If the discount rate declines, investment will then be… | Appealing (or more money maker). Because more money is being made. |

Nominal rate can be determined by…Example: Calculating nominal rate when Treasury bill rate is 2% and inflation premium is equal to 4% | Adding return on risk free investments and rate of inflation.K =? K = 2% + 4% K= 6%K* = 2%IP = 4% |

#3If market rate is above the coupon rate then bond will be | Trading at a discount |

#3If the market rate has gone down (below the coupon rate) this bond will | Tarde at a premium |

Annuity (aka ordinary annuity)Find the future value of an ordinary annuity that requires payment of 100 at the end of the first, second, and third year & annuity offers you 5% | PV = 0FV = 0 FV = 315.25 FV = PMT ((1+i)^(n)-1/i)I = 5N = 3PMT = 100 |

The basic relationship in interest rate theory is that bonds with a longer maturity will have a larger price fluctuation, and bond with a shorter maturity will have a smaller change | Longer maturity will have a larger priceShorter maturity will have a smaller change in price. |

A bond with longest maturity is a riskier bonda. 7% coupon rate treasury bond matures in 12 yearsb. 10% coupon rate treasury bond matures in 9 yearsc. 6% coupon rate treasury bond matures in 15 yearsd. 7% coupon rate treasury bond matures in 5 years | Answer is C. C is more riskier. |

You plan to invest in bonds that pay 6% compounded annually. If you invest $10,000 how long will it take to become $30,000. | PV= 10,000FV= 30,000 I/y= 18.85 yearsI= 6N= ? |

Suppose a state of California bond will pay you $1,000 in ten years. If the going rate of interest on a 10 year security is 5.5%, find the PV. | PV= ?FV= 1,000 PV= 585.43N= 10I/y= 5.5Pmt= 0 |

How much would $20,000 due in 50 years be worth today if the discount rate is 7.5% | PV= ?FV= 20,000 PV= 537.78I/y= 7.5N= 50Pmt= 0 |

Last year ABC Inc’s sales were $525 million. If sales grew at 7.5% per year, how large will ABC sales be in 8 years? | PV= 525FV= ? FV= 936.33I/y= 7.5N= 8Pmt= 0 |

ABC, Inc, issued (i.e. sold) 20 year non callable 7.5 annual coupon bonds (i.e. face value of each is 1,000) one year ago. Today the market rate is 5.5%. Calculate the value of this bond today? | PV= ? Payment= (coupon rate)(face value)FV= 1,000 (7.5%) (1,000)I/y= 5.5 0.075 (1,000)N= 20-1= 19 = 75Pmt= 75 PV= 1,232.15 |

A 25-year $1,000 face value bond with a coupon rate of 8.5% is selling in the market for $925. If yield-to-matuirty remains at the current level, what will the price be for this bond 5 years from today?(there are two parts) | PART 1:PV= 925 Pmt= (8.5)(1,000)FV= 1,000 0.085 (1,000)I/y= ? pmt= 85N= 25Pmt= 85 I/y= 9.281%PART 2: PV= ?FV= 1,000I/y= 9,281 Pmt= 85 PV= 930.11 |

Current YieldA $1,000 face value bond matures in 20 years is selling in the market for $900. Then its current yield will be greater than…. | the coupon rate |

If a $1,000 face value bond that matures in 20-years and is selling in the market for $1,100 then its current yield will be… | smaller/lower than the coupon rate. |

Yield-to-maturity (different prob, same #s as question 12)A 25-year, $1,000 face value bond has a 8.5% annual coupon rate. This bond is selling in the market for $925. Find the yield-to-maturity (YTM) | PV= 925FV= 1,000 I/y= 9.281%I/y= ?N= 25Pmt= 85 |

Which of the following will have a higher than average coupon rate | Callable or call provision |

Pre-emptive right is important for the current stockholders because it protects them from | Dilution of ownership |

Find the price at which shares of ABC will be trading if the expected rate of return equals 10% and ABC’s last paid dividend was $3 per share. These dividends are to grow at a constant rate of 6% | Formula: Po= (D1/Ks-g)Po= Stock Price ?Ks= Expected rate of return (aka required rate of return) 10%g= Growth Rate (constant) 6%D1= Next dividend or year-end-dividend 3.18%Do= Last paid or current dividendD1= Next dividend or year-end-dividendD1= Do(1+g) = 3(1+0.06)= 3.18 3.18/ (0.10-0.06) = 79.5 |

If stock of a XYZ is trading for $80 per share and XYZ year-end dividend was $2 per share and constant growth rate is 5%. Calculate the required rate of return for XYZ’s stock (please note expected rate of return is the same as the required rate). | Ks= (D1/Po) +gPo= 80 (2/80)+0.05 = 0.075 7.5%D1= 2g= 5%Ks= ? |

Another method to calculate Ks. If risk-free rate is 4% and market rate premium is 6% with a beta (coefficient) of 1.2, calculate Ks. | Ks= Krf + (Km-Krf) (b)(Km-Krf)= Market Risk Premium (MRP)Krf= 4% 4%+6% (1.2)Km-Krf= MRP 6% 0.04+0.72 = .112 11.2%b= 1.2 |

There is a 25% chance that a stock will earn 30%, and a 50% chance it will earn 12%. Another 25% of the time it will lose 18% | Ki Pi Ki(Pi)0.30—0.25 0.0750.12—-0.50 0.060-0.18—0.25 -0.045Ks= the sum of(KiPi) = 0.09 9% |

