CUNY Bernard M Baruch College Use of the DDM Valuation Method in Finance Worksheet

  

Attached is an Excel assignment based on trading stocks, bonds, and options.

The other two attachments are the materials and similar excel sheets for the assignment.

OPTIONS BASIC
S0
Su
Sd
X
C
P
i
t
σ
δ
Today’s Stock Price
Estimated Stock price – upper limit (used in the Binomial Option Pricing Model)
Estimated Stock price – lower limit (used in the Binomial Option Pricing Model)
Exercise Price (Contractual Future Price)
Call Premium (Cu and Cd higher and lower payoffs respectively – used in BOPM)
Put Premium (Pu and Pd higher and lower payoffs, respectively – used in BOPM)
Free interest rate or borrowing rate
Time to exercise
Standard Deviation of the Stock
Dividend Yield
Basic Option:
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Call Options Payoff= Max (0, S – X)
Put Option Payoff= Max (0, X – S)
Profit = Payoff – Premium – Bullish View
Profit = Payoff – Premium – Bearish View
Basic Strategies:
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Protective Put:
Covered Call:
Straddle:
Collar:
Own the Stock and Buy Put Option – Protective View
Own the Stock and Sell Call – View of selling the stock
Buy Call and Buy Put – Volatility View
Buy Put and Sell Call – Protective View paying $0 premium
Advanced Strategies:
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Bull Spreads (Vertical Spread):
o Buy Low (Call) Exercise Price (X1) and Sell High (Call) Exercise Price (X2) with
the same expiration – Bullish – View and paying less premium
o Sell High (Put) Exercise Price (X1) in-the-money and Buy Low (Put) Exercise
Price (X2) out-of-the-money with the same expiration – Bullish View
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Bear Spreads (Vertical Spread):
o Buy high (Put) Exercise Price (X1) in the money and Sell Low (Put) Exercise
Price (X2) out-of-the-money with the same expiration – Bearish View
o Buy High (Call) Exercise Price (X1) and Sell Low (Call) Exercise Price (X2) with
the same expiration – Bearish View and paying less premium
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Butterfly Spreads (Combination of Bull and Bear Spreads) with 3 strike prices:
o Buy the Low (Call) Exercise Price (X1), Sell two middle (Call) Exercise Price,
Buy the High (Call) Exercise Price (X3) – Stability View and paying less
premium
Option Valuation Approaches:
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Binomial Option Pricing Model – Single Period Approach:
o Calculating Call Premiums – Method #1:

C = [S0 – (Sd / ((1 + i) t )] [ (Cu-Cd) / (Su-Sd)] where
Cu = Su – X and Cd = Max (0, Sd- X)
o Calculating Call Premiums – Method #2:

C = [ p (Cu) + (1-p) (Cd) ] / (1+i) where Cu = Su – X and
Cd = Max (0, Sd- X)
o and p = [ (1+i) – d] / (u – d ) for probability
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Binomial Option Pricing Model – Two Period Approach:
o Calculating Call Premiums – using the two period approach

[ (p2 Cu2) + (2p (1-p) Cud ]+ (1-p)2 Cd2] / (1 + i)2
where Cu = Su – X, Cud = Max (0, Sud – X) and Cd = (Max (0, Sd – X)
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Black-Sholes Valuation Model:
o Calculating Call and Put Premium:


C = S0 e-δt N (d1) – X e-it N (d2) where
P = X e-it N (1 – d2) – S0 e-δt N (1 – d1)
 d1 = [ ln (S0/X) + (i – δ + σ2 /2) t ] / (σ √𝑡) and
ï‚· d2 = d1 – (σ √𝑡)
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Put Call Parity Method
C – P = S0 – X e-it then,
C = S0 – X e-it + P or P = X e-it – S0 + C
Initial Purchase of Stock
Year 0
Buying on Margin
Buying on Margin
without margin
Purchase Number of
Stock Price
Shares
@
Purchased
$
$
$
50.00
50.00
100.00
200
200
100
Total
Cost
$ (10,000)
$ (10,000)
$ (10,000)
Margin Loan
Margin
Obtaining
Percentage Margin Loan
%
(Amount)
50.00% $
5,000
25.00% $
2,500
0% $
-m%*Tcst
Final Sale of Stock
Year 1
without margin
10f. Selling Short
Selling Short
Selling Short
Selling Short
Profit
Sell Stock Number of
Total
Price
Shares
Proceeds
@
Purchased
Payment of
Margin
Loan
Payment of
Interest
Expense
$
$
$
$
$ (5,000)
$ (5,000)
$ (5,000)
$
=-OML
$
(250)
$
(250)
$
(250)
$
PML*APR%
46.00
50.00
54.00
80.00
200
200
200
100
$ 9,200
$ 10,000
$ 10,800
$ 8,000
sold*shares
Initial Short Sale
Credit
Short Sell
Shares
on Short
Stock Price Borrowed
Sale
$
50.00
400
$ 20,000
$
50.00
400
$ 20,000
$
50.00
400
$ 20,000
Sp*shares
Buying the Stock / Cover Short Sale
Payment to
Stock
Purchase
Price
New Shares
$
54 $
(21,600)
$
50 $
(20,000)
$
46 $
(18,400)
-shares*Nsp
Margin Loan
Investment
Annual
Interest
on Margin
Loan (Cost) %
Initial
Cash
by Investor
5.00%
5.00%
$
(5,000)
$
(7,500)
$ (10,000)
TcSt + OML
