Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
A property is expected to earn net rent of €10 000 next year. The rent is expected to grow by 3% per year forever. The required return is 7% per year. Find the value PV of the property today.
A loan of €200 000 is repaid with equal monthly payments over 30 years at 5.4% per year, compounded monthly. How much interest I is paid in total over the life of the loan?
An investment of €45 000 gives these cash flows at the end of years 1 to 4: €10 000, €9 000, €18 000, €21 000. The cost of capital is 10%. Find the net present value NPV.
A project costs €25 000 and returns €18 500, €12 500, €14 000 at the end of years 1 to 3. Find its internal rate of return IRR in percent.
A bond with a face value of €1 000 pays an annual coupon of 6% and matures in 11 years. Its yield to maturity changes from 3% to 2.5%. By how much ΔP does the bond price change?
A bond with a face value of €1 000 pays an annual coupon of 2% and matures in 4 years. The yield to maturity is 5.5%. Find the Macaulay duration D in years.
A company is financed with ordinary shares worth €10 000 000, preferred shares worth €1 000 000 and debt worth €3 000 000. The cost of equity is 9%, the cost of preferred stock 7% and the pre-tax cost of debt 4%. The tax rate is 25%. Find the WACC.
A company has 5 000 000 shares trading at €29.00; the book value of its equity is €58 000 000. It just paid a dividend of €2.30 per share, and dividends grow by 5% per year. Its debt has a market value of €145 000 000 and a pre-tax cost of 3%. The tax rate is 21%. Find the WACC, using the dividend growth model for the cost of equity.
A company sells 1 880 units at €32 each. The variable cost is €30 per unit and fixed costs are €3 000. Find the degree of operating leverage DOL at this sales level.
A product sells for €16 per unit, with a variable cost of €6 per unit and fixed costs of €5 000 per year. Budgeted sales are 900 units. Find the margin of safety MS as a percentage of budgeted sales.
Answer: PV = 250000 €
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.
Answer: I = 204302 €
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.
Answer: NPV = −604.1 €
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.
NPV is negative, so the project earns less than the required return.
Answer: IRR = 38.97 %
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.
NPV falls as the rate rises, so the IRR lies between a rate with positive NPV and one with negative NPV.
Linear interpolation gives a first estimate; repeating it (or a calculator's IRR function) gives the exact rate.
Answer: ΔP = 55.42 €
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: D = 3.875 years
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.
Answer: WACC = 7.571 %
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 = 7.849 %
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: DOL = 4.947
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Answer: MS = 44.44 %
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