- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 5. The Future Value and Present Value of a Series of Uneven Cash Flows

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**CFA Practice Question**

An investment promises to pay $1,000 one year from today, $1,500 two years from today and $2,000 three years from today. If the required rate of return is 11% compounded annually, what is the value of the investment today?

Correct Answer: $3,580.72

The frequency of the cash flow is Fnn. If it occurs only once, F01 will be displayed.

CF0 is displayed as a value from a previous calculation. Clear it using 2nd CLR WORK and enter 0 as your first cash flow.

The final amount is the net present value (NPV).

2nd QUIT: 0.00

CF: CFo = previous value

2nd CLR WORK: CFo = 0.00

arrow ENTER: CFo = 0.00

DownArrow: C01 = 0.00

1000 ENTER: C01 = 1,000.00

DownArrow: F01 = 1.00

DownArrow: C02 = 0.00

1500 ENTER: C02 = 1500.00

DownArrow: F02 = 1.00

DownArrow: C03 = 0.00

2000 ENTER: C03 = 2000.00

NPV: I = 0.00

11 ENTER: I = 11.00

DownArrow: NPV = 0.00

CPT: NPV = 3,580.72

We must calculate the present value of the 3 investments separately and then add these amounts.

As usual, we use the formula PV = FV / (1 + r)

^{N}1,000/(1.11)

^{1}+ 1,500/(1.11)^{2}+ 2,000/(1.11)^{3}= 900.90 + 1217.4 + 1462.3 = $3,580.71You can also use the Cash Flow Keys on the Texas Instrument BA Plus II:

The cash flows are designated CF0, C01, C02, and so on.

The frequency of the cash flow is Fnn. If it occurs only once, F01 will be displayed.

CF0 is displayed as a value from a previous calculation. Clear it using 2nd CLR WORK and enter 0 as your first cash flow.

The final amount is the net present value (NPV).

All the keystrokes are given below. Keystrokes: Display

2nd QUIT: 0.00

CF: CFo = previous value

2nd CLR WORK: CFo = 0.00

arrow ENTER: CFo = 0.00

DownArrow: C01 = 0.00

1000 ENTER: C01 = 1,000.00

DownArrow: F01 = 1.00

DownArrow: C02 = 0.00

1500 ENTER: C02 = 1500.00

DownArrow: F02 = 1.00

DownArrow: C03 = 0.00

2000 ENTER: C03 = 2000.00

NPV: I = 0.00

11 ENTER: I = 11.00

DownArrow: NPV = 0.00

CPT: NPV = 3,580.72

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**User Contributed Comments**
5

User |
Comment |
---|---|

Beret |
Or on the HP12C: 0 [g][CF0] 1000 [g][CFj] 1500 [g][CFj] 2000 [g][CFj] [f][NPV] |

hpersey |
Another quick way on the Texas BA II Plus Pro is to solve for individual cash flows, then sum their present values (according to the addivity principal of cash flows) like so: 1000,FV 11,I/Y 1,N CPT PV STO, 1 then 1500,FV 2,N CPT, PV STO + 1 finally 2500,FV 3,N CPT, PV STO + 1 then RCL 1 will give you the answer, 3580.72! |

johntan1979 |
Your "quick" is slower than the CF method, and prone to errors. By right, you SHOULD clear the TVM menu before the next batch of numbers, and you forgot each round to enter the I/Y. |

chipster |
Why would the cash flows not be designated as PMT using a financial calculator, as opposed to a PV? thanks |

gerdvar |
PMT or payment refers to equal payments, ie. multiple yet equal individual cashflows which is PMT or A in your formulas remains A=A and allows the use of expontentials to calculate PV or FV. The calc is programmed to use PMT under this premise, in this LOS these payments or cash flows are not equal, therefore they can't be put under the same definition of PMT or A |