Profit
HPR%
Net Proceeds Net Profit
After
Less Initial
Loan
Cash by
Payment
Investor
$
3,950
$
4,750
$
5,550
$
8,000
TP+PML+PIE
$ (1,050) 10a(i)
$
(250) 10a(ii)
$
550 10a(iii)
$ (2,000)
=NET+IC
the Stock / Cover Short Sale
Profit/Loss
HPR%
$
(1,600)
-8.0% 10f(i)
$
0.0% 10f(ii)
$
1,600
8.0% 10f(iii)
credit+paym =P.L / credit
Profit /
Initial
Investment
-21.00% 10d(i)
-5.00% 10d(ii)
11.00% 10d(iii)
-20.00%
=NETp/-IC
Hyatt Hotels Corporation
Stock Price
Book Value Equity
$
31.46
Market Value / Using the Stock Price
$
71.00
Intrinsic Value
Dividend Discount Model (DDM)
Average EBITDA Industry Trading Multiples
Discount Cash Flow Valuation Analysis
Average of other methods
$
$
$
$
81.88
93.40
73.28
66.69
using stock price
BUY
BUY
hold
SELL
$
78.81
=avg
Fig. 10.5
If “X” > Stockp = BUY
If “X” is near(positive) Stockp = HOLD
If “X” < Stockp = SELL Hyatt Hotels Corporation Intrinsic Value Using CAPM = k = Rf + ( Beta * Premium ) Intrinsic Value = V0 = [ E(D1) + E (P1)] / (1+k) Risk Free = D1= $1.80 1.18x Analyst Est. $1.64 (Average Earnings per share) 9.00% PE Multiple 17.00x *don’t need* 10.50% Exp (P1)= Beta = Premium= Market Return (Rf + Premium)= 1.50% $90.00 (Avg Target by Analysts for 9/ k= RoR/ CAPM = 12.12% rf + (beta*Prem) V0 (Stock Price)= 12.1% $ 81.88 (D1 + P1) / (1+k) (Average Earnings per share) (Avg Target by Analysts for 9/19) Figure 10.6 Hyatt Hotels Corporation Dividend Discount Model (DDM) Constant-Growth DDM (Gordon Model) V0 = D1 / (k-g) D1 = $1.80 Expected Equity Return (k)= 12.12% Expected Growth (g) = 10.00% Expected HPR = E 9r) = [E (d1) + (E(p1) - P0) / P0 Dividend (d1) $1.80 P1 = P0+D1 $72.80 P0 $ 71.00 V0 (Stock Pice) = Exp. HPR= $ 93.40 D1*(1+g)/(k-g) 5.07% (D1+(P1-p0))/p0 = [E (d1) + (E(p1) - P0) / P0 (No growth) P1 = P0+D1 (D1+(P1-p0))/p0 Figure 10.7 Hyatt Hotels Corporation Average EBITDA Industry Trading Multiples (Hotels) SP SO SP * SO = EQ EQ = Stockprice x Shares Outstandin Symbol Stock Price Stocks Outstanding ($000) Choice Hotels International CHH $83.20 56,572 4,706,804 Hilton Worldwide Holdings Inc. HLT $80.96 298,190 24,141,462 Intercontinental Hotel IHG $62.58 190,000 11,890,200 Marcus Corporation MCS $40.80 19,680 802,944 Marriott International MAR $130.90 346,990 45,420,991 Park Hotels & Resorts Inc. PK $32.89 201,180 6,616,810 Belmond (A/K Orient Express Hotels Ltd) BEL $17.00 102,960 1,750,320 Wyndham Worldwide WYN $136.73 108,640 14,854,347 Hyatt HOT $71.00 117,448 8,338,808 EBITDA * Average Multiple 585,000 Company Hyatt's Enteprise Value Less Debt Plus Cash Equity Price Shares Outstanding Stock Price 15.67x 9,167,303 ^ (1,440,000) 879,000 8,606,303 117,448 $ 73.28 =Eprice / shares outstanding Equity Value ($000) D C EQ + D - C = EV Q = Stockprice x Shares Outstanding Debt (ST<) ($000) Cash ($000) E EV / E [EBIT+(+dep.)] Enterprise Value ($000) EBITDA ($000) EBITDA Multiple Beta 796,200 37,150 5,465,854 335,560 16.29x 1.13x 7,580,000 423,000 31,298,462 1,760,000 17.78x 1.45x 2,040,000 233,000 13,697,200 843,000 16.25x 1.59x 317,420 18,070 1,102,294 139,930 7.88x 0.32x 8,990,000 366,000 54,044,991 2,850,000 18.96x 1.36x 3,080,000 421,000 9,275,810 734,000 12.64x 1.28x 785,170 162,010 2,373,480 103,750 22.88x 1.51x 8,310,000 1,500,000 21,664,347 1,790,000 12.10x 1.33x 1,440,000 879,000 8,899,808 585,000 15.21x 1.18x EV = EQ + Debt - Cash Average 15.60x Outliers 15.67x 1.24x 8338808 8,899,808 Figure 10.8 Hyatt Hotels Corporation Discount Cash Flow Valuation Analysis year = Discout Cash Flow Valuation Analysis Historical Projected Input Actual Assumptions Assumptions 12/31/2019 Revenues Revenue Growth Cost of Revenues (CoGS) Operating Expenses (Excl. Non-rec.) EBIT Less Taxes (tax rate x of EBIT) Plus Depreciation 4,763,000 Less Working Capital Less Capex Cash Flow 82.0% 13.4% 82.0% 13.0% 7.6% 0.0% 7.8% 22.0% 7.5% 0.0% 7.5% (3,905,660) (636,340) 221,000 364,000 (369,999) 215,001 EBITDA Debt (assuming 5% reduction of intial principal per year) 585,000 1,440,000 Terminal Value Growth Assumptions EBITDA Multiple Method Perpetuity Method Average Less Debt Outstanding (at Exit) Plus Cash (at Exit) Equity Value at Terminal 15.67x Equity Cash Flows 12.1% 8.00% 9.86% (80% of WACC) PV (for $1) $170,647.26 $162,854.59 $155,417.78 $148,320.57 $7,195,153.89 PV (1) = PV (2) = PV (3) = PV (4) = PV (5) = 0.8919015 0.7954883 0.7094973 0.6328017 0.5643968 PV= Enterprise Value = PV of Equity = $170,647 $162,855 $155,418 $148,321 $7,195,154 $7,832,394 PV of Equity + PV of Debt $7,832,394 Shares Outstanding Stock Price $ 117,448 66.69 1 2 3 4 5 6 12/31/2020 12/31/2021 12/31/2022 EXIT YEAR 12/31/2023 12/31/2024 4,905,890 5,249,302 5,616,753 6,009,926 6,430,621 