The minimum attractive rate of return is the rate
Answer: A
It reflects the cost of capital, the returns available elsewhere and the organisation's attitude to risk, and it is the rate used to discount the alternatives. Setting it too high rejects sound projects and too low accepts poor ones.
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A firm's cost of capital as a discount rate represents the
Answer: B
Correct answer: weighted cost of its debt and equity
The cost of capital is what the firm must earn to satisfy everyone who has funded it, so it weights the cost of debt and the required return on equity by their proportions in the capital structure. A project earning less than that destroys value even if it shows an accounting profit.
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A riskier project is normally evaluated at a
Answer: C
Adding a risk premium to the discount rate penalises distant and uncertain cash flows more heavily, so the project must promise more to be accepted. Adjusting the cash flows instead, by expected values, is the alternative treatment.
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The rule of 72 estimates the
Answer: D
Correct answer: time for a sum to double at a given interest rate
\[ n \approx \frac{72}{i}, \] with \( i \) as a percentage. At 8 per cent a sum doubles in about nine years, against the exact figure of 9.01. The approximation is good between about 6 and 15 per cent and is useful precisely because it needs no tables.
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1000 invested at 10 per cent simple interest for 3 years grows to
Answer: A
Simple interest is charged on the original 1000 alone, so it gives 100 in each of the three years and the total is 1300. Compound interest at the same rate would give 1331, the extra 31 being interest earned on interest.
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1000 invested at 10 per cent compounded annually for 3 years grows to
Answer: B
Correct answer: 1331
\[ F = 1000 \times 1.1^3 = 1000 \times 1.331 = 1331. \] Simple interest would have given 1300, so the 31 is the interest earned on interest over three years. The gap widens rapidly: over thirty years the same rate gives 17,449 compound against 4,000 simple.
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The present worth of 1331 receivable in 3 years at 10 per cent is
Answer: C
Dividing by 1.1 three times returns the original sum, since discounting is the exact inverse of compounding. It is the same relation as the previous question read in the opposite direction, and a useful check on any such calculation.
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The present worth of 10 000 receivable in 5 years at 8 per cent is about
Answer: D
Correct answer: 6806
\[ P = \frac{10{,}000}{1.08^5} = \frac{10{,}000}{1.4693} = 6{,}806. \] Multiplying by 1.4693 instead of dividing gives 14,693, which is offered as a distractor and is the classic error - a present worth must always be smaller than the future sum at a positive rate.
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Raising the discount rate from 8 to 12 per cent changes the present worth of that same 10 000 to about
Answer: A
One point one two raised to the fifth power is 1.7623, and dividing 10 000 by it gives 5674 against the 6806 obtained at 8 per cent. Four percentage points on the rate have cost over a sixth of the present worth, which is why the rate is argued over so hard.
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A nominal 12 per cent compounded monthly gives an effective annual rate of about
Answer: B
The monthly periodic rate is 1 per cent, and raising 1.01 to the twelfth power gives 1.1268. Continuous compounding of the same nominal rate would give 12.75 per cent, which is the ceiling on the effect however often one compounds.
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