Corporate Finance: practice problems and exam questions

Time value of money, annuities and loans, net present value and internal rate of return, and break-even analysis: the calculations behind every investment decision.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Time value of moneyfuture value · compounding and discounting · annuities and loanscalculations
  2. NPV & IRRequal cash flows · uneven cash flows · internal rate of returncalculations
  3. Bond pricing & yieldannual coupons · semi-annual coupons · yield to maturitycalculations
  4. CAPM & WACCCAPM · WACC · WACC with CAPM and market valuescalculations
  5. Break-even analysisbreak-even units · target profit · margin of safetycalculations

Exam tips for Corporate Finance

  • Match the rate to the period: monthly payments need a monthly rate and the number of months.
  • A cash flow at t = 0 is not discounted.
  • The IRR is the rate at which NPV = 0, so check it by recalculating the NPV.

Worked examples

Time value of moneyEasy
years012n = ?€1 000€2 500

You deposit €1 000 at 8% interest per year, compounded annually (interest is added at the end of each year). After how many whole years n does the balance first reach at least €2 500?

PV = €1 000FV = €2 500i = 8%

Find n (years)

Show hints
  1. Write FV = PV·(1 + i)ⁿ and solve for the exponent n.
  2. Take the natural log of both sides: n = ln(FV/PV)/ln(1 + i).
  3. FV/PV = 2.5, ln(2.5) = 0.9163.
Show the answer and the step-by-step solution

Time value of money: money today is worth more than the same amount later, because it can earn interest. With interest rate i per period, an amount grows as FV = PV·(1 + i)n. A series of equal payments (an annuity) is valued by adding up each payment, which gives the annuity formulas.

Set up the equation

1 000·(1 + 0.08)n = 2 500 → (1.08)n = 2.5

Solve with logarithms

n = ln(2.5)/ln(1.08) = 0.9163/0.07696 = 11.91

Round up to whole years

Interest is only added at the end of each year, so after 11 years the balance is still below the target.

1 000·1.0811 = €2 331.64 < €2 500
1 000·1.0812 = €2 518.17 ≥ €2 500
n = 12

Answer

n = 12 years
NPV & IRRMedium
years01234−45 00011 00010 00013 00014 000

An investment of €45 000 gives these cash flows at the end of years 1 to 4: €11 000, €10 000, €13 000, €14 000. The cost of capital is 12%. Find the net present value NPV.

r = 12%CF0 = −45 000CF1 = 11 000CF2 = 10 000CF3 = 13 000CF4 = 14 000

Find NPV (€)

Show hints
  1. Bring each cash flow back to year 0 by dividing by (1 + r)ᵗ.
  2. The initial cost is already at year 0 and counts as negative.
  3. CF1/(1 + r) = 9 821.43.
Show the answer and the step-by-step solution

Net present value: discount every cash flow back to today with the required rate of return r, then add them up: NPV = Σ CFₜ/(1 + r)ᵗ. A project with NPV > 0 earns more than r and adds value. The internal rate of return (IRR) is the rate at which NPV = 0.

Present value of each cash flow

CF0 = −45 000
CF1/(1 + 0.12)1 = 11 000/1.12 = 9 821.43
CF2/(1 + 0.12)2 = 10 000/1.254 = 7 971.94
CF3/(1 + 0.12)3 = 13 000/1.405 = 9 253.14
CF4/(1 + 0.12)4 = 14 000/1.574 = 8 897.25

Add them up

NPV = €−9 056.24

Answer

NPV = €−9 056.24

NPV is negative, so the project earns less than the required return.

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Compound interest calculatorLoan payment calculatorNPV and IRR calculatorBond price calculatorWACC calculatorCAPM calculatorBreak-even point calculatorROI calculator (return on investment)Payback period calculator (simple and discounted)

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Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.