12/31/2025 6,945,071 3.0% 7.0% 7.0% 7.0% 7.0% 8.0% (4,022,830) (637,766) 245,295 (53,965) 367,942 (367,942) (4,304,428) (682,409) 262,465 (57,742) 393,698 (393,698) (4,605,738) (730,178) 280,838 (61,784) 421,257 (421,257) (4,928,139) (781,290) 300,496 (66,109) 450,744 (450,744) (5,273,109) (835,981) 321,531 (70,737) 482,297 (482,297) (5,694,958) (902,859) 347,254 (76,396) 520,880 (520,880) 191,330 204,723 219,053 234,387 250,794 270,858 613,236 1,368,000 656,163 1,296,000 702,094 1,224,000 751,241 1,152,000 803,828 1,080,000 868,134 1,008,000 (EBITDA x EBITDA Multiple) Next Year's Cash Flow / (Discount Rate - Growth) 12,596,464 14,558,739 13,577,601 (1,080,000) 12,497,601 $191,330 191,330 204,723 219,053 234,387 12,748,396 Cost of Equity Calc V of Equity + PV of Debt Interest 12/19 ($ 000s) Risk Free Rate (5 year) Premium based on MC = Hyatt Beta = 1.50% 9.00% 1.18x Expected Equity Return = 12.1% 75,000 5.21% Rate =eQ / shares WACC Calc: Debt BV Equity 1,440,000 3,695,000 % Cap AT RoR WACC 28.0% 72.0% 100.0% 4.063% 12.120% 1.139% 8.721% 9.860% Figure 10.9 Chapter 11 - Probem 11-10 INPUT WEEKENDS Trading Date Settlement Date (T+3 Business Days) Market Price Coupon Rate Coupon Dates Semi-Annual Coupon Payment Face Value Accrued Basis Thursday, July 22, 2010 Tuesday, July 27, 2010 101.25 6.750% skip weekends M&N (May 31 and Nov 30) $33.75 $1,000 360 Days OUTPUT =+M11+M14 Market Price Paid $1,012.50 Accrued Expenses $10.69 Invoice Price $101.25 x 10 33.75 x (57 / 180) = 10.68 $1,023.19 Total Days 57 DRAW THE DATES 7/27 $33.75 5/31 DAYS = $33.75 6/30 30 7/31 8/31 27 T + 3 business Days 57 Days Chapter 11 - Probem 11-9 INPUT WEEKDAY Trading Date Settlement Date (T+3 Business Days) Market Price Coupon Rate Coupon Dates Semi-Annual Coupon Payment Face Value Monday, May 15, 2017 Thursday, May 18, 2017 96.50 8.250% M&S (Mar 31 and Sep 30) $41.25 $1,000 9/30 10/31 11/30 IN Accrued Basis 360 Days OUTPUT =+M11+M14 Market Price Paid $965.00 Accrued Expenses $11.00 Invoice Price $96.50 x 10 41.25 x (48 / 180) = 11.00 $976.00 Total Days 48 DRAW THE DATES 5/18 $33.75 3/31 DAYS = $33.75 4/30 30 5/31 6/30 18 T + 3 business Days 48 Days 7/31 8/31 9/30 INPUT Trading Date Settlement Date (T+3 Business Days) Market Price Coupon Rate Coupon Dates Semi-Annual Coupon Payment Face Value Accrued Basis Thursday, July 22, 2010 Tuesday, July 27, 2010 101.25 6.750% M&N (May 31 and Nov 30) $33.75 $1,000 360 Days OUTPUT =+M11+M14 Market Price Paid $1,012.50 Accrued Expenses $10.69 Invoice Price INPUT Total Days Trading Date Settlement Date (T+3 Business Days) Market Price Coupon Rate Coupon Dates Semi-Annual Coupon Payment Face Value $1,023.19 57 ** Monday, May 15, 2017 Thursday, May 18, 2017 96.50 8.250% M&S (Mar 31 and Sep 30) $41.25 $1,000 IN Accrued Basis 360 Days OUTPUT =+M11+M14 Market Price Paid $965.00 Accrued Expenses $11.00 Invoice Price Total Days $976.00 48 ** SS20 Calculate the Market Price, Invoice Price and Current Yield of the Corporate Bond given the following information (Based T+3 INPUT weekends Trading Date Settlement Date (T+3 Business Days) Market Price Coupon Rate Coupon Dates Semi-Annual Coupon Payment Face Value Accrued Basis Friday, March 20, 2020 Wednesday, March 25, 2020 98.25 8.500% skip weekends June 30, December 31 $42.50 $1,000 360 Days OUTPUT =+M11+M14 Market Price Paid $982.50 Accrued Expenses $20.07 Invoice Price 33.75 x (57 / 180) = 10.68 $1,002.57 Total Days CY $101.25 x 10 100 85 -0.262778553 YIELD TO MAURITY (YTM), YIELD TO CALL (YTC), YIELD TO WORSE (YTW EXCEL FORMULAS YTM Issuance Date = Trading Date = 1/16/2017 Friday, March 20, 2020 Settlement Date (T+3) (SD) Wednesday, March 25, 2020 **+3+5** Maturity Date / Call Date (MD) 6/18/2027 Coupon Rate (CR) 8.50% Market Price (MP) 98.25 Redemption (Final payment % of Par) (R ) 100.00 Frequency (payments per year) (F) 2 Call Provision = YIELD (SD,MD,CR,MP,R,F) rate = cRATE pv = Market price Face Value Coupon Payment $ Years (Term) YTM= 8.828% =yield YTW= #REF! =min $1,000 $43 =+E10*E21/2 10 Years CY= following information (Based T+3 and 360 days) Maturity Day = 6/18/2027 Redemption Price = 100 First Call Date = Accrued Interest= 20.069 First Call Price = 103 IELD TO WORSE (YTW) and CURRENT YIELD (CY) 8.6514% =cPAY*freq/(MP*10) cPAY =CR*Fvalue/Freq A B C D E F G YIELD TO MAURITY (YTM), YIELD TO CALL (YTC), YIELD TO WORSE (YTW) and C EXCEL FORMULAS YTM Issuance Date = Trading Date = 1/16/2017 Friday, March 20, 2020 Settlement Date (T+3) (SD) Wednesday, March 25, 2020 **+3+5** Maturity Date / Call Date (MD) 6/18/2027 Coupon Rate (CR) 8.50% Market Price (MP) 98.25 Redemption (Final payment % of Par) (R ) 100.00 Frequency (payments per year) (F) 