- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 10. Interest Rate Risk and Return
- Subject 1. Sources of Return
CFA Practice Question
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
Correct Answer: B
If the investor placed this money in a bank, it would accumulate to a total of $1,272.06 by the end of three years in order to generate a 10% rate of return. The composition of the $322.82 in cash flows ($1,272.06 - 949.24) equals:
Interest payments (coupons): 40*6 = $240
Capital gain: 1000-949.24 = $50.76
Interest on interest: $32.06
Total cash flow return: $322.82
The future value of all coupon payment: [(1+0.05)6 - 1]/0.05 * 40 = $272.08.
First compute that the price of the bond is 949.24.
If the investor placed this money in a bank, it would accumulate to a total of $1,272.06 by the end of three years in order to generate a 10% rate of return. The composition of the $322.82 in cash flows ($1,272.06 - 949.24) equals:
Interest payments (coupons): 40*6 = $240
Capital gain: 1000-949.24 = $50.76
Interest on interest: $32.06
Total cash flow return: $322.82
The future value of all coupon payment: [(1+0.05)6 - 1]/0.05 * 40 = $272.08.
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 |