Q4. Given the following cash flow stream:
End of Year Annual Cash Flow
1 $4,000
2 $2,000
3 -0-
4 -$1,000
Using a 10% discount rate, the present value of this cash flow stream is:
A) $3,415.
B) $3,636.
C) $4,606.
Q5. Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.
Year 1 -2,000
Year 2 -3,000
Year 3 6,000
Year 4 25,000
Year 5 30,000
A) $58,164.58.
B) $65,144.33.
C) $33,004.15.
答案和详解如下：
Q4. Given the following cash flow stream:
End of Year Annual Cash Flow
1 $4,000
2 $2,000
3 -0-
4 -$1,000
Using a 10% discount rate, the present value of this cash flow stream is:
A) $3,415.
B) $3,636.
C) $4,606.
Correct answer is C)
PV(1): N = 1; I/Y = 10; FV = -4,000; PMT = 0; CPT → PV = 3,636
PV(2): N = 2; I/Y = 10; FV = -2,000; PMT = 0; CPT → PV = 1,653
PV(3): 0
PV(4): N = 4; I/Y = 10; FV = 1,000; PMT = 0; CPT → PV = -683
Total PV = 3,636 + 1,653 + 0 − 683 = 4,606
Q5. Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.
Year 1 -2,000
Year 2 -3,000
Year 3 6,000
Year 4 25,000
Year 5 30,000
A) $58,164.58.
B) $65,144.33.
C) $33,004.15.
Correct answer is A)
N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00
Sum the cash flows: $58,164.58.
Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.
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Q1. Which one of the following statements best describes the components of the required interest rate on a security?
A) The nominal risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
B) The real risk-free rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
C) The real risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
Correct answer is C)
The required interest rate on a security is made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.
Q2. T-bill yields can be thought of as:
A) nominal risk-free rates because they do not contain an inflation premium.
B) real risk-free rates because they contain an inflation premium.
C) nominal risk-free rates because they contain an inflation premium.
Correct answer is C)
T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal risk-free rates rather than real risk-free rates since they contain a premium for expected inflation.
Q3. The real risk-free rate can be thought of as:
A) exactly the nominal risk-free rate reduced by the expected inflation rate.
B) approximately the nominal risk-free rate reduced by the expected inflation rate.
C) approximately the nominal risk-free rate plus the expected inflation rate.
Correct answer is B)
The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:
Nominal risk-free rate = real risk-free rate + expected inflation rate.
Therefore we can rewrite this equation in terms of the real risk-free rate as:
Real risk-free rate = Nominal risk-free rate – expected inflation rate
The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal)
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