2 Call Provision = YIELD (SD,MD,CR,MP,R,F) rate = cRATE pv = Market price YTM= 8.828% YTC= =yield YTW= 8.828% CY= =min $1,000 $43 =+E10*E21/2 10 Years Face Value Coupon Payment $ Years (Term) Yield to Maturity Calculation Settlement Date (SD) = 1/15/2018 # pmts Maturity Date (MD) = 1/15/2025 0 Coupon Rate (CR) = 4.250% 1 CALCULATING THE YTM Market Price (MP) = Redemption value % (R) = Coupon Pmts per year (Frequency (F) = Yield to Maturity (YTM) = 2 96.179 100 3 2 4 5 4.902% = YIELD (SD,MD,CR,MP,R,F) 6 rate = cRATE 7 pv = Market price 8 9 10 11 12 13 14 hw Chapter 11 - Probem 11-14 CALCULATING THE YTM Settlement Date (SD) = Maturity Date (MD) = Coupon Rate (CR) = Market Price (MP) = Redemption value % (R) = Coupon Pmts per year (Frequency (F) = Yield to Maturity (YTM) = 2/15/2020 6/30/2025 7.500% 98.750 100 2 7.79% =YIELD(D6,D7,D8,D9,D10,D11) = YIELD (SD,MD,CR,MP,R,F) INTERNAL RATE OR RETURN METHOD IRR = # Pmts Coupon Dates 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1/16/2019 7/16/2019 1/16/2020 7/16/2020 1/16/2021 7/16/2021 1/16/2022 7/16/2022 1/16/2023 7/16/2023 1/16/2024 7/16/2024 1/16/2025 7/16/2025 1/16/2026 7/16/2026 1/16/2027 YTM (982.50) 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 42.50 1,042.50 8.797% =IRR(E28:E45)*2 H I J K L TO WORSE (YTW) and CURRENT YIELD (CY) YTC1 YTC2 YTC3 YTC4 YTC5 1/16/2017 3/20/2020 1/16/2017 3/20/2020 1/16/2017 3/20/2020 1/16/2017 3/20/2020 1/16/2017 3/20/2020 3/25/2020 1/16/2018 8.50% 98.25 105.00 2 3/25/2020 1/16/2019 8.50% 98.25 104.00 2 3/25/2020 1/16/2020 8.50% 98.25 103.00 2 3/25/2020 1/16/2021 8.50% 98.25 102.00 2 3/25/2020 1/16/2022 8.50% 98.25 101.00 2 103.00 -1 102.00 -1 101.00 -1 105.00 =(par*5%)+par NA -1 104.00 NA NA 13.236% =yield 8.6514% =cPAY*freq/(MP*10) cPAY =CR*Fvalue/Freq Remaining Dates Cash Flow (961.79) 7/15/2018 21.25 1/15/2019 21.25 7/15/2019 21.25 1/15/2020 7/15/2020 21.25 21.25 1/15/2021 21.25 7/15/2021 21.25 1/15/2022 21.25 7/15/2022 21.25 1/15/2023 21.25 7/15/2023 21.25 1/15/2024 21.25 7/15/2024 21.25 =YIELD(J9,J9,J11,J12,J13) =YIELD(SD,MD,CR,MP,R,F) 10.085% 1/15/2025 1,021.25 IRR = 4.902% =IRR(I7:I21)*2 Figure 11.5 YTC1 YTC2 YTC3 YTC4 YTC5 (982.50) 1,082.50 (982.50) 42.50 42.50 1,072.50 (982.50) 42.50 42.50 42.50 42.50 42.50 1,062.50 (982.50) 42.50 42.50 42.50 42.50 42.50 42.50 42.50 1,052.50 9.777% 9.246% =+$E$10/$E$13*$E$21+K12*10 Payment $40 Redemption $1020 N/A 20.356% 11.693% =IRR(I28:I45)*2 Figure 11.6 B 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 C D E F MARKET PRICE & INVOICE PRICE CALCULATION CALCULATING THE PRICE Settlement Date= Maturity Date= Coupon Rate= Yield to Maturity= Redemption value %= Coupon Pmts per year= 3/15/2015 1/15/2025 4.250% 4.740% 100 2 Market Price = Market Value = 96.179 $ Day since last coupon= Days in coupon period= Accrued Interest= $ Invoice Price= $ 961.79 60 180 7.08 968.87 =PRICE(D5,D6,D7,D8,D9,D10) =+D12*10 =COUPDAYBS(D5,D6,D10,0) =COUPDAYS(D5,D6,D10,0) =(last coupon/cPeriod)*cRATE*par/freq Acrd int + MarketValue Figure 11.4 =+D18+D14 =(D16/D17)*D7*1000/2 A B C D E F G H YIELD TO MAURITY (YTM), YIELD TO CALL (YTC), YIELD TO WORSE (YTW) and C EXCEL FORMULAS YTM YTC1 1/16/2017 Wednesday, July 11, 2018 Issuance Date = Trading Date = Settlement Date (T+3) (SD) Maturity Date / Call Date (MD) Coupon Rate (CR) Market Price (MP) Redemption (Final payment % of Par) (R ) Frequency (payments per year) (F) 1/16/2017 7/11/2018 Monday, July 16, 2018 **+5+3** 7/16/2018 1/16/2018 8.00% 98.50 105.00 2 1/16/2027 8.00% 98.50 100.00 2 Call Provision 105.00 =(par*5%)+par = YIELD (SD,MD,CR,MP,R,F) rate = cRATE pv = Market price YTM= 8.249% YTC= =yield YTW= 8.249% =yield CY= 8.1218% =cPAY*freq/(MP*10) cPAY =CR*Fvalue/Freq =min $1,000 $40 =+E10*E21/2 10 Years Face Value Coupon Payment $ Years (Term) NA Yield to Maturity Calculation # Remaining pmts Dates CALCULATING THE YTM Settlement Date (SD) = 1/15/2018 Maturity Date (MD) = 1/15/2025 0 Coupon Rate (CR) = 4.250% 1 7/15/2018 2 1/15/2019 100 3 7/15/2019 2 4 5 1/15/2020 = YIELD (SD,MD,CR,MP,R,F) 6 1/15/2021 rate = cRATE 7 7/15/2021 pv = Market price 8 1/15/2022 9 7/15/2022 10 1/15/2023 11 7/15/2023 12 1/15/2024 13 7/15/2024 Market Price (MP) = Redemption value % (R) = Coupon Pmts per year (Frequency (F) = Yield to Maturity (YTM) = 96.179 4.902% 7/15/2020 14 1/15/2025 IRR = =IRR(I7:I21)*2 hw Chapter 11 - Probem 11-14 CALCULATING THE YTM Settlement Date (SD) = 2/15/2020 Maturity Date (MD) = 6/30/2025 Coupon Rate (CR) = 7.500% Market Price (MP) = 98.750 Redemption value % (R) = 100 Coupon Pmts per year (Frequency (F) = 2 Yield to Maturity (YTM) = 7.79% =YIELD(D6,D7,D8,D9,D10,D11) = YIELD (SD,MD,CR,MP,R,F) INTERNAL RATE OR