COMMERCE 298 Intro to Finance Midterm Review Package Tutor: Chanwoo Yim BCom 2016, Finance 1. Time Value 2. DCF (Discounted Cash Flow) 2.1 Constant Annuity 2.2 Constant Perpetuity 2.3 Growing Annuity 2.4 Growing Perpetuity 3. Interest Rates 4. Bond Valuation 5. Stock Valuation
1. Time Value 1.1 Future Value : The process of going from present value to future value Annually Compounding PV 0 =100 r = 10% n = 4 0 1 2 3 4 $100 110 121 133.1 146.41 * (1.1) * (1.1) * (1.1) * (1.1) Value at t = 1: 100 (1 + 0.1) = 110 t = 2: 100 (1 + 0.1) (1 + 0.1) = 121 t = 3: 100 (1 + 0.1) (1 + 0.1) (1 + 0.1) = 133.1 t = 4: 100 (1 + 0.1) (1 + 0.1) (1 + 0.1) (1 + 0.1) = 146.41 Annually compounding FV n = PV (1 + r) n m per year compounding FV n = PV (1 + r m )n m Example) On 1/1/2015, you will deposit $1,000 into a savings account that pays 8%. a) If the bank compounds interest annually, how much will you have in your account on 1/1/2017? b) What amount is your 1/1/2017 balance if the bank used a quarterly compounding?
1.2 Present Value : The process of going from future value to present value Annually Discounting 0 1 2 3 4 $68.30 $75.13 $82.64 $90.91 $100 (1.1) (1.1) (1.1) (1.1) Value at t = 3: 100 (1 + 0.1) = 90.91 t = 2: 100 (1 + 0.1) (1 + 0.1) = 82.64 t = 1: 100 (1 + 0.1) (1 + 0.1) (1 + 0.1) = 75.13 t = 0: 100 (1 + 0.1) (1 + 0.1) (1 + 0.1) (1 + 0.1) = 68.3 Annually compounding FV at time n PV = (1 + r) n m per year compounding PV 0 = FV n (1+ r m )n m Example) a) What amount is worth more at 12% compounded quarterly: $1,000 in hand today or $1,200 due in 2 years?
2. Discounted Cash Flow (DCF) 2.1 Constant Annuity : A series of payments of an equal amount at fixed intervals a) Ordinary Annuity (Annuity in arrear) : An annuity whose payments occur at the end of each period b) Annuity Due (Annuity in advance) : An annuity whose payments occur at the beginning of each period : Ordinary Annuity (1 + r) Present Value of an Ordinary Annuity C= $100 r= 8% 0 1 2 3 4 5 $100 $100 $100 $100 $100 92.59 (1.08) 1 85.73 (1.08) 2 79.38 (1.08) 3 73.50 (1.08) 4 68.06 (1.08) 5 =399.26 PV = C r (1 1 (1 + r) n)
Present Value of an Annuity Due 0 1 2 3 4 5 $100 $100 $100 $100 $100 100 92.59 (1.08) 1 85.73 (1.08) 2 79.38 (1.08) 3 73.50 (1.08) 4 68.06 (1.08) 4 = 431.21 PV of annuity due = C r (1 1 (1 + r) n) (1 + r)
2.2 Perpetuity : A stream of equal payments expected to continue forever PV of perpetuity = Payment r Can be applied to valuation of perpetual bond Can be applied to valuation of preferred stock PV = C (1 + r) 1 + C (1 + r) 2 +.. + C (1 + r) t + = C r 2.3 Growing Annuity C = $100 r = 8% g = 5% 0 1 2 3 4 5 $100 $100(1.05) $100(1.05)^2 $100(1.05)^3 100(1.05^4 92.59 (1.08) 1 90.02 (1.08) 2 87.52 (1.08) 3 85.09 (1.08) 4 82.72 (1.08) 5 =437.95 PV = C t + g (1 (1 r g 1 + r ) )
2.4 Growing Perpetuity PV = C C(1 + g) C(1 + g)t 1 + +.. + (1 + r) 1 (1 + r) 2 (1 + r) t + = C r g r > g Examples) a) Chanwoo has preferred stock outstanding that pays a dividend of $10 per year. If the required rate of return on this preferred stock is 10%, what is the value of Chanwoo s preferred stock? b) Suppose interest rate levels rise to the point where the preferred stock yields 12% with a growth rate of 5%. What would be the value of the preferred stock? c) Assume dividends are paid semiannually. What would the value of the preferred stock?
