Rate of Return Analysis Questions and Answers

Answer: A

Correct answer: ignores all cash flows after payback is reached

Two projects paying back in three years rank equally under the criterion even if one then stops and the other runs profitably for twenty more. Since everything of value in a long-lived project happens after payback, the measure is blind to precisely what matters most. It also ignores the time value of money, which the discounted form corrects.

Answer: B

Correct answer: discounting the receipts before accumulating them

The discounted form applies the required rate to each receipt before adding it to the running total, so the recovery must cover both the capital and the interest on it. This removes one of the two objections to the simple form; it does not remove the other, since flows beyond the payback point are still ignored.

Answer: C

Correct answer: how long capital is at risk

Payback is a crude measure of liquidity and exposure, and that is a genuine concern - particularly in an unstable market or a politically uncertain country, where a project recovering its cost in two years is safer than one taking eight regardless of what the present worths say. Used as a supplementary screen it is defensible; used alone it is not.

Answer: D

The series present worth factor required is 10 000 over 2500, that is 4.0, and at 6 years the tables give 4.0 at about 13 per cent. Total receipts of 15 000 against 10 000 spent would suggest far more if timing were ignored.

Answer: A

Correct answer: 14 per cent

Linear interpolation between the two points gives \[ i \approx 12 + 3 \times \frac{800}{800 + 400} = 12 + 2 = 14\ \mathrm{per\ cent}. \] The present worth function is convex rather than straight, so interpolation over a wide interval understates slightly; over three percentage points the error is small.

Answer: B

Negative to positive is one change, positive to positive is none, and positive to negative is the second, so there are two in all. Descartes' rule therefore permits at most two positive roots, and the project is not a conventional investment.

Answer: C

Correct answer: 12.5 per cent

\[ 5000(1+i)^4 = 8000 \quad\Rightarrow\quad (1+i)^4 = 1.6 \quad\Rightarrow\quad 1+i = 1.6^{0.25} = 1.125, \] giving 12.5 per cent. A single future sum makes the internal rate a direct calculation with no trial and error, which is worth recognising when it occurs.

Answer: D

Correct answer: 3500 a year for 8 years

The increment is the difference between the two cash flows, term by term: a further 20,000 spent at the outset in exchange for a further \( 15{,}500 - 12{,}000 = 3{,}500 \) a year over the same eight years. The question to be asked of that increment is whether it alone earns the minimum attractive rate.

Answer: A

The series present worth factor needed is 20 000 over 3500, that is 5.714, which at 8 years corresponds to about 8 per cent. If the minimum attractive rate were 10 per cent the increment would fail and X would be preferred.

Answer: B

Correct answer: 4 years

\[ \frac{40{,}000}{10{,}000} = 4\ \mathrm{years}. \] With uniform receipts the simple payback is a single division. Note what the figure ignores: no interest is charged on the money while it is out, and whatever happens after year four does not enter the calculation.