RETURN METHOD IRR = # Pmts Coupon Dates 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1/16/2019 7/16/2019 1/16/2020 7/16/2020 1/16/2021 7/16/2021 1/16/2022 7/16/2022 1/16/2023 7/16/2023 1/16/2024 7/16/2024 1/16/2025 7/16/2025 1/16/2026 7/16/2026 1/16/2027 YTM (985.00) 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 1,040.00 8.249% =IRR(E28:E45)*2 YTC1 =+$E$10/$E$13*$E$21+K Payment $40 Redemption $1020 N/A I J K L RSE (YTW) and CURRENT YIELD (CY) YTC2 YTC3 YTC4 YTC5 1/16/2017 7/11/2018 1/16/2017 7/11/2018 1/16/2017 7/11/2018 1/16/2017 7/11/2018 7/16/2018 1/16/2019 8.00% 98.50 104.00 2 7/16/2018 1/16/2020 8.00% 98.50 103.00 2 7/16/2018 1/16/2021 8.00% 98.50 102.00 2 7/16/2018 1/16/2022 8.00% 98.50 101.00 2 103.00 -1 102.00 -1 101.00 -1 -1 104.00 =(par*5%)+par 19.289% cPAY*freq/(MP*10) AY =CR*Fvalue/Freq Cash Flow (961.79) 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 21.25 11.006% 9.415% =YIELD(J9,J9,J11,J12,J13) =YIELD(SD,MD,CR,MP,R,F) 8.757% 1,021.25 4.902% =IRR(I7:I21)*2 Figure 11.5 YTC2 YTC3 YTC4 YTC5 (985.00) 1,080.00 (985.00) 40.00 40.00 1,070.00 (985.00) 40.00 40.00 40.00 40.00 40.00 1,060.00 (985.00) 40.00 40.00 40.00 40.00 40.00 40.00 40.00 1,050.00 9.177% 8.666% +$E$10/$E$13*$E$21+K12*10 Payment $40 Redemption $1020 19.289% 11.006% =IRR(I28:I45)*2 Figure 11.6 Chapter 11 - Probem 11-14 Face Value Coupon Rate Life in Years Yield Frequency Bond Price 1,000 7.75% 4 8.25% 2 $983.25 =-pv(yield/freq,nper*freq,cRATE*facevalue/freq,facevalue) Macaulay Duration 3.51 Modified Duration 3.4% =duration/(1+yield/nper)/100 Convexity Period 0 1 2 3 4 5 6 7 8 1.31% =convex / bPrice 12.88 Cash Flow PV Cash Flow ($983.25) 38.75 38.75 38.75 38.75 38.75 38.75 38.75 1,038.75 PRICE 37.21 =$facevalue*$cRATE/$freq 35.74 PVCF =PV($yeild/$freq,period,,-CF) 34.32 32.96 31.66 30.40 29.20 751.75 =$fvalue*$cRATE/$freq + PAR(facevalue) 983.25 SUM PVCF BOND PRICE, DURATION & CONVEXITY Sensitivity to interest rate movements Face Value Coupon Rate Remaining Years Yield Frequency Bond Price 1,000 6.25% 5.5836 (Maturity -Settment Date )/365 days) 9.75% 2 $852 =-PV(E9/E10,E8*E10,E7*E6/E10,E6) Macaulay Duration 4.31 Modified Duration 4.2% =+E13/(1+E9/E8)/100 Convexity Period 0 1 2 3 4 5 6 7 8 9 10 18.71 Cash Flow 2.20% =+E17/E11 PV Cash Flow ($851.99) 31.25 31.25 31.25 31.25 31.25 31.25 31.25 31.25 31.25 1,031.25 29.80 28.41 27.09 25.83 24.63 23.49 22.39 21.35 20.36 640.68 =+C21/(1+($E$9/2))^B21 PRICE 864.05 =SUM(D20:D30) q,facevalue) Weighted Duration Calc 3.785% 3.635% 3.491% 3.353% 3.220% 3.092% 2.970% 76.455% 0.03785 =PVCF/$bprice 0.07270 =weighted*periods 0.10473 0.13411 0.16099 0.18554 0.20788 6.11639 100.000% 7.02018 =SUM DURATION 3.51 sum/freq =+G31/2(freq) Convexity Factor years Calc 2.000 6.000 12.000 20.000 30.000 42.000 56.000 72.000 74.43 =periods+periods^2 214.44 =factoryrs*PVCF 411.90 659.30 949.77 1,277.00 1,635.21 54,125.69 59,347.74 CONVEXITY sum 12.88 =((sum/((1+yield)^2))/(bprice*freq^2)) Weighted 3.449% 3.288% 3.135% 2.990% 2.851% 2.718% 2.592% 2.471% 2.356% 74.149% 100.000% DURATION Duration Calc Factor years 0.03449 =+F21*B21 0.06577 0.09406 =+B21+B21^2 0.11959 0.14254 0.16309 0.18143 0.19771 0.21208 7.41494 8.62569 =SUM(G21:G30) 4.31 =+G31/2 2.000 6.000 12.000 20.000 30.000 42.000 56.000 72.000 90.000 110.000 CONVEXITY Convexity Calc 59.59 170.47 325.10 516.64 738.94 986.43 1,254.11 1,537.47 1,832.50 70,475.30 77,896.56 =+I21*D21 =SUM(J20:J30) 18.71 =+((J31/((1+E9)^2))/(D33*E10^2)) Figure 11.12 Figure 11.12 DURATIO DURATION AND CONVEXITY FORMULAS Problem 13-1 INPUT OUTPUT Action Option Exercise Price Premium Stock Price Payoff Profit /Loss BE Stock Buy Call 140 9 165 25 16 149 Buy Call 62 5 59 0 -5 67 Buy Put 46 5 38 8 3 41 Buy Put 66 9 66 0 -9 57 Sell Put 132 11 126 -6 5 121 Sell Put 127 9 128 0 9 118 Sell Call 156 6 152 0 6 162 Sell Call 143 8 145 -2 6 151 Sell Straddle 120 21 135 -15 6 141 Buy Straddle 95 13 125 30 17 108 Problem 13-1 Please Complete the Output section given the information below INPUT OUTPUT Action Option Buy Buy Buy Buy Sell Sell Sell Call Call Put Put Put Put Call Exercise Price 140 62 46 66 132 127 156 9 5 5 9 11 9 6 Stock Price 165 59 38 66 126 128 152 Sell Call 143 8 145 Sell Buy Straddle Straddle 120 95 21 13 135 125 Premium 25 0 8 0 -6 0 0 Profit /Loss 16 -5 3 -9 5 9 6 -2 6 151 -15 30 6 17 99 82 Payoff s-x x-s s-x x-s s-x* call* BE Stock 149 67 41 57 121 118 162 BE Stock 2 99 82 177.78% -100.00% 60.00% -100.00% n/a n/a n/a BE Stock n/a 2 141 28.57% 108 130.77% Problem 13-2a-13.2b CALL Exercise Price PUT March April May March April May 150 20.00 21.50 23.00 3.00 3.50 4.45 155 15.50 16.25 17.75 4.10 4.90 5.90 160 12.50 12.85 13.50 5.30 6.00 6.80 