this problem as rebuilding a bond from strips. The zero coupon provides the final payment and the annuity provides the coupons for the next 10 years. Since both are at 8% YTM and the market rate is 8% the reconstituted bond will sell at par AKA $1000
got it. I took the annuity as another bond with a FV = 1000! the FV should be 0. thanks all.
aussie_jaco Wrote: ------------------------------------------------------- > An easier way is to think of this problem as > rebuilding a bond from strips. The zero coupon > provides the final payment and the annuity > provides the coupons for the next 10 years. > > Since both are at 8% YTM and the market rate is 8% > the reconstituted bond will sell at par AKA $1000 Aussie_Jac0 - Excellent Perspective: You can also just do a simple TVM calculation and obtain: N = 10*2= 20 i/y = 8.0/2 = 4.0 FV= 1000 Pmt = 40 (from annuity) CPT PV = 1000
aussie_jaco Wrote: ------------------------------------------------------- > An easier way is to think of this problem as > rebuilding a bond from strips. The zero coupon > provides the final payment and the annuity > provides the coupons for the next 10 years. > > Since both are at 8% YTM and the market rate is 8% > the reconstituted bond will sell at par AKA $1000 that’s the way to go.