Overview of Relevant Formulas Corporate Finance (B40.2302) _________________________________________________________________________________________ 1. Present value of $1 to be received after t years at discount rate r: 2. Present value of annuity of $1 per year for t years at discount rate r: $1 (1 + r )t

⎡1 − (1 + r ) − t ⎤ ⎢ ⎥ × $1 r ⎣ ⎦ 1 ⎡ (1 + g )t ⎤ 3. Present value of growing annuity of $1 at rate g per year at discount rate r: ⎢1 − ⎥ × $1 r − g ⎣ (1 + r )t ⎦ $1 r

4. Present value of perpetuity of $1 per year at discount rate r:

5. Present value of perpetuity of $1 with constant growth rate g at discount rate r:

$1 r−g

6. Measures of risk for individual financial asset i:

Variance of returns:
Standard deviation of returns: Covariance of returns assets i and j:

Var (ri ) = σ i2 = Expected value of [ri − E (ri )]2

σ i = σ i2
Cov(ri , rj ) = σ ij = Exp. value of [ri − E (ri )][rj − E (rj )]

Correlation between returns i and j: Expected portfolio return (N assets):

ρij =

σ ij σ iσ j
N i =1 N

E (rp ) = ∑ wi ri (weights wi)

Portfolio variance (N assets): 7. Beta of financial asset i:

σ = ∑∑ wi w jσ ij (weights wi, wj)
2 p i =1 j =1

N

βi =

Cov(ri , rm ) σ im = 2 Var (rm ) σm

8. Capital Asset Pricing Model → Expected return financial asset i: r = rD ×

E ( ri ) = rf + [ E (rm ) − rf ] × β i

9. Weighted Average Cost of Capital (WACC):

D E × (1 − T ) + rE × V V

D⎤ D ⎡ 10. Cost of capital levered firm: r = rA ⎢1 − T × ⎥ (scenario 1) or r = rA − T × rD × (scenario 2) V V⎦ ⎣ D D 11. Cost of equity levered firm: rE = rA + [rA − rD ] × × (1 − T ) (scenario 1) or rE = rA + [rA − rD ] × (scenario 2) E E D D 12. Equity beta levered firm: β E = β A + [ β A − β D ] × × (1 − T ) (scenario 1) or β E = β A + [ β A − β D ] × (scenario 2) E E 13. Asset beta levered firm: β A = (1 − T ) D E D E × βD + × β E (scenario 1) or β A = × β D + × β E (scenario 2) V V E + (1 − T ) D E + (1 − T ) D

...1、Formulas：
(1) Sustainable growth rate=retention ratio*ROE=PRAT (P: Profit margin, R:
retention ratio=retained E/E; A: Asset turnover ratio=sales/asset; T:
Asset/beginning of the period equity)
(2) Compounding an investment m times a year for T years provides for future
value of wealth: FV=C0*(1+r/m)^(m*T)
(3) Future value of an investment compounded continuously over many
periods: FV=C0*e^(r*T) e=2.718
(4) Perpetuity: PV=C/r; Growing Perpetuity: PV=C/(r-g) g=growth...

...if it were the firm’s only asset
-Corporate or within-firm risk reflects effect of project on firm’s risk, measured by project’s effect on firm’s earnings variability
-Market or Beta risk reflects effects of project on stockholders’ risk, measured by project’s effect on firm’s beta coefficient
-Risk-adjusted cost of capital is cost of capital appropriate for given project, given its risk. Greater the risk, higher the cost of capital
Chapter 11
-Corporate...

...Advanced CorporateFinance I SS 2012
Problem Set 1 Valuing Cash Flows
Problem Set 1
Valuing Cash Flows
Exercise 1 (Ex. 11.2 - 11.6 GT): Assume that Marriott’s restaurant division has the following joint distribution with the market return: Market Scenario Bad Good Great .25 .50 .25 Probability Market Return (%) -15 5 25 YR 1. Cash Flow Forecast $40 million $50 million $60 million
Assume also that the CAPM holds. 11.2 Compute the expected year 1...

...be used as the required return when analyzing a potential acquisition of a retail outlet.
C. is the return investors require on the total assets of the firm.
D. remains constant when the debt-equity ratio changes.
E. is unaffected by changes in corporate tax rates.
7. Which one of the following is the primary determinant of a firm's cost of capital?
A. debt-equity ratio
B. applicable tax rate
C. cost of equity
D. cost of debt
E. use of the funds
8. Scholastic Toys is...

...cash flows: (Time) receive $CFt each period until time T. Constant discount rate 10%. Investment of $100 in time 0. CFs of $22 in t=1 and $121 in t=2
Annuity: receive $CF each period until time N Perpetuity: receive $CF each period forever
Gordon Formula- (perpetuity) for valuing a firm with growing dividends
π =risk premium.the risk premium is everything above the risk free rate, r+π = Risk Adjusted Discount Rate (RADR)
Nominal rate - Actual rate of return( using actual...

...firm
* VL = VU + PV (Tax Benefits) + Corporate Benefits (Debt) – Costs of Financial Distress
* VL is the value of the firm with leverage, VU is the value of the all-equity firm
* 2 methods used to incorporate tax benefits to previous valuation techniques: APV & WACC
* APV (Adjusted Present Value – adjusts for tax by increasing the cash flows due to the tax benefit
* Increase each annual CF by Debt capacity * Debt Rate * Corporate Tax...

...e TCH321 – CORPORATEFINANCE MOCK EXAM Time: 1 hour 30 minutes The exam lasts 1 hour and 30 minutes and consists of 5 questions. Approved calculators are permitted. You are not allowed to use Excel. This is a closed book exam. You are NOT permitted to access any other material in either written or electronic form. All numerical answers should be reported to TWO decimal places. To ensure the accuracy of your answer, you should perform all intermediate calculations...

...ﬁve years, and after ﬁve years will be sold at an estimated 20 million Euros. The company estimates that the EBITDA from the sale of purple trousers will be 12 million Euros per year for the coming 5 years. The company’s earnings are subject to a corporate tax rate of 40%. If the ﬁrm’s equity cost of capital is 9.6% what is the NPV of this project? (a) 0.48 million Euros (b) 0.72million Euros (c) 0.26 million Euros (d) 0.92 million Euros Instead of selling the machines after ﬁve...