165 8.10 9.00 10.65 7.00 8.00 9.20 170 5.20 6.30 8.50 9.40 10.75 12.45 175 3.25 4.25 5.75 13.00 14.30 14.20 180 2.50 3.40 4.45 15.00 16.10 17.75 (X) INPUT a OUTPUT Action Date Option Exercise Price Stock Price Premium (Pay)/Rec Payoff Buy March Call 150 175 -20.00 25 Buy April Call 165 165 -9.00 0 Buy May Put 170 160 -12.45 10 Buy March Put 180 162 -15.00 18 Sell May Put 165 125 9.20 -40 Sell April Put 175 165 14.30 -10 Sell May Call 155 180 17.75 -25 Sell April Call 150 165 21.50 -15 Sell May Straddle 175 200 19.95 -25 Buy March Straddle 180 185 -17.50 5 Action Date Option Exercise Price 1 Exercise Price 2 Stock Price Premium (Pay)/Rec Buy March Bull Call Spread 150 160 170 -7.50 Buy April Bull Put Spread 160 180 162 10.10 INPUT b May Bear Put Spread 170 180 150 -5.30 April Bear Call Spread 160 170 170 6.55 Buy March Butterfly Call Spread 150 160 165 -1.50 Sell May Butterfly Call Spread 170 180 200 1.45 Buy Buy Problem 13-2a-13.2b Use the table below to complete the spreadsheets below CALL Exercise Price (X) 150 155 160 165 170 175 180 PUT March April May March April May 20.00 15.50 12.50 8.10 5.20 3.25 2.50 21.50 16.25 12.85 9.00 6.30 4.25 3.40 23.00 17.75 13.50 10.65 8.50 5.75 4.45 3.00 4.10 5.30 7.00 9.40 13.00 15.00 3.50 4.90 6.00 8.00 10.75 14.30 16.10 4.45 5.90 6.80 9.20 12.45 14.20 17.75 INPUT a OUTPUT Action Date Option Buy Buy Buy Buy Sell Sell Sell Sell Sell Buy March April May March May April May April May March Call Call Put Put Put Put Call Call Straddle Straddle Exercise Price 150 165 170 180 165 175 155 150 175 180 Stock Price 175 165 160 162 125 165 180 165 200 185 Premium (Pay)/Rec -20.00 -9.00 -12.45 -15.00 9.20 14.30 17.75 21.50 19.95 -17.50 Payoff 25 0 10 18 -40 -10 -25 -15 -25 5 INPUT b Action Date Buy March Buy April Buy May Buy April Buy March Sell May LONG SHORT Option Bull Call Spread Bull Put Spread Bear Put Spread Bear Call Spread Butterfly Call Spread Butterfly Call Spread Exercise Price 1 Exercise Price 2 Stock Price Premium (Pay)/Rec 150 160 170 -7.50 160 180 162 10.10 170 180 150 -5.30 160 170 170 6.55 150 160 165 -1.50 170 180 200 1.45 X call BUY SELL SELL BUY 150 155 155 160 X 8.50 -5.75 -5.75 4.45 1.45 call SELL BUY BUY SELL 170 175 175 180 Profit /Loss BE (Stock) HPR % 5.00 170.00 25.00% -9.00 174.00 -100.00% -2.45 157.55 -19.68% 3.00 165.00 20.00% -30.80 174.20 4.30 189.30 -7.25 137.25 6.50 128.50 BE (Stock) -5.05 194.95 155.05 -12.50 197.50 162.50 OUTPUT Total Payoff Total STRATEGY Profit/Loss 10 2.50 Bull Call Spread = Buy Low Call / Sell High Call -18 -7.90 Bull Put Spread = Buy Low Put / Sell High Put 10 4.70 Bear Put Spread = Buy High Put / Sell Low Put -10 -3.45 Bear Call Spread = Buy High Call / Sell Low Call 0 -1.50 Long Buttefly Call Spread = Buy High Call / Buy Low Call / Sell Average Call twice 0 1.45 Short Buttefly Call Spread =Sell High Call / Sell Low Call /Buy Average Call twice Profit /Loss BE (Stock) 5.00 -9.00 -2.45 3.00 -30.80 4.30 -7.25 6.50 -5.05 -12.50 170.00 174.00 157.55 165.00 174.20 189.30 137.25 128.50 155.05 197.50 HPR % 25.00% -100.00% -19.68% 20.00% 3.3478261 BE2 (Stock) 194.95 162.50 OUTPUT Total Payoff Total Profit/Loss 10 2.50 -18 -7.90 10 4.70 -10 -3.45 0 -1.50 0 1.45 STOCK p 165 165 165 165 STOCK p 200 200 200 200 15.00 -10 -10 5 0.00 -30.00 25 25 -20 0.00 Problems 13.4 a-13.4b INPUT OUTPUT Single Period (Call Option) Method 2 (Probability Method) PERIOD 0 PERIOD 1 S = $ 45.00 u= 1.25x d= 0.95x X = $ 49.50 i= 5.00% Freq= 1 Periods= 1 S= p= 1-p= C(E)= need one way put!! Su= 56.25 Sd = 42.75 45.00 0.33 0.67 2.14 European Option Premium OUTPUT FORMULAS Method 1 (Leverage 6-Step Method) Su = S . u Sd = S . d Cu= 6.75 Step 1 Su - Sd = 13.50 Step 2 Cu - Cd = 6.75 Step 3 h= 0.50 Step 4 Step 5 Step 6 PV (Sd) = S-PV(Sd)= h(S-Pv(Sd)= 40.71 4.29 2.14 2.14 Cd= - Cu = Max (0, Su - X) Cd = Max (0, Sd - X) p = [(i+1) - d )] / (u - d) C= [ (p . Cu) + [(1-p) Cd)] ] / [(1+i)^Fre h= 0.500 Hedge Ratio (Buy Shares / Write Calls) TWO-PERIOD BINOMIAL OPTION PRICING MODEL - Call and Put Opt INPUT OUTPUT CALL OPTION PERIOD 0 PERIOD 1 PERIOD 2 Su^2= 93.75 S = $ 60.00 u= 1.25x d= 0.80x X = $ 55.00 i= 3.50% Frequency= 1 Periods= 2 Frequency: ( Annual =1, Semiannual = 2, Quarterly=4) Su= 75.00 Cu= 20.00 S= (Payoff) 60.00 Sd = p= 1-p= C(E)= C(A)= PUT OPTION 48.00 (Payoff) 0.52 0.48 60.00 Cd= Sd^2= 12.19 European Option Premium 10.09 American Option Premium PERIOD 0 PERIOD 1 Su^2= S = $ 60.00 u= 1.25x d= 0.80x X = $ 55.00 i= 3.50% Frequency= 1 Periods= 2 Frequency: ( Annual =1, Semiannual = 2, Quarterly=4) Su= S= P(E)= P(A)= 0.52 0.48 PERIOD 2 93.75 75.00 0.00 Pu= (Payoff) 60.00 Sd = p= 1-p= 38.40 60.00 48.00 7.00 (Payoff) Pd= Sd^2= 3.54 