Cumulative level test: Measurement and Applied Planning: Numbers You Can Defend

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12 questions · 80% to pass · no timer. This longer test revisits both units in the level. These authored questions assess recognition and application of the taught distinctions, not professional qualification. You may review the lessons and retry. Repeat attempts reuse the question bank; a remembered answer is not proof of transfer to a new situation.

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Question 1

A borrower is offered a $12,000 two-year instalment loan at an assumed 6 percent, a 60-month version of the same loan at the same rate, and a $12,000 advance priced at a factor rate of 1.25 repaid over 24 equal monthly payments. The offer sheet states that all three cost about the same because the first two share a rate and the third is quoted as a multiple. Using the level's methods, give the three costs and state which single assumption the comparison depends on.The 24-month loan costs $764.34 of interest on payments of $531.85, the 60-month version costs $1,919.62 on payments of $231.99, and the 1.25 factor repaid over 24 equal monthly payments of $625 implies a monthly rate of about 1.868 percent or roughly 22.4 percent annualised, so the three are not equivalent and the comparison depends on the term, the payment schedule and whether interest is charged on a declining balanceAll three cost about $1,440 in interest, because each is a $12,000 advance at a rate or multiple of roughly 25 percent or 6 percent applied to the full amount over the term

Question 2

A facility of $40,000 offered for 36 months at an assumed 8 percent carries $1,300 of fees, while a competing offer of the same amount for the same term carries a 6.75 percent rate and $150 of fees. A summary ranks the second offer below the first on cost because 6.75 percent is lower than 8 percent plus fees. Check the ranking using total cost against money received, and say whether the summary's reason holds.The first offer is cheaper because its 8 percent rate applies to a smaller principal once the fees are deducted, so the fee reduces the interest as wellThe 8 percent offer with $1,300 of fees gives payments of $1,253.45, total payments of $45,124.37 and an all-in cost of $6,424.37 against $38,700 received, while the 6.75 percent offer with $150 of fees gives payments of $1,230.52, total payments of $44,298.61 and an all-in cost of $4,448.61 against $39,850 received, so the lower-rate offer is cheaper but the stated reason for that ranking is wrong

Question 3

A firm reports a month with $66,000 invoiced, $58,900 collected, $47,500 of recognised expenses including $1,200 of depreciation, payables up $2,300 and $4,100 of inventory bought for cash. It holds $27,000 of cash and its average monthly net cash outflow is $1,500. Separately, a quarterly insurance deposit of $4,000 falls in one month of each quarter. Compute the operating cash, the runway and the effect of the deposit month.Profit is $18,500 and operating cash is $10,800, the bridge being $7,100 of receivables, minus the $2,300 payable increase and $1,200 depreciation, plus the $4,100 inventory purchase, so the runway is 27,000 divided by 1,500 or 18 months, and the deposit month raises the outflow to $5,500 and cuts the runway to about 4.9 months if that outflow were sustainedThe runway is 18 months from the reported profit of $18,500, because the profit is the cash the month generated and the deposit is a one-off that can be financed when it arrives

Question 4

A firm with $520,000 of assets, $315,000 of liabilities including $180,000 of floating-rate debt, $92,000 of earnings before interest and taxes and $23,000 of interest is negotiating a loan whose covenant requires debt-to-equity to stay below 1.80 and times interest earned to stay above 3.50. A vice-president says the firm has room on both. Test that claim under a two point rate rise and a $60,000 expansion funded by new debt.The firm has room, because 1.54 is comfortably below 1.80 and coverage of 4.0 times is comfortably above 3.50, and covenants are tested on the reported balance sheet rather than on stressed figuresDebt-to-equity is 1.54 today and a $60,000 debt-funded expansion would raise liabilities to $375,000 against unchanged equity of $205,000, taking the ratio to 1.83 and breaching the 1.80 limit, while times interest earned of 4.0 falls to 3.46 under a two point rise on the floating debt alone, which is below the 3.50 floor before any interest on the new debt is counted

Question 5

A product sells at $52 with a $31 variable cost and $26,000 of monthly fixed costs. The owner wants both to cut the price to $46 and to add a $1,850 monthly fixed cost for a delivery vehicle. Compute the break-even volume under each change and under both together, and say what the combination requires.Break-even is about 1,238 units as it stands, 1,733 units after the price cut alone, 1,326 units after the added fixed cost alone, and about 1,857 units with both, so the combination requires 50 percent more volume than today before a cent of additional profit is earnedBreak-even rises to about 1,857 units with both changes, and because a 50 percent volume increase would spread the existing fixed costs further the added fixed cost is self-financing

Question 6

A household plans $3,180 of essentials, $1,240 of variable spending and $420 of sinking funds, which includes $150 a month for an $1,800 annual premium, against $5,400 of income. The month delivered $3,290 of essentials, $1,690 of variable spending, the planned sinking funds, and an $980 repair, and its worst week showed a $1,250 shortfall because income arrived on the first and $2,450 of bills fell on the twenty-eighth. Diagnose the plan and state the two changes it implies.The variance is $1,540 and the fix is to reduce the essentials line, since at $3,290 it is the largest single outflow and therefore the cause of the overrunThe variance is $1,540 made up of $110 of essentials, $450 of variable spending and the $980 repair, the shortfall is a timing problem rather than a total problem, and the two changes are to convert the repair class into a sinking fund and to move bill dates or hold a weekly buffer so the fourth week does not go negative

