Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
You need €15 000 in 4 years. An account pays 4% per year, compounded monthly. How much must you deposit today? Find the present value PV.
You save €250 at the end of every month for 10 years. The account pays 3.6% per year, compounded monthly. How much have you saved at the end? Find FV.
You buy a bond with 4 years to maturity (face value €1 000, annual coupon 3%) when its yield to maturity is 6%. One year later, just after receiving the first coupon, you sell it when the yield to maturity is 7.5%. Find your holding period return HPR in percent.
A bond with a face value of €1 000 and an annual coupon of 7% matures in 3 years and sells for €1 055. Find its yield to maturity YTM in percent.
A company has equity worth €6 000 000 and debt worth €1 000 000. Its cost of equity is 10%, its pre-tax cost of debt is 5% and the tax rate is 30%. Find the WACC.
A company has 2 500 000 shares at €49.00 each and 20 000 bonds trading at €1 050 each. The pre-tax cost of debt is 7% and the tax rate is 28%. The share’s beta is 1.2, the risk-free rate 1.5% and the market return 7%. Find the WACC.
A project costs €500 000 today. It generates €40 000 at the end of the first year, and the cash flow then grows by 1% per year forever. The cost of capital is 11%. Find the net present value NPV.
A project costs €150 000 today. Its cash flow is €18 000 at the end of year 1 and grows by 2% per year until the last cash flow at the end of year 10. The cost of capital is 12%. Find the net present value NPV.
Answer: PV = 12786 €
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 = 36046 €
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 €30 000 yourself; the rest is interest.
Answer: HPR = 1.889 %
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 = 4.981 %
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 = 9.071 %
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 = 7.652 %
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: NPV = −100000 €
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 = −40647 €
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.
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