European Option Premium 3.23 American Option Premium 38.40 ll and Put Options FORMULAS Su = S . u Cu^2= 38.75 (Payoff) 21.86 Sd = S . d Su^2 = S . u^2 Sd^2 = S . d^2 Cud= 5.00 (Payoff) 2.52 Cd^2= 0.00 (Payoff) Pu^2= 0.00 (Payoff) Pud= 0.00 (Payoff) 7.66 Pd^2= 16.60 (Payoff) Cu^2 = Max (0, Su^2 - X) Cd^2 = Max (0, Sd^2 - X) Cud = Max (0, Sud - X) p = [(i+1) - d )] / (u - d) Cu= [ (p . Cu^2) + [(1-p) Cud)] ] / [(1+i)^Freq] Cd= [ (p . Cud) + [(1-p) Cd^2)] ] / [(1+i)^Freq] C= [ (p . C1) + [(1-p) C2)] ] / [(1+i)^Freq] Su = S . u Sd = S . d Su^2 = S . u^2 Sd^2 = S . d^2 Pu^2 = Max (0, X - Su^2) Pd^2 = Max (0, X - Sd^2) Pud = Max (0, X - Sud ) p = [(i+1) - d )] / (u - d) Pu= [ (p . Pu^2) + [(1-p) Pud)] ] / [(1+i)^Freq] Pd= [ (p . Pud) + [(1-p) Pd^2)] ] / [(1+i)^Freq] P= [ (p . P1) + [(1-p) P2)] ] / [(1+i)^Freq] TWO-PERIOD BINOMIAL OPTION PRICING MODEL WITH DIVIDENDS INPUT OUTPUT Using Dividend Yield % S = $ 100.00 u= 1.10x d= 0.85x X = $ 105.00 i= 3.50% Div (δ)= 4.00% (at 1st Period) PERIOD 0 PERIOD 1 Su= S= 110.00 5.00 PERIOD 1(x-div) x-dividend 105.60 (Payoff) 100.00 Sd = 85.00 0.00 81.60 (Payoff) Annual= Periods= 1 2 p= 1-p= 0.74 0.26 C(E)= C(A)= 5.70 European Option Premium 3.57 American Option Premium Using Dividend Yield $ PERIOD 0 S = $ 100.00 u= 1.10x d= 0.85x X = $ 90.00 i= 3.50% Div $ = $ 2.00 (at 1st Period) PERIOD 1 Su= S= 110.00 20.00 1 2 Sd = p= 1-p= C(E)= C(A)= x-dividend 108.00 (Payoff) 100.00 85.00 0.00 (Payoff) Annual= Periods= PERIOD 1(x-div) 0.74 0.26 15.37 European Option Premium 14.30 American Option Premium 83.00 WITH DIVIDENDS- Call Options FORMULAS PERIOD 1(x-div) PERIOD 2 Su^2= 116.16 x-dividend Cu = 89.76 89.76 Cd = Sd^2= 91.80 91.30 Pd= Sd^2= 70.55 11.16 Cud= - Cd^2= 0.00 Cu^2= 28.80 Cud= 1.80 Cd^2= 0.00 x-dividend = Su (1-δ) x-dividend = Sd (1-δ) 7.98 - 69.36 PERIOD 1(x-div) PERIOD 2 Su^2= 118.80 x-dividend Pu= Cu^2= x-dividend = Su - Div $ x-dividend = Sd - Div $ 21.04 1.29 Figure 13.18 Problem 13.6 INPUT OUTPUT Using Dividend Yield % S= $ u= d= X= $ i= Div (δ)= (at 1st Period) Annual= Periods= 100.00 1.15x 0.90x 110.00 5.00% 7.00% PERIOD 0 PERIOD 1 Su= S= 115.00 5.00 (Payoff) 100.00 Sd = 90.00 0.00 (Payoff) 1 2 p= 1-p= C(E)= PERIOD 1(x-div) Su^2= x-dividend 106.95 0.60 0.40 11.02 European Option Premium 83.70 Sd^2= FORMULAS PERIOD 2 122.99 Cu = 96.26 96.26 Cd = 75.33 Pu^2= - Pud= Pud= 13.75 13.75 Pd^2= 34.67 5.24 21.06 x-dividend = Su (1-δ) x-dividend = Sd (1-δ) BLACK-SCHOLES VALUATION CALL OPTION A B C D E 4 5 INPUT 6 7 Standard Deviation (σ) = 0.4 8 Expiration (in years) (T) = 0.5 9 Risk-Free Rate (Annual) (i) = 0.05 10 Stock Price (S ) = 100 11 Exercise Price (X) = 110 12 Dividend Yield (annual) (δ) = 0 13 F G H OUTPUT d1 = d2 = N(d1) = N(d2) = C= -0.107 -0.390 0.457 0.348 8.3696 BLACK-SCHOLES VALUATION PUT OPTION A B C D 20 21 INPUT 22 23 Standard Deviation (σ) = 0.4 24 Expiration (in years) (T) = 0.5 25 Risk-Free Rate (Annual) (i) = 0.05 26 Stock Price (S ) = 100 27 Exercise Price (X) = 110 28 Dividend Yield (annual) (δ) = 0 29 E F G OUTPUT d1 = d2 = N(d1) = N(d2) = P= -0.107 -0.390 0.457 0.348 15.6537 H I FORMULAS =(LN(D11/D12)+(D10-D13+(D8^2)/2)*D9)/(D8*SQRT(D9)) =+G8-D8*SQRT(D9) =NORMSDIST(G8) =NORMSDIST(G9) =+D11*EXP(-D13*D9)*G10-D12*EXP(-D10*D9)*G11 Figure 13.21 I FORMULAS =(LN(D11/D12)+(D10-D13+(D8^2)/2)*D9)/(D8*SQRT(D9)) =+G8-D8*SQRT(D9) =NORMSDIST(G8) =NORMSDIST(G9) =D11*EXP(-D9*D8)*(1-G10)-D10*EXP(-D12*D8)*(1-G9) Figure 13.22 Black Schole S=100 x=110 t=.5 i=5.0 s=.40 no dividend D1 D1 NORMALYZED D2 100 110 0.5 0.05 0.4 0 -0.10716 0.45733 First Part d1 d2 -0.09531 + Second Part 0.065 / = MAX(0,S-X) Figuring out call = Max(0,x-s) Firguring out put Third Part 0.282843 Problem 13.5 INPUT OUTPUT CALL OPTION PERIOD 0 PERIOD 1 PERIOD 2 Su^2= 93.60 S = $ 65.00 u= 1.20x d= 0.95x X = $ 60.00 i= 5.00% Frequency= 1 Periods= 2 Frequency: ( Annual =1, Semiannual = 2, Quarterly=4) Su= 78.00 Cu= 18.00 S= (Payoff) 65.00 Sd = p= 1-p= C(E)= 0.40 0.60 74.10 61.75 1.75 (Payoff) Cd= Sd^2= 11.01 European Option Premium 58.66 FORMULAS Su = S . u Cu^2= 33.60 (Payoff) 20.86 Sd = S . d Su^2 = S . u^2 Sd^2 = S . d^2 Cud= 14.10 (Payoff) 5.37 Cd^2= 0.00 (Payoff) Cu^2 = Max (0, Su^2 - X) Cd^2 = Max (0, Sd^2 - X) Cud = Max (0, Sud - X) p = [(i+1) - d )] / (u - d) Cu= [ (p . Cu^2) + [(1-p) Cud)] ] / [(1+i)^Freq] Cd= [ (p . Cud) + [(1-p) Cd^2)] ] / [(1+i)^Freq] C= [ (p . C1) + [(1-p) C2)] ] / [(1+i)^Freq] Problem 13.8 Call Premium = $ 13.00 Stock Price (S) = $ 65.00 Exercise Price (x) = $ 60.00 Risk Free Rate (i) = 2.00% Time (t) = 1 P = Xe(-it) – S + C e (-it) Put Premium= 0.980199 $ 6.81 year BOND VALUATION & ANALYSIS 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 B C D E F