Chapter 3 - Principles of Investment Risk & Return Flashcards
(143 cards)
Which of the following best describes the concept of Time Value of Money (TVM)?
a) Money held today and money received in the future have the same value if inflation is low.
b) Future cash flows should always be discounted using the risk-free rate to determine their present value.
c) A sum of money today is worth more than the same sum in the future due to its potential to generate returns.
d) The value of money remains constant over time if interest rates are stable.
Answer: c
Explanation: TVM states that money today has greater value than the same amount in the future because it can be invested and earn returns. This principle applies regardless of inflation or interest rates.
A firm expects to receive £500,000 in five years. Assuming a discount rate of 7% per annum, what is the approximate present value of this future sum?
a) £356,490
b) £410,210
c) £356,130
d) £392,480
Answer: a
Explanation: Present Value (PV) is calculated using the formula:
PV = FV/(1+r)^t
PV = 500,000/(1.07)^5 = 356,490
This shows how discounting adjusts for the time value of money.
An investor has the option to receive £50,000 today or £70,000 in six years. If the investor’s required rate of return is 5% per annum, which option is financially preferable?
a) Taking the £50,000 today is better, as future money is always worth less.
b) Taking the £70,000 in six years is better, as it is a larger sum.
c) Both options are equivalent in value when adjusted for the time value of money.
d) The decision depends on the risk-free rate rather than the investor’s required return.
Answer: b
Explanation: To compare, we discount £70,000 back to present value:
𝑃𝑉 = £70,000 / (1.05)^6 ≈ £52,300
Since £52,300 (discounted value) is greater than £50,000, the future amount is slightly preferable. However, if opportunity costs or risk are considered, taking £50,000 now may still be reasonable.
Which of the following best describes the time value of money (TVM)?
A) Money today is worth the same as money in the future due to inflation adjustments.
B) Money today is worth more than money in the future because of its potential earning capacity.
C) Money today is worth less than money in the future due to risk factors.
D) Money today and in the future have the same value if invested at a risk-free rate
✅ Answer: B
📖 Explanation: The time value of money principle states that a sum of money is worth more today than in the future because it can be invested to generate returns.
If an investor deposits £5,000 in a savings account offering 6% annual compound interest, how much will they have after 8 years?
A) £7,540.20
B) £7,969.24
C) £8,540.60
D) £8,961.40
✅ Answer: B
📖 Explanation: Use the future value formula:
FV = PV × (1 + r)ⁿ
= £5,000 × (1.06)⁸ = £7,969.24
An investment of £10,000 grows to £16,000 in 6 years. What is the approximate annual compound interest rate?
A) 7.9%
B) 8.2%
C) 8.6%
D) 9.2%
✅ Answer: B
📖 Explanation: Use the compound interest formula solved for r:
FV = PV × (1 + r)ⁿ
16,000 = 10,000 × (1 + r)⁶
(1 + r) = (16,000/10,000)^(1/6)
r ≈ 8.2%
What is the present value of £50,000 received in 10 years, assuming a discount rate of 5%?
A) £30,675
B) £33,891
C) £30,695
D) £41,322
✅ Answer: B
📖 Explanation: Use the present value formula:
PV = FV / (1 + r)ⁿ
= 50,000 / (1.05)¹⁰ = £30,695
An investment requires an initial outlay of £20,000 and returns £5,000 per year for 6 years. If the discount rate is 10%, what is the net present value (NPV)?
A) £2,150
B) £2,890
C) £1,776
D) £4,275
✅ Answer: C
📖 Explanation: Use the PV of an annuity formula
= £1,776
A 10-year bond pays a fixed interest rate of 4% per annum. If inflation is consistently 5% per annum, what is the real rate of return?
A) -1.00%
B) -0.95%
C) 0.96%
D) 1.02%
✅ Answer: B
📖 Explanation: Use the Fisher equation:
Real Rate ≈ (1 + Nominal Rate) / (1 + Inflation Rate) - 1
= (1.04 / 1.05) - 1 ≈ -0.95% (indicating a real loss).
If the inflation rate is 4% per year, how much will a £10,000 product cost in 15 years?
A) £15,231
B) £18,009
C) £18,006
D) £20,121
✅ Answer: B
📖 Explanation: Use the inflation-adjusted future value formula:
FV = PV × (1 + inflation rate)ⁿ
= 10,000 × (1.04)¹⁵ = £18,009
What is the future value of an annuity that pays £2,500 annually for 10 years at an interest rate of 5%?
A) £31,444
B) £32,578
C) £34,719
D) £36,288
✅ Answer: A
📖 Explanation: Use the future value of an annuity formula:
FV = P × [(1 + r)ⁿ - 1] / r
= £2,500 × [(1.05)¹⁰ - 1] / 0.05
= £31,444
If an investment earns 8% per year, how long will it take for it to double in value?
