FE 323 Review Session

Jessica Crusco and Jay Chen

Topics } EAR vs. APR } Bonds } Stocks

} Dividend growth rate, dividend yield, stock price in future year } Supernormal dividends

} NPV, IRR } Mutually exclusive projects

} Operating Cash Flow

Using EAR and APR } EAR = annualized rate adjusted for compounding } APR = compounded, reinvested each period

} EAR = APR compounded annually } EAR > APR compounded semiannually, quarterly etc

} Use EAR to convert APR! } Need to convert when # payments per year are different

than APR compounded # times } Ex: Annual payments need EAR, or APR annually } Ex: Semi-annual payments need APR semi-annually

Example: EAR and APR 1) You want to buy a new sports coupe for $68,500, and the finance office at the dealership has quoted you a 6.9% APR loan for 6 years to buy the car. Assume monthly compounding.

a) What is your monthly payment? P/YR: 12 } N: 72 (6 x P/YR) } PV: 68,500 } I/YR: 6.9 } PMT: ?

} 1,164.57

P/YR: 1 } N: 72 (6 x 12) } PV: 68,500 } I/YR: 0.575 (6.9/12) } PMT: ?

} 1,164.57

Example: EAR and APR 1) You want to buy a new sports coupe for $68,500, and the finance office at the dealership has quoted you a 6.9% APR loan for 6 years to buy the car. Assume monthly compounding.

b) What is your effective annual rate? } Continuing from previous slide: touch EFF% } Or repeat steps in previous slide: } P/YR: 12 } NOM%: 6.9 } EFF%: ?

} 7.1224%

Example: EAR and APR c) Suppose they were semi-annual payments. What is the semi-annual payment? What is the effective annual rate? } Need APR with semi-annual compounding but given monthly

compounding so need to convert } P/YR: 12 } NOM%: 6.9 } EFF%: ?

} 7.1224% } Used later for other

question

} EFF%: 7.1224% } P/YR: 2 } NOM%: ?

} 7% } If you now RCL I/YR youll see

7% is already there so no need to insert it into I/YR to finish the problem

Example: EAR and APR } With APR of 7% compounded semi-annually, we have the

right APR and can continue: P/YR: 2 } N: 12 (6 x 2) } I/YR: 7% } PV: 68,500 } PMT: ?

} 7,088.64

} What is your effective annual rate? } In case you forgot, RCL EFF% } 7.1224%

P/YR: 1 } N: 12 (6 x 2) } I/YR: 3.5% (7/2) } PV: 68,500 } PMT: ?

} 7,088.64

Bonds } FV (Face Value) always = $1,000 } Watch out for Coupon Rate % vs. Yield to Maturity %

} Coupon rate = % of $1000 = total coupon for the year } If semi-annual payments, and coupon = 10%, each payment is = $50 } If annual payments, and coupon = 10%, each payment is = $100

} PV always negative (outflow you pay today) } FV and PMT always positive (inflow in future) } Holding period yield vs. Yield to Maturity

} YTM: rate of return on a bond held to maturity (assumes reinvestment at same rate)

} Holding period yield (HPY) is what you actually earn on a bond } HPY: PV = price purchased, FV = price sold for/current price,

N = # years held, PMT = coupon payment, Solve for I/YR = Rate of return or HPY

Bonds YTM, and HPY 2) Suppose that today, you buy a 12 percent annual coupon bond for $995. The bond has 13 years to maturity.

a) What is the yield to maturity on this bond? } P/YR: 1 } PV: -995 } FV: 1,000 } PMT: 120 (12% x 1,000) } N: 13 } I/YR: ?

} 12.08%

Bonds YTM, and HPY b) Two years from now, the yield-to-maturity has declined by 1 percent and you decide to sell. What is your holding period yield?

} I/YR: 11.08% (12.08 1) } (Rcl I/YR 1= I/YR)

} N: 11 } PV: ?

} - 1,057.02 } Value of bond in 2 years

PV now becomes FV (make it positive): } FV: +/- 1,057.02 } PV: -995 } PMT: 120 (12% x 1,000) } N: 2 } I/YR: ?

} 14.96%

Stocks } Constant growth is treated like a perpetuity

} Pt = Dt+1 / (r g) } Recall that you are treating the dividends as cash payments that you will

receive in the future } Remember to use timelines to visualize

} Dont forget that in constant growth using above equation, like a perpetuity, you capture the PV of all future cash flows which falls in the period prior to the first cash flow (i.e. Pt is one period before Dt+1)

} Pt can be considered a cash flow because it represents all those dividend payments in constant growth and the stock could be sold for that value (we call this terminal value in valuing cash flows in finance)

} You can now discount Pt and all dividends up to and including

Pt at the appropriate discount rate (r)

Finding Dividend Growth Rate 3) Home Canning Products common stock sells for $44.96 a share and has a market rate of return of 12.8 percent. The company just paid an annual dividend of $1.04 per share. What is the dividend growth rate?

