Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
You need €15 000 in 6 years. An account pays 4.8% per year, compounded quarterly. How much must you deposit today? Find the present value PV.
You save €300 at the end of every month for 11 years. The account pays 4.8% per year, compounded monthly. How much have you saved at the end? Find FV.
An investment of €30 000 gives these cash flows at the end of years 1 to 4: €11 000, €10 000, €11 000, €10 000. The cost of capital is 10%. Find the net present value NPV.
A project costs €100 000 today. Its cash flow is €14 000 at the end of year 1 and grows by 5% per year until the last cash flow at the end of year 8. The cost of capital is 10%. Find the net present value NPV.
A bond with a face value of €1 000 pays a 5% annual coupon in two half-yearly payments and matures in 7 years. The yield to maturity is 7% per year. Find the price P of the bond.
A bond with a face value of €1 000 and an annual coupon of 4% matures in 9 years and sells for €895. Find its yield to maturity YTM in percent.
A company has equity worth €3 000 000 and debt worth €3 000 000. Its WACC is 5.58%, its pre-tax cost of debt is 4.5% and the tax rate is 30%. Find the cost of equity re.
A company has equity with a market value of €8 000 000 and a cost of equity of 9%. Its debt consists of 4 000 bonds (face value €1 000, annual coupon 6%, 6 years to maturity) that trade at €1 025 each. The tax rate is 25%. Find the WACC, using the yield to maturity of the bonds as the pre-tax cost of debt.
A product sells for €12 with a variable cost of €8 per unit. Fixed costs are €4 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
A product sells for €30 per unit, with a variable cost of €20 per unit and fixed costs of €50 000 per year. Budgeted sales are 6 000 units. Find the margin of safety MS as a percentage of budgeted sales.
Answer: PV = 11266 €
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 = 52031 €
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.
You paid in €39 600 yourself; the rest is interest.
Answer: NPV = 3359 €
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 positive, so the project earns more than the required return.
Answer: NPV = −12988 €
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: P = 890.8 €
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 is above the coupon rate, so the bond sells at a discount.
Answer: YTM = 5.511 %
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: re = 8.01 %
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 = 7.348 %
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 = 16.67 %
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