A) 9 years
B) 8.9 years
C) 9.1 years
D) 10.2 years
✅ Answer: A
📖 Explanation: Use the Rule of 72:
Time (years) = 72 / interest rate
= 72 / 8 = 9 years
What is the main reason that future value calculations require compounding?
A) To account for declining purchasing power.
B) To reflect the time value of money and reinvestment of earnings.
C) To ensure cash flows remain constant.
D) To match inflationary adjustments.
✅ Answer: B
📖 Explanation: Future value accounts for reinvestment of returns, compounding interest over time.
A pension fund is expected to grow at an annual rate of 7%. How much should an investor contribute annually for 20 years to accumulate £1,000,000?
A) £18,289
B) £20,503
C) £22,657
D) £24,393
✅ Answer: D
📖 Explanation: Use the future value of an annuity formula:
FV = P × [(1 + r)ⁿ - 1] / r
Solving for P gives £24,393 per year.
If an investor requires a real return of 3% and expects inflation to be 2.5%, what nominal return should they target?
A) 5.62%
B) 5.57%
C) 5.93%
D) 6.05%
✅ Answer: B
📖 Explanation: Using the Fisher equation:
Nominal Rate ≈ (1 + Real Rate) × (1 + Inflation Rate) - 1
= (1.03 × 1.025) - 1 = 5.57%
A company is evaluating a project that requires an investment of £500,000 and generates annual cash flows of £120,000 for 5 years. If the discount rate is 6%, should the company proceed?
A) Yes, because the NPV is positive.
B) Yes, because the IRR exceeds the discount rate.
C) No, because the NPV is negative.
D) No, because the payback period exceeds 5 years.
✅ Answer: A
📖 Explanation: Using NPV formula, the NPV is positive, meaning the investment adds value.
What impact does a higher discount rate have on the present value of future cash flows?
A) Increases the present value.
B) Decreases the present value.
C) Has no effect on the present value.
D) Causes future cash flows to grow at a higher rate.
✅ Answer: B
📖 Explanation: A higher discount rate reduces present value, as future cash flows are discounted more heavily.
If an investor deposits £1,500 monthly into an account earning 5% compounded monthly, how much will they have in 10 years?
A) £193,685
B) £204,122
C) £232,923
D) £238,901
✅ Answer: C
📖 Explanation: Use the future value of an annuity formula for monthly contributions.
What is the main risk of relying solely on the Rule of 72 for estimating investment growth?
A) It only applies to interest rates below 5%.
B) It does not account for inflation.
C) It assumes simple interest instead of compound interest.
D) It becomes inaccurate for very high or low rates.
✅ Answer: D
📖 Explanation: The Rule of 72 is an approximation, and becomes less accurate at extreme interest rates.
If inflation is consistently 3% per year, how much will £5,000 be worth in real terms in 25 years?
A) £2,388
B) £2,890
C) £3,050
D) £3,290
✅ Answer: A
📖 Explanation: Use the inflation-adjusted present value formula:
PV = FV / (1 + inflation rate)ⁿ
= £5,000 / (1.03)²⁵ = £2,388
A company is considering two investments: Project A with a 10% annual return and Project B with a 12% annual return. If inflation is 4%, what is the real rate of return for each?
A) 5.8% for A and 7.7% for B
B) 5.9% for A and 7.7% for B
C) 6.0% for A and 7.6% for B
D) 6.1% for A and 7.8% for B
✅ Answer: A
📖 Explanation: Use the Fisher equation for each:
Real Rate = (1 + Nominal Rate) / (1 + Inflation Rate) - 1
Project A: (1.10 / 1.04) - 1 ≈ 5.8%
Project B: (1.12 / 1.04) - 1 ≈ 7.7%
What happens when interest is compounded continuously rather than annually?
A) The final amount is always twice the principal.
B) The investment grows at an exponentially higher rate.
C) The interest rate becomes less important.
D) The investment’s value decreases over time.
✅ Answer: B
📖 Explanation: Continuous compounding leads to exponential growth, as per the formula:
FV = PV × e^(rt)
If an investor has the option to receive £50,000 today or £75,000 in 10 years, what discount rate would make them indifferent?
A) 3.8%
B) 4.5%
C) 4.1%
D) 6.0%
✅ Answer: C
📖 Explanation: Solve using FV = PV (1 + r)ⁿ and find r that equates the present values.
What is the primary factor influencing the risk premium required by investors for holding a particular asset?
A) The risk-free rate of return
B) The asset’s correlation with market movements
C) The standard deviation of historical returns
D) The investor’s subjective risk tolerance
✅ Answer: B
📖 Explanation: The risk premium compensates for the systematic risk of an asset, which is measured by its beta (correlation with the market).