Sum $4,000.00nper 6rate 4%PV $3,161.26

PMT 30000Nper 13interest rate 14%PMT growth rate 6%PV $237,113.28

1 2 3 4 5 6 7PMT -200000 -200000 -200000 -200000 -200000 -200000 300000DCF -175438.5965 -153893.50569 -134994 -118416 -103874 -91117.31 119891.2NPV -64815.86742IRR 12.66%

Investment perpetuity fromgrowth value of perperuityProject A -10.5 1.87 1.87 1.87 1.87 1.87 1.87Project B -10.5 1.43 $1.47 $1.51 $1.54 $1.58 $1.63

16%13%

MT302 2000 200 10MY456 3000 240 12.5MT347 6000 450 13.33333OFFICE 1250 14MG201 2500 150 16.66667MC237 4900 250 19.6MB345 4000 200 20MG231 4000 150 26.66667

NOPAT 250Dep Exp 114Capex 215

change in NWC 11

FCF

1 2 3 4 5cash 4 11 16 16 16A/R 21 25 24 21 25Inv 5 9 12 12 13A/P 17 22 23 27 35NWC 13 23 29 22 19Change in NWC 10 6 -7 -3

GB SAshares 25 20price 10 15debt 50

300 300

8 9 10 11 12 13 14 15 16300000 300000 300000 300000 300000 300000 300000 300000 300000

105167.7 92252.38 80923.14 70985.21 62267.73 54620.82 47913 42028.94 36867.5

1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.87$1.67 $1.71 $1.76 $1.80 $1.85 $1.90 $1.95 $2.00 $2.05

=NPV() Present value of a stream of cash flows

rate 4%

t 0 1 2 3 4CF ($1,000) $4,000 $4,000 $4,000

PV(CF) ($1,000.00) $3,846.15 $3,698.22 $3,555.99 $0.00

PV $10,100.36 Using equations from cheat sheet

=PV() Present value of an annuity

rate 6%nper 13.00pmt 30000.00PV $265,580.49 =PV(discount rate, number of periods, -1*periodic cash flow)

t 1 2 3 4CF $100 $100 $100 $100

PV(CF) $94.34 $89.00 $83.96 $79.21

PV $346.51 Using equations from cheat sheet

=PV() Present value of a bond

rate 8%

t 1 2 3 4 5CF $100 $100 $100 $100 $1,100

PV(CF) $92.59 $85.73 $79.38 $73.50 $748.64

PV $1,079.85 Using equations from cheat sheet

PV $1,079.85 =PV(discount rate, number of periods, -1*coupon payment, -1*face value)

=FV() Future value of an annuity

rate 8%nper 18.00

pmt 4000.00FV $75,528.55 =FV(discount rate, number of periods, -1*periodic cash flow)

t 1 2 3 4CF $100 $100 $100 $100

PV(CF) $92.59 $85.73 $79.38 $73.50

PV $450.61 Using equations from cheat sheet

=PMT() Size of annuity payments

rate 8% Example: 10-year annuity with PV=$300.

periods 10

PV $300

CF $44.71 Using equations from cheat sheet

CF $44.71 =PMT(discount rate, number of periods, -1*present value of annuity)

=NPER() Number of periods for annuity

rate 8% Example: Annuity with PV=$300, making annual payments of $44.71

CF $44.71

PV $300

periods 10 Using equations from cheat sheet

periods 10 =NPER(discount rate, -1*periodic cash flow, present value of annuity)

=IRR() Internal rate of return

t 0 1 2 3CF ($500) $200 $200 $200

IRR 9.70% =IRR(<range of cells, beginning with initial cost and including end of period cash flows for each year>)

or IRR 9.70% =IRR({initial cost, cash flow 1, cash flow 2, cash flow 3, …})

=EFFECT() Effective annual rate (EAR)

APR 10.00% Example: EAR corresponding to APR of 10%, compounded quarterly.

periods/year 4

EAR 10.38% Using equations from cheat sheet

EAR 10.38% =EFFECT(APR, number of periods per year)

=NOMINAL() Annual percentage rate (APR)

EAR 10.00% Example: APR corresponding to EAR of 10%, compounded quarterly.

periods/year 4

APR 9.65% Using equations from cheat sheet

APR 9.65% =NOMINAL(EAR, number of periods per year)

Two ways to calculate yield to maturity:

Example: There is a bond making annual payments of $85 each, with $1000 par value, maturing in 3 years.