} Pt = Dt+1 / (r g) } 44.96 = (1.04 x (1+g) / (12.8 g) } g = 10.25%

Finding Dividend Yield 4) Great Lakes Health Care common stock offers an expected total return of 9.2 percent. The last annual dividend was $2.10 a share. Dividends increase at a constant 2.6 percent per year. What is the dividend yield? } Pt = Dt+1 / (r g) } r g = Dt+1 / Pt } What is r g ?

} Dividend yield!

} So, dividend yield = 9.2% - 2.6% = 6.6%

Finding Stock Value in Future Year 5) Winter Time Adventures is going to pay an annual dividend of $2.86 a share on its common stock next year. This year, the company paid a dividend of $2.75 a share. The company adheres to a constant rate of growth dividend policy. What will one share of this common stock be worth five years from now if the applicable discount rate is 11.7 percent?

} Dt = D0 (1+g)t

} D6 = D0 (1+g)6

} D6 = 2.75 (1+ .04)6

} D6 = 3.4796

} Pt = Dt+1/(r-g) } P5 = D6/(r-g) } P5 = 3.4796/(.117-.04) } P5 = 45.19

} What is the growth rate? } g = (D1 D0)/D0 } g = (2.86 2.75) / 2.75 } g = .04

Supernormal Dividends 6) Rizzi Co. is growing quickly. Dividends are expected to grow at a 30 percent rate for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 13 percent and the company just paid a $1.80 dividend, what is the current share price?

} Pt = Dt+1/(r-g) } P3 = D4/(r-g) } P3 = 4.1919/(.13 - .06) } P3 = 59.8839 STO 3

} D4 = D0 (1+ g1)3 (1+g2)1

} D4 = 1.8 (1+ .3)3 (1+.06)1

} D4 = 4.1919

} P3 is known as a terminal value in finance it captures all the value of the future cash flows and the stock could be sold for this at t=3

} P0 captures the value of P3 (is the PV of P3) plus PV of these dividends: D1 and D2 and D3

Step 1: find the price of stock when the dividend levels off

Supernormal Dividends } Continued from previous slide

Formula: } P0 = [$1.80(1.30) / 1.131] + [$1.80(1.30)2 / 1.132] +

[$1.80 (1.30)3 / 1.133] + [$59.88 / 1.133] } P0 = $48.70

Calculator: 13 I/YR then } CF0 = 0 } CF1 = 2.34 (1.8 x 1.3) } CF2 = 3.043 (2.34 x 1.3) } CF3 = 63.8385 (D3 + P3 = 3.9546 (3.043 x 1.3) + Rcl 3) } NPV = $48.70

Step 2: The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price ($59.88)

Finding IRR, and NPV of projects } Recall the relationship with IRR and NPV when

comparing mutually exclusive projects } Be sure to find the crossover points for projects, and

choose the firm with highest NPV

Mutually Exclusive Projects 7) Boston Chicken is considering two mutually exclusive projects with the following cash flows. What is the crossover rate? If the required rate of return is lower than the crossover rate, which project should be accepted?

Year Project A Cash Flow

Project B Cash Flow

0 -$50,000 -$50,000

1 $31,000 $42,000

2 $26,000 $21,000

3 $27,000 $18,000

Cash flows for (A-B)

$0

$-11,000

$5,000

$9,000

I = 15% NPVA = $14,369.20

I = 15% NPVB = $14,236.05

IRR = 15.99%

} The crossover rate is 15.99 percent. At a rate lower than the crossover rate, such as 15 percent, Project A will have the higher NPV and should be accepted.

OCF 8) Jefferson & Sons is evaluating a project that will increase annual sales by $138,000 and annual costs by $94,000. The project will initially require $110,000 in fixed assets that will be depreciated straight-line to a zero book value over the 4-year life of the project. The applicable tax rate is 32 percent. What is the operating cash flow for this project?

} OCF = (Sales Costs) * (1 T) + Depreciation * T } OCF = ($138,000 - $94,000)(1 - 0.32) + ($110,000/4)(0.32) } OCF = $38,720

Project Cash Flow Problems } Solve problems using a grid

} The grid above would be for a 3 period project } NWC is normally recovered at the end } Net capital spending, usually includes an

} Initial investment cost (usually negative) in period 0 } After tax salvage value (usually positive) in last period

} Cash flow from assets is total cash flow

t 0 1 2 3

OCF

NWC -20 +20

NCS -300 ATSV

CFFA

Study Tips from TA } Keep practicing problems, and study in pairs } Use the formula sheet while you do problems so you are

prepared for using it during the exam. } Always check your answers to your problems, otherwise

you will never know if youre doing something wrong! } Post any questions to the CORE MASTER forum. It will

be monitored heavily by the TAs.

Exam Taking Tips from the TA

} Before every problem on calculator } CA and check P/YR, make sure BEG key is off unless needed

} Start with Long Answers first } You can always guess on MC

} Read each question carefully, and circle information needed } When you see words signifying begin, write BEGIN on the question

and remember to turn off your BEGIN key before the next question both answers will probably be there

} For each problem, write down your calculator steps. This will make it easier for you to remember your thinking process if you go back OR easily check your answers and also to get partial credit

Questions?