Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.
You invest €2 000 at 2% per year with continuous compounding. Find the value FV after 17 years.
A loan of €150 000 is repaid with equal monthly payments over 20 years. The interest rate is 4.2% per year, compounded monthly. Find the monthly payment A.
An investment of €45 000 gives these cash flows at the end of years 1 to 4: €21 000, €10 000, €20 000, €9 000. The cost of capital is 8%. Find the net present value NPV.
A project costs €200 000 today. Its cash flow is €33 500 at the end of year 1 and grows by 2% per year until the last cash flow at the end of year 6. The cost of capital is 12%. Find the net present value NPV.
A bond with a face value of €1 000 pays a 7% annual coupon in two half-yearly payments and matures in 10 years. The yield to maturity is 3% per year. Find the price P of the bond.
A bond with a face value of €1 000 and an annual coupon of 8% matures in 3 years and sells for €1 055. Find its yield to maturity YTM in percent.
A company has equity worth €10 000 000 and debt worth €3 000 000. Its cost of equity is 14%, its pre-tax cost of debt is 4% and the tax rate is 30%. Find the WACC.
A company has 5 000 000 shares trading at €27.00; the book value of its equity is €54 000 000. It just paid a dividend of €2.90 per share, and dividends grow by 5% per year. Its debt has a market value of €108 000 000 and a pre-tax cost of 6%. The tax rate is 25%. Find the WACC, using the dividend growth model for the cost of equity.
A product can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €25 per unit. Method B, more automated, has fixed costs of €40 000 per year and a variable cost of €19 per unit. At what yearly volume Q do both methods cost the same?
A company sells 5 000 units per month at €18 each, with a variable cost of €12 per unit and fixed costs of €15 000 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Answer: FV = 2810 €
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: A = 924.9 €
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 present value of N equal payments A is A·(1 − (1 + i)⁻ᴺ)/i. Set it equal to the loan and solve for A.
Answer: NPV = 5510 €
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 = −56134 €
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 = 1343 €
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 below the coupon rate, so the bond sells at a premium.
Answer: YTM = 5.945 %
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: WACC = 11.42 %
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 = 11.04 %
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 = 2500 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).
Below this volume method A is cheaper; above it the automated method B is cheaper.
Answer: Q = 7500 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).
ExamProblems · examproblems.com/courses/corporate-finance