The formula for the present value of a bond is:

where 'y' is the yield to maturity, 'Coupon' is the size of each coupon payment, 'Par' is the bond's par value, and 'T' is the number of payments.

(1) First method: Goal Seek

Step 1. Enter the bond's information into Excel.

Step 2. Create cell for YTM and (important) set it to 5% (a random guess at the YTM).

Step 3. Enter PV formula into Excel, making references to the YTM, coupon, par, and T.

TTbond y

Par

yyyCouponPV

)1()1(

11

Step 4. Select "Data: What-If Analysis: Goal Seek..."

Step 4(a). Make "Set cell:" the cell where you entered the PV formula (cell J132).

Step 4(b). In the "To value" box, type the price of the bond (in this example, $1040.2).

Step 4(c). Make "By changing cell:" the cell where you entered the YTM (cell J129).

If you've done this correctly, you should get a YTM of 6.969%.

(2) Second method: YIELD() formula

Step 1. Enter the bond's information into Excel.

Step 2. Enter a random date into one cell, and then a date exactly 'T' years later, whereT' is the number of years that the bond makes payments (in this example, 3 years).

Step 3. Enter the yield formula into Excel, making references to the price, coupon rate,par, and the dates that you entered in the previous steps.

bond; 'redemption' is the par value, in units of $100, so we must again divide by10 in this example; 'frequency' is the number of payments per year, 1 in this case.

Notes: in the formula, 'settlement' and 'maturity' refer to the dates entered above;rate' refers to the coupon rate; 'pr' refers to the bond's price per hundred dollarsof par value, so you need to divide this by 10 in the formula for a $1000 par value

5 6 7 8

$0.00 $0.00 $0.00 $0.00

=PV(discount rate, number of periods, -1*periodic cash flow)

Example: PV of a 4-year annuity paying $100 per year.

Example: PV of a 4-year bond paying $100 coupons, $1000 face value.

=PV(discount rate, number of periods, -1*coupon payment, -1*face value)

=FV(discount rate, number of periods, -1*periodic cash flow)

Example: FV of $100 at the end of the next 4 years.

Example: 10-year annuity with PV=$300.

=PMT(discount rate, number of periods, -1*present value of annuity)

Example: Annuity with PV=$300, making annual payments of $44.71

=NPER(discount rate, -1*periodic cash flow, present value of annuity)

Example: Project with initial cost of $500, producing $200 cash flows for 3 years.

=IRR(<range of cells, beginning with initial cost and including end of period cash flows for each year>)

=IRR({initial cost, cash flow 1, cash flow 2, cash flow 3, …})

Example: EAR corresponding to APR of 10%, compounded quarterly.

Using equations from cheat sheet

=EFFECT(APR, number of periods per year)

Example: APR corresponding to EAR of 10%, compounded quarterly.

Using equations from cheat sheet

=NOMINAL(EAR, number of periods per year)

Example: There is a bond making annual payments of $85 each, with $1000 par value, maturing in 3 years.

where 'y' is the yield to maturity, 'Coupon' is the size of each coupon payment, 'Par' is the bond's par value, and 'T' is the number of payments.

Coupon Par # Paymts$85 $1,000 3

YTM5.000%

PV$1,095.31

Step 4(a). Make "Set cell:" the cell where you entered the PV formula (cell J132).

Step 4(b). In the "To value" box, type the price of the bond (in this example, $1040.2).

Step 4(c). Make "By changing cell:" the cell where you entered the YTM (cell J129).

Price Coup rate Par$1,040.20 8.50% $1,000

Date 1 Date 21/1/2000 1/1/2003

YTM6.969%

bond; 'redemption' is the par value, in units of $100, so we must again divide by10 in this example; 'frequency' is the number of payments per year, 1 in this case.

