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Basic Question 3 of 13
Suppose an investor purchases a three-year, 8% coupon bond that has a YTM equal to 10% and face value of $1,000. What is the total dollar amount of ALL cash flows received, assuming the semi-annual bond is held to maturity?
B. 322.82
C. 317.39
A. 219.64
B. 322.82
C. 317.39
User Contributed Comments 26
| User | Comment |
|---|---|
| Sheikh | Yeah, just add to initial data that face value is 1000 and reinvestment of all cash payments is assumed at the current YTM for 3 year bond! Then it would be perfectly solvable |
| cgeek | PV= 949.24 N=6 Y/I=10 -> FV=1272.07 interest on interest = FV of interest - interest = (PMT=40 I/Y = 10 N=6) - PMT * N = 272.08 - 40* 6 = 32.08 = 32.07 |
| cgeek | p/y =2 FV=1000 N=6 PMT=40 Y/I=10 -> PV = 949.24 |
| cgeek | how to get the price of the bond is 949.24 ? |
| synner | FV of coupon payments + principal - PV of the bond = total cash received |
| chenyx | agree with synner or total cash received=FV-PV |
| melissatt | How did that $1,272.06 come about? I actually got 1,263.4425 'coz I did $949.24(1.10)(1.10)(1.10) |
| anricus | Another way is to calculate the interest on the interest seperatly to no interest t1 40*(1.05^5)-40 = 11.05 t2 40*(1.05^4)-40 = 8.62 t3 40*(1.05^3)-40 = 6.30 t4 40*(1.05^2)-40 = 4.10 t5 40*(1.05)-40 = 2 t6 40 (no interest on this as received at end) Total interest on interest is 32.07 Gap Gain is same as explanation 1000-949.24 Interest is 6 cashflows of 40 = 240 Total flow is 240(intereset)+ 50.76 (CapGain)+32.07 (interest on interest) = 322.83 |
| Winner | How is the 949.24 computed using the Texas BAII |
| quantwannabe | I have been trying to use HP12C Platinum to calcualte and I got lost. Don't know!!! |
| mchu | Texas BAII: I/Y=5, N=6,, FV=1000, PMT=40, CPT PV=-949.24 Interest on Interest= FV of a series of equal cash flow- total interest income. |
| quantwannabe | Using HP 12C Platinum to calculate PV FV = 1000, PMT = 80/2 = 40 (Semi annual coupon payment in dollar amount), N = 6 (six semi annual periods in three years in percentage), i = 10/2 = 5(YTM is used as discounted) FV, PMT, N, and I, you would get PV = 949.243 |
| achu | The answer contemplates using 1.05^6 instead of 1.1^3 . |
| thekapila | for any bond always use semi annual during calculations. |
| chamad | BAA II: PV -949.24 N=3*2 I=10/2 CPT FV 1272.07 |
| steved333 | Ok. N=6, I/Y=5, PMT=40, FV=1000: CPT PV= -949.24. Then change PMT to 0 and solve for new FV= 1272.07. The diff b/w PV and FV= 322.83 |
| Richie188 | Two concepts in the answer: 1) if the price and YTM are given, the FV of the bond, including all coupon payment, can be calculated by using price x (1+YTM/2)^2t 2) the FV of all coupon payments can be calculated by using the annuity formula |
| cong | Two ways: Total Dollar returns=capital gain/loss + reinvestment income forwarded to maturity + coupon payment forwarded to maturity OR Price of the bond forward to maturity - redemption value. |
| fmhp | Mchu: Ba II plus: N=6,I/Y=5,PMT=-40,FV=-1000,CPT PV=949.24 |
| 2014 | For BA professional= enter cash flows 40 f5, 1040, i =5, nfv =1272.06 , nfv- npv = 322.83 If u want to calculate 322.83 minus 240 (cashflows) - 50.76 (capital gain) = interest income (32.06) |
| johntan1979 | steved333's way is the best and fastest |
| johntan1979 | After counting PV, zero the PMT, CPT FV. Total cash flow = FV - PV Note: PV is a negative number, so in practice, press FV + PV |
| jonan203 | i love how some of you guys come up with methods that take so long you wouldn't have enough time to finish the actual exam. |
| robbiecow | Thought I'd add one more which helps me Step 1. Calculate interest-on-interest from reinvesting the coupon using the annuity formula = $40 x ((1.05^6-1)/.05) = $272.08 Step 2. Calculate the cost of the bond (i.e., the PV of $1000 + PV of the annuity PMT) = [$1000/1.05^6] + [$40 x ((1-(1.05^(-6))/.05] = 949.24 Step 3. Add the Face Value to the Step 1 and subtract the cost in Step 2 = $322.83 Granted everything can be done with calculator, but understanding the flow of money is also important |
| AmirSh | N=6, I/Y=, PMT=40, FV=1000 Get PV=949.24. Then 949.24(1.05)^6-949.24. Takes about 30 seconds |
| seejs8396 | Interest on Interest Calc: N:6 I/Y:5 PV:0 PMT:-40, CPT FV: 272.08 Total cashflow from coupon pmt: 6*40=240 Interest on Interest: 272.08-240=32.08 |
I am using your study notes and I know of at least 5 other friends of mine who used it and passed the exam last Dec. Keep up your great work!
Barnes
Learning Outcome Statements
calculate and interpret the sources of return from investing in a fixed-rate bond;
CFA® 2025 Level I Curriculum, Volume 4, Module 10.