Question 7

A business collects 9.5 percent tax on $62,000 of monthly taxable sales, and pays four employees $2,850 each with illustrative federal withholding of $250, employee social security at 6.2 percent and Medicare at 1.45 percent. It has been using both collected amounts to fund seasonal inventory. Compute the amounts at stake over a year and state the exposure.Sales tax collected is $5,890 a month, or $70,680 over a year, and the employee payroll share is $218.03 per employee a month, roughly $10,465 a year across four employees, and the payroll amount is trust fund money whose unpaid balance can be assessed against a responsible person personally, while the sales tax liability remains with the registered seller with additional tax, penalty and interestThe amounts are $70,680 and about $10,465, and both can be funded from seasonal inventory sales because the liability is settled annually and the business remains open

Question 8

A business holds a 2026 income tax return with supporting schedules, employment tax records for 2026, the invoice and proof of payment for a machine bought in 2026 and still in use, a file of customer credit applications, and a spreadsheet listing expenses with no underlying receipts. State what may be destroyed and when, and what must be created or disposed of instead.Everything except the machine records may be destroyed after three years, and the customer credit applications may be stored indefinitely because keeping records is always safer than destroying themSupporting records run to the end of that return's period of limitations, employment tax records at least four years from when the tax became due or was paid, the machine records until the year of disposal plus the assessment window because they support depreciation and basis, the credit applications must be disposed of under the FTC rule by burning, pulverising or shredding, and the receipt-free spreadsheet is a summary rather than substantiation and needs its source documents

Question 9

A memo compares option X, costing $50,000 and returning $11,000 a year for seven years, with option Y, costing $75,000 and returning $15,000 a year for seven years, and reports only that Y is preferable because it costs more and returns more each year. Rewrite the conclusion using an assumed 9 percent discount rate, and state what the memo must also contain.At 9 percent the net present value is $5,362.48 for X against $494.29 for Y, with internal rates of return of 12.13 percent and 9.20 percent, so X is preferable on both criteria; the memo must state its discount rate, report both criteria, bound the result across at least one case that would reverse it, and give a review date with a specific observation that would prove it wrongY is preferable because it is the larger commitment returning more dollars a year, and the difference of $4,868.19 in present value is within the tolerance of an assumed discount rate

Question 10

A saver is told that an assumed 7 percent nominal return over a long horizon will preserve purchasing power comfortably. Inflation is assumed at 3 percent, the return is taxable at an assumed 22 percent marginal rate, and a competitor's product is quoted at 1.75 percent per month on a declining balance. Compute the real after-tax return and identify which quoted figure belongs to which measurement.The real return is 4 percent because the Fisher approximation of 7 percent minus 3 percent is exact, and the 1.75 percent monthly figure equals 21 percent a yearThe nominal 7 percent against 3 percent inflation is 3.8835 percent real before tax; after an assumed 22 percent tax the nominal return is 5.46 percent, which is 2.3883 percent real, while the 1.75 percent monthly figure is a stated periodic rate that must be compounded and priced against the payment schedule before it can be compared with an annual return

Question 11

A firm has revenue of $720,000, a 32 percent gross margin, $168,000 of fixed costs and $150,000 of floating-rate debt at an assumed rate. Compute the operating profit, break-even revenue and cushion, then test a 10 percent fall in revenue and a four percentage point fall in margin, and state which assumption the business depends on more.Operating profit is $62,400, break-even revenue is $525,000 and the cushion is $195,000 or 27.1 percent of revenue; a 10 percent revenue fall with the margin held reduces profit by $23,040 to $39,360, while a four point margin fall at unchanged revenue reduces it by $28,800 to $33,600, so the margin assumption carries more weight, and a two point rate rise on $150,000 would add $3,000 of interest on topThe revenue fall is the greater risk because revenue is the larger number, so a $23,040 reduction outweighs the effect of the margin change at $28,800

Question 12

A lender's summary of a financing offer states that the rate is a 1.30 factor which annualises to 26 percent, that the borrower receives $48,750 on a $50,000 facility because of $1,250 of fees, and that the deal is cheaper than a 12 percent instalment loan of the same size and term because the total repayment is lower. Identify every defect in the summary and give the correct treatment of each figure.The factor rate of 1.30 is equivalent to 30 percent for the year, and because the fee reduces the amount advanced the borrower pays no interest on money never received, which brings the effective cost below the 12 percent instalment loanThe factor rate is a multiple rather than a rate and its annualised equivalent depends on the repayment schedule: 1.30 on $50,000 fixes $65,000 to repay, and discounting twelve equal payments of $5,416.67 against the $48,750 actually received gives a monthly rate of about 4.73 percent and an annualised figure near 56.75 percent nominal, while a 12 percent instalment loan of the same size repays $4,442.44 a month or $53,309.27 in total, so the factor deal is more expensive on both total repayment and annualised cost and the two can only be ranked by discounting each payment stream against the money received

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