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 €2 000 next year. The rent is expected to grow by 1.5% per year forever. The required return is 6.5% per year. Find the value PV of the property today.
You deposit €2 500 at the start of every year for 21 years, the first deposit today. The account pays 6% per year. How much is in the account at the end of year 21? Find FV.
An investment of €75 000 gives these cash flows at the end of years 1 to 4: €18 000, €25 000, €18 000, €24 000. The cost of capital is 8%. Find the net present value NPV.
A project costs €50 000 today. Its cash flow is €12 000 at the end of year 1 and grows by 2% per year until the last cash flow at the end of year 5. The cost of capital is 10%. Find the net present value NPV.
A bond with a face value of €1 000 pays an annual coupon of 2% and matures in 12 years. Its yield to maturity changes from 2.5% to 2%. By how much ΔP does the bond price change?
A bond with 17 years to maturity (face value €1 000, annual coupon 9%) sells for €1 091. The issuer can call it in 5 years at a call price of €1 090. Find the yield to call YTC in percent.
A company has equity worth €8 000 000 and debt worth €6 000 000. Its cost of equity is 8%, its pre-tax cost of debt is 4% and the tax rate is 25%. Find the WACC.
A company's shares have a beta of 1.4 at its current debt-to-equity ratio of 0.5. It plans to raise its debt-to-equity ratio to 1.5. The tax rate is 21%, the risk-free rate 3.5% and the market risk premium 4%. Find the cost of equity re after the change.
A product sells for €32 with a variable cost of €30 per unit. Fixed costs are €2 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 000 after tax?
A product sells for €26 per unit, with a variable cost of €20 per unit and fixed costs of €24 000 per year. Budgeted sales are 7 200 units. Find the margin of safety MS as a percentage of budgeted sales.
Answer: PV = 40000 €
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: FV = 105981 €
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: NPV = −4970 €
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: NPV = −2832 €
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: ΔP = 51.29 €
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: YTC = 8.234 %
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.
The yield to maturity is 8.002%. Investors in a premium bond expect it to be called, so the lower yield to call is the more realistic one.
Answer: WACC = 5.857 %
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: re = 12.27 %
Levered beta (Hamada): debt makes equity riskier. βL = βU·(1 + (1 − T)·D/E), where βU is the beta of the business without debt. To move a beta to another capital structure, unlever it first and then relever it at the new D/E.
Answer: Q = 1625 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 = 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