Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
A credit card charges a nominal interest rate of 18% per year, compounded quarterly. Find the effective annual rate EAR in percent.
You deposit €6 000 at the start of every year for 14 years, the first deposit today. The account pays 3% per year. How much is in the account at the end of year 14? Find FV.
A project costs €60 000 today and returns €16 500, €27 000, €13 500, €17 000 at the end of years 1 to 4. The cost of capital is 8%. Assume cash flows arrive evenly through each year. Find the discounted payback period DPB in years.
An investment of €40 000 returns €9 500 at the end of each year for 10 years. Find its internal rate of return IRR in percent.
A bond with a face value of €1 000 matures in 10 years and pays annual coupons. It sells for €1 077 when the yield to maturity is 5%. Find the coupon rate c in percent.
A bond trades at €1 080 with a yield to maturity of 7% (annual compounding) and a Macaulay duration of 4.4 years. Use the modified duration to estimate the new price P if the yield falls by 25 basis points.
A share with a beta of 1.25 has a required return of 10.13%. The risk-free rate is 2%. What expected market return rm does CAPM imply?
A company has 5 000 000 shares at €43.50 each and 20 000 bonds trading at €1 000 each. The pre-tax cost of debt is 3% and the tax rate is 20%. The share’s beta is 1.3, the risk-free rate 2.5% and the market return 9.5%. Find the WACC.
A product sells for €26 per unit with a variable cost of €6 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €10 000?
A product sells for €25 per unit, with a variable cost of €15 per unit and fixed costs of €12 000 per year. Budgeted sales are 1 380 units. Find the margin of safety MS as a percentage of budgeted sales.
Answer: EAR = 19.25 %
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.
The EAR is always above the nominal rate when interest compounds more than once a year.
Answer: FV = 105593 €
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.
Each deposit is invested one year longer.
Answer: DPB = 3.869 years
Payback period: the time until the cumulative cash flows repay the initial investment. Cash is assumed to come in evenly during each year, so the last part is a fraction of a year. The simple payback ignores the time value of money; the discounted payback period uses the discounted cash flows instead.
The discounted payback is always longer than the simple payback (3.176 years).
Answer: IRR = 19.87 %
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.
The annuity factor falls as the rate rises; bracket the rate and narrow down.
Answer: c = 5.997 %
Bond pricing: a bond’s price is the present value of its cash flows, discounted at the yield to maturity (YTM): the coupons form an annuity and the face value is paid back at maturity. P = C·(1 − (1 + y)⁻ⁿ)/y + F/(1 + y)ⁿ. When the yield is above the coupon rate the bond trades below face value, and the other way round.
Answer: P = 1091 €
Duration: the Macaulay duration is the weighted average time at which a bond pays its cash flows, with the present values of the cash flows as weights: D = Σ t·PVₜ/P. The modified duration D/(1 + y) estimates the percentage price change for a small change in yield: %ΔP ≈ −Dmod·Δy.
Duration is a linear estimate; for large yield changes convexity makes the true price a little higher.
Answer: rm = 8.504 %
Cost of capital: CAPM gives the return shareholders require: re = rf + β·(rm − rf). The weighted average cost of capital mixes equity and debt by their market values: WACC = E/V·re + D/V·rd·(1 − T), with V = E + D. Interest is tax-deductible, hence the (1 − T).
Answer: WACC = 10.83 %
Cost of capital: CAPM gives the return shareholders require: re = rf + β·(rm − rf). The weighted average cost of capital mixes equity and debt by their market values: WACC = E/V·re + D/V·rd·(1 − T), with V = E + D. Interest is tax-deductible, hence the (1 − T).
Answer: Q = 1500 units
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Answer: MS = 13.04 %
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
ExamProblems · examproblems.com/courses/corporate-finance