CFA Practice Question

There are 266 practice questions for this study session.

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?

A. 219.64
B. 322.82
C. 317.39
Correct Answer: B

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
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