: in the formula, 'settlement' and 'maturity' refer to the dates entered above;per hundred dollars

, so you need to divide this by 10 in the formula for a $1000 par value

Life (for Depr) 1Salvage value 0NPV 5,021.69 FCF=Net income+depreciation-CapEx-Change NWCInvestment (t=0) - Discount rate 8%IRR 300.00%tax rate 0%

0 1 2 3 4Revenues - 4,000 4,000 4,000 Expenses 1,000 5,000 DEPR - - - - - Gain on Capital

EBIT (1,000) 4,000 (1,000) 4,000 - TAX - - - - - CAPEX - - - - - Net Earnings (1,000) 4,000 (1,000) 4,000 - Adding back Depr (1,000) 4,000 (1,000) 4,000 -

Net WCChange in WC - - - - -

CF (1,000) 4,000 (1,000) 4,000 -

DCF (1,000) 3,704 (857) 3,175 -

FCF=Net income+depreciation-CapEx-Change NWC

5

- * diff between sale value and depreciated value

- -

* salvage value - -

- -

-

-

Stock price S0 117.01strike price X 97Periods T 0.2602739726

Rf 6.43%option price C0 23.00 26.72061

P0 1.43 5.15

u and d are given sigma is givenStock price S0 40 Stock pricestrike price X 40 strike priceup rate u 1.105 annulaized SD of stockdown rate d 0.905 length of period as fraction of a yearrisk free rate r 1.467% up rate

Cu 4.200 down rateCd 0 annual risk free rateDelta 0.525 one period interest rateB -18.730

option price C0 2.270risk neutral probability q 0.548

option price for one periodrisk neutral probability

S0 40X 40sigma 0.2h 0.25 4u 1.105d 0.905rf 6%r 1.467%Cu 4.207Cd 0Delta 0.525B -18.726C0 2.273q 0.548

Stock price S0 72strike price X 72Periods T 1

r* 5.00%Sigma 26%PV(X) 68.571d1 0.318d2 0.058

option price C0 9.111P0 5.682

Delta N(d1) 0.625

Investment Opportuninty Variable Call OptionPresent value of Project's Assets S Stock priceCost to aquiore projects X Strike pricelength of time to make decision T Time to expirationtime value of money Rf Risk free returnriskiness of project assets Sigma^2 Variance of stock return

"Regular" NPV S-X"Modified" NPV S-PV(X)

NPVq S/PV(X)

Comulative Volatility (CVol) Sigma*SQRT(t)

Furmula

S 940160 * discounted cf (w/o future investment) of the projectX 9.6 * can be the future investment (looks like a strike price)t 1Rf 11.60%Sigma 35% G 0

1040000PV(X) 8.6021505376 1040000NPVq 109,293.60 937,731 Cvol 0.35 Value from table: 18.10%C0 $170,168.96

1+ revenue 1+ cost 1+ profit PV 11088880 940160 148720 1606759 1606759

940160 940160 0 4600001033380

Corporate Tax Rate 40%Total Shares before restructure 60

Current StateAssets including Cash $ 600.00 Equity $ 500.00

Debt $ 100.00

Announce Debt IssueAssets $ 600.00 Equity $ 500.00 Cash from Debt $ - Debt $ 100.00

incremental Debt Tax Shield $ -

Debt issuanceAssets $ 600.00 Equity $ 500.00 Cash from Debt $ - Debt $ 100.00 Tax Shield $ -

Repurchase EquityAssets $ 520.00 Equity $ 420.00

Old Cash used to repurchase 80 Cash from Debt $ - Debt $ 100.00 Tax Shield $ -

Value changes due to announcement of something good/badAssets $ 780.00 Equity $ 780.00 Cash from Debt $ - Debt $ 100.00 Tax Shield $ -

Total Shares Stock Price60 $ 8.33

Total Shares Stock Price60 $ 8.33

Total Shares Stock Price60 $ 8.33

Total Shares Stock Price 50.40 $ 8.33

Total Shares Stock Price 50.40 $ 15.48

Beta of equity 0.5D/E 0.8D/(D+E) 0.444444Risk free rate (rD) 4%Risk premuim 5%Tax Rate 0%rA 6.5%rE 8.5%rWAAC 6.500%

Firm A Total Shares Stock PriceAssets including Cash $ 600.00 Equity $ 600.00 60 $ 10.00

Debt $ -

Firm B Total Shares Stock PriceAssets including Cash $ 400.00 Equity $ 400.00 10 $ 40.00

Debt $ -

Stock Price

Stock Price

Corporate Tax rate 40% TcDividend Tax rate 18% TeInterest income tax rate 30% TdEquity 500Debt 100interest rate on debt 5%Per dollar tax advantage $0.297 T*