3. Interest Rate Nominal Rate vs. Effective Annual Rate: Nominal Rate (APR) Effective Annual Rate (EAR) The contracted, quoted, or stated Annual rate of interest actually interest being earned, as opposed to the quoted rate EAR = (1 + ( r m m ) 1 * : m per year compounding Example) a) If the nominal rate is 6% and semiannual compounding is used, find the effective interest annual rate b) If the nominal rate is 6% and quarterly compounding is used, find the EAR Conversion from APR to Effective rate 1. r m = Effective m rate = APR m m 2. Use this rate to calculate PV and FV unless instructed otherwise FV n PV 0 = (1 + r m ) n m. FV n = PV 0 (1 + r m ) n m Equivalence Equation: (1 + Rm) m = (1 + Rn) n
Example) a) What is r 1 if APR 2 is 8%? b) Effective Annual Rate? Continuously Compounding: m = r = e APR t 1 FV = PV e APR t PV = FV e APR t
1. Time Value 2. DCF (Discounted Cash Flow) 2.1 Constant Annuity 2.2 Constant Perpetuity 2.3 Growing Annuity 2.4 Growing Perpetuity 3. Interest Rates 4. Bond Valuation 5. Stock Valuation
Balance Sheet Asset Debt Equity Sales CGS Income Statement xxx (xxx) Gross Margin Operating Cost SG&A EBIT Interest EBT Tax NI xxx xxx (xxx) xxx (xxx) xxx (xxx) xxx
4. DCF Application to Bond Valuation Face Value = $1,000 Maturity = 4 years Stated Rate (Coupon) = 10% Market Rate = 12% Issuer
1) Zero-Coupon Bond (or Discount Bond) Face Value = $1,000 Maturity = 4 years Stated Rate(Coupon) = 0% Market Rate = 12% 0 1 2 3 4 $1,000 $635.5 (1.12) 4 PV = Face Value (1 + r) t
2) Coupon Bond Face Value = $100 at maturity Maturity = 4 years Stated Rate (Coupon) = 10% fixed Market Rate = 12% Total 140 Now give 93.91 0 1 2 3 4 $10 $10 $10 $10+$100 8.92 (1.12) 1 7.97 (1.12) 2 7.12 (1.12) 3 69.9 (1.12) 4 =93.91 Bond Value = PV of Principal Payment + PV of Interest Payments(Annuity) Bond Value = C r (1 1 Face Value (1 + r) t) + (1 + r) t
Example) Face Value = $1,000 Maturity = 5 years Stated Rate(Coupon) = 8% Market Rate = 10% 0 1 2 3 4 5 $80 $80 $80 $80 80+1000 72.73 (1.10) 1 66.12 (1.10) 2 60.11 (1.10) 3 54.64 (1.10) 4 670.6 (1.10) 5 =924.20 Bond Value = PV of Principal Payment + PV of Interest Payments(Annuity) Bond Value = C r (1 1 Face Value (1 + r) t) + (1 + r) t Bond Value = 80. 1 (1 1 1000 (1.1) 5) + 1.1 5
5. DCF Application to Stock Valuation 5.1 Zero-Growth Model (=perpetuity) P 0 = D r 5.2 One-period Dividend Discount Model (DDM) P 0 = D 1 + P 1 (1 + k e ) 1 Two-Period DDM P 0 = D 1 + (D 2 + P 2 ) 1 + k e (1 + k e ) 2 5.3 Holding Period DDM P 0 = P n (1 + k e ) n + D t (1 + k e ) t n t=1 5.4 Constant Growth Model (Gordon s Model) P 0 = D 1 k e g D 1 = D 0 (1 + g) k > g
Example) a) An investor plans to buy a common stock and hold it for one year. The investor expects to receive both $2.75 in dividends and $26 from the sale of stock at the end of the year. If the investor wants to earn a 15% return, what is the maximum price the investor would pay for the stock today? b) If we do not know k e, and we know that P 0 is $25 c) Assume that CWY Corporation is expected to pay a $2.00 dividend per share one year from now, an increase from the current dividend of $1.50 per share. After that, the dividend is expected to increase at a constant rate of 5%. If you require a 12% return on stock, what is the value of the stock? d) Assume that McDonald s Corp is expected to pay a $1.20 dividend per share one year from now and continue to grow at 6%. If you require a 12% return on stock, what is the value of the stock?