Your company paid a dividend of $2 per share six years ago. Today, this company paid a dividend of $4 per share, calculate the growth rate of dividend. | PV= 2FV= 4 I= 12.25% 12%N= 6I= ?Pmt= 0 |

Stock A has a required rate of 10%, its last paid dividend was $0.07 per share and it is trading for $25 per share. Stock B has a required rate of 12% and its last paid dividend was $0.11 per share. This stock is trading for $40 per share. What can be paid about these twos stocks. | Current (dividend) yield = Do/ stock priceStock A= 0.07/25 = 0.0028Stock B= 0.11/40 = 0.0028* The two stocks have the same dividend yield |

Preferred StockFor the preferred stock of an ABC, Inc, dividend was $10 per share and the required rate is 10.3%. Find the value of the preferred | VP= Dp/rpV= Value of preferred Dp= Preferred dividendRp= Rate of return for preferred rate 10.00/10.3% = $97.09 |

Present value of any asset can be determined by discounting future cash flows, i.e. | PV can be determined by discounting |

Your company sold bonds of $1,000 face value that mature in 20 years and have a coupon rate of 10%. Find the cost of debt after-taxes if your company pays taxes at 40%. | Kd(1-T) Kd= 10% = 10%(1-40%) = .06 6%T= 40% |

Ks =Formula | Ks= Cost of Equity1st Formula: Ks= (D1/Po)+gWhere, Ks= Expected rate of return, aka, required rate of return aka (cost of equity or cost of common equity)2nd Formula: Ks= Krf + (Km-Krf)(b)Where, Ks= Required rate of return or expected rate of return or cost of equity.Krf= Risk free rateKm= Market rateKm-Krf= MRPb = beta coefficient |

If stock of ABC is selling for $80 per share, the year-end dividend is $2 per share and the constant growth rate is 5% using this information calculate Ks for ABC | Po= $80 Ks= (D1/Po)+g = 2/80 +0.05 = 0.75 7.5%g= 5%D1= $2 |

If risk free rate is 5% and market risk premium is 1% with a beta coefficient of 1.2. Calculate Ks. | Krf= 5% ks=krf + (km-krf)bMRP= (km-krf)= 1% 5% + 1%(1.2)b= 1.2 5% + 1.2% = 6.2% Ks= 6.2%Always a percentage |

If Ks is equal to 13%, and risk-free rate equals 5%, with MRP equal to 4%. Calculate beta. | Ks= 13% ks=krf + (km-krf)bKrf= 5% 13% = 5% + (4%)bMRP=(Km-Krf) 4% b = 2%b= ? |

Weighted average cost of capital | WACC= WaKd (1-T) + Wskswhere;WACC= Weighted average cost of capitalwd= Debt portion of capital aka (debt component)ws= Equity portion of capital aka (equity component)Kd= Cost of debtT= Tax rateKs= Cost of equity |

An ABC, Inc. is trying to find the weighted average cost of capital and for this ABC has collected the following information-ABC has 40% debt and 60% equity i.e. Wd= 40% 0.40 & ws=60% 0.60-ABC has a 20-year bond issue with a coupon rate of 8% and the bond is trading at par.-ABC is in 40% tax bracket-Risk free rate is 5%MRP equals 4% and ABC’s beta is 1.2 using this information calculate WACC. | Wd= 0.40Ws= 0.60 WACC=WdKd (1-T) +WsKsT= 40% Step1: (Find Ks)= Krft (km-kmf)bKrf= 5% bc kerf is givenMRP= 4% 5% + 4% (1.2)= .098 9.8% Percentb= 1.2 Ks= 9.8%Kd= 8%Ks= ? Step 2: WACC= WdKd(1-T)+WsKs ?= (0.04)(0.08)(1-.40)+ 0.6(0.098) .1092 + 0.0588 = .078 7.8% |

WACC= WdKd(1-T) + WsKs + WpKp | Wp = Preferred StockKp= Cost of preferred stock and return of preferred stock. |

A company paid a dividend of $1 per share 12 years ago. This year it paid a dividend f $2 per share. Calculate the growth rate of these dividends | I= 5.95% |

Payback period has some drawbacks such as | -It ignores the time value of money-It ignores cash-flow after the recovery. |

Your company has invented $5,000 on a project & it generates the following cash flows:Investment= $5,000 | Year CF Cumulative CF Payback Period yrs1 1,500 1,500 – 3 years2 1,250 2,7503 2,250 5,000 –> It ignores cash flow 4 2,250 7,250 after the recovery5 2,250 9,500 (A&B or C&D) answer |

A project acceptable i.e. should be accepted if its NPV>0 | You invested $750 & it generated cash flows.Year CF [email protected]%0 -750 -7501 2450 2,227.272 3175 2,623.963 4400 3,305.78 7,407.01 = NPV1. PV=? 2. PV=? 3.PV=?FV= 2450 FV= 3175 FV= 4400N= 1 N= 2 N= 3I= 10 I= 10 I= 10Pmt= 0 Pmt= 0 Pmt= 0= 2,227.27 =2,623.96 =3,305.78 |

If IRR>WACC, accept the project also, IRR is similar to… | yield-to-maturity |

Riskiness of a project is accounted for by adjusting discount rate upward. PV will be… | Smaller (increasing discount rate) |

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