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 1.5% per year forever. The required return is 5.5% per year. Find the value PV of the property today.
You want €75 000 in 5 years. You save the same amount at the end of every month in an account paying 4.8% per year, compounded monthly. Find the monthly deposit A.
An investment of €30 000 gives these cash flows at the end of years 1 to 3: €6 000, €10 000, €10 000. The cost of capital is 7.000000000000001%. Find the net present value NPV.
A project costs €50 000 and returns €20 000, €17 000, €21 500, €27 500 at the end of years 1 to 4. Cash flows can be reinvested at the cost of capital of 10%. Find the modified internal rate of return MIRR in percent.
A bond with a face value of €1 000 pays an annual coupon of 5% and matures in 7 years. Its yield to maturity changes from 7% to 6%. By how much ΔP does the bond price change?
A bond with a face value of €1 000 pays a 4% annual coupon in two half-yearly payments and matures in 9 years. It sells for €696. Find its yield to maturity YTM as an annual rate (twice the half-yearly yield), in percent.
A company has a debt-to-equity ratio (at market values) of 1.5. Its cost of equity is 8%, its pre-tax cost of debt is 3% and the tax rate is 30%. Find the WACC.
A company has equity with a market value of €12 000 000 and a cost of equity of 12%. Its debt consists of 8 000 bonds (face value €1 000, annual coupon 7%, 10 years to maturity) that trade at €1 036 each. The tax rate is 20%. Find the WACC, using the yield to maturity of the bonds as the pre-tax cost of debt.
A product sells for €10 per unit with a variable cost of €6 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €2 000?
A product sells for €18 per unit, with a variable cost of €12 per unit and fixed costs of €15 000 per year. Budgeted sales are 4 000 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: A = 1108 €
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 = −7495 €
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: MIRR = 18.42 %
Modified IRR: compound every inflow forward to the end of the project at the reinvestment rate (usually the cost of capital) to get the terminal value TV. MIRR is the rate that turns the initial investment into TV: MIRR = (TV/C₀)^(1/n) − 1.
Answer: ΔP = 51.96 €
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: YTM = 9 %
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 = 4.46 %
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 = 9.222 %
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 = 3000 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 = 37.5 %
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