G MARKET PRICE/INVOICE PRICE (Manual) Manual Example: Bought (Traded) F&A the 7.50% Corporate Bond at 98.50 on Thursday, January 17, 2019 Trading Date = Settlement Date (T+3 BD) = Market Price = =PRICE(M4,M5,M6,M7,M8,M9) Coupon Rate = =COUPDAYBS(M4,M5,2,1) Coupon Dates = =COUPDAYS(M4,M5,2,1) Face Value = =(M12/M13)*M6*100/2 Accrued Basis= =+M11+M14 Market Price Paid = Accrued Expenses = Invoice Price = Thursday, January 17, 2019 Tuesday, January 22, 2019 98.50 7.500% F&A (Feb 28 and Aug 31) $1,000 360 Days $985.00 $29.58 $1,014.58 1/22 $37.50 8/31 DAYS = Total Days= B 9/30 10/31 11/30 12/31 30 142 30 30 30 22 C D E F G MARKET PRICE/INVOICE PRICE (Using Excel) CALCULATING THE PRICE Settlement Date= Maturity Date= Coupon Rate= Yield to Maturity= Redemption value %= Coupon Pmts per year= Flat Price (% Par) Day since last coupon= Days in coupon period= Accrued Interest= Invoice Price= Current Yield = 3/15/2015 1/15/2025 4.250% 4.740% 100 2 CALCULATING THE YTM Settlement Date= Maturity Date= Coupon Rate= Market Price = Redemption value %= Coupon Pmts per year= 96.179 =PRICE(M4,M5,M6,M7,M8,M9) Yield to Maturity (YTM) = 59 =COUPDAYBS(M4,M5,2,1) 181 =COUPDAYS(M4,M5,2,1) 0.692679558 =(M12/M13)*M6*100/2 96.871 =+M11+M14 4.419% 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 B C D E F G YIELD TO MAURITY (YTM), YIELD TO CALL (YTC), YIELD TO WORSE (YTW) and YTM 1/16/2017 Tuesday, November 13, 2018 Issuance Date = Trading Date = Settlement Date (T+3) Friday, November 16, 2018 Maturity Date / Call Date 1/16/2027 Coupon Rate 8.00% Market Price 98.50 Redemption (Final payment % of Par) 100.00 Frequency (payments per year) 2 Call Provision YTM= 8.253% YTC= YTW= 8.253% CY= $1,000 $40 10 Years Face Value Coupon Payment $ Years (Term) B C D E F G PRICE, ANNUAL DURATION AND CONVEXITY Face Value = Coup. Rate= Int.Rate = Frequency = Time until Payments 1 2 3 4 5 6 7 8 9 10 1,000 8.00% 10.00% 1 CF 80 80 80 80 80 80 80 80 80 1,080.00 PV of CF 72.727 66.116 60.105 54.641 49.674 45.158 41.053 37.321 33.928 416.387 % Weight 8.29% 7.54% 6.85% 6.23% 5.66% 5.15% 4.68% 4.25% 3.87% 47.47% 100.00% Duration 0.0829 0.1508 0.2056 0.2492 0.2832 0.3089 0.3276 0.3404 0.3481 4.7473 93 94 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 B 877.109 C D Duration= E 7.0439 F G MACAULAY SEMI-ANNUAL DURATION AND CONVEXITY Sensitivity to interest rate movements Face Value Coupon Rate Life in Years Yield Frequency Bond Price 1,000 8.00% 10 10.00% 2 $875.38 Macaulay Duration Modified Duration Convexity Period 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 135 137 Price= B 2 6.84 6.51 51.47 Cash Flow PV Cash Flow Weighted Duration Calc ($875.38) 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 1,040.00 38.10 36.28 34.55 32.91 31.34 29.85 28.43 27.07 25.78 24.56 23.39 22.27 21.21 20.20 19.24 18.32 17.45 16.62 15.83 391.97 4.352% 4.145% 3.947% 3.759% 3.580% 3.410% 3.247% 3.093% 2.946% 2.805% 2.672% 2.544% 2.423% 2.308% 2.198% 2.093% 1.994% 1.899% 1.808% 44.777% 100.000% 0.04352 0.08289 0.11842 0.15037 0.17901 0.20459 0.22732 0.24742 0.26510 0.28052 0.29388 0.30533 0.31503 0.32310 0.32970 0.33493 0.33892 0.34177 0.34357 8.95533 13.68074 PRICE 875.38 DURATION 6.84037 C D E F G 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 177 178 179 180 181 182 BOND PRICING Par/Face Value Coupon % = Maturity/Term = $ 1,000.00 8.00% 20 yrs Semi-Annual Coupon = Semi-Annual Payment = Semi-Annual # Paymants = Present Value of Coupon Pmts= Present Value of Principal Pmt= Total $791.71 =PV(B4/2,G5,-G4) $208.29 =PV(B4/2,G5,0,-B3,0) $1,000.00 Net Present Value $1,000.00 $0.00 $1,000.00 Long-Form Period 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 $ 4.00% 40.00 40 Coupon Payment Principal Payment Total Payment $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ - $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ (1,000.00) 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 183 184 185 186 187 188 189 190 191 192 193 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 32 33 34 35 36 37 38 39 40 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 1,040.00 $ $ $ $ $ $ $ $ $ - IRR = B C $ $ $ $ $ $ $ $ $ 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 1,040.00 4.00% D E F G 229 230 H I J K L M N J K L M N Thursday, January 17, 2019 $37.50 1/31 2/28 H 3/15/2015 1/15/2025 4.250% 96.179 100 2 4.740% I H I J K L M N M N D TO WORSE (YTW) and CURRENT YIELD (CY) YTC1 YTC2 YTC3 YTC4 YTC5 1/16/2017 1/16/2017 1/16/2017 1/16/2017 1/16/2017 11/13/2018 11/13/2018 11/13/2018 11/13/2018 11/13/2018 11/16/2018 1/16/2018 8.00% 98.50 105.00 2 105.00 NA 11/16/2018 1/16/2019 8.00% 98.50 104.00 2 104.00 11/16/2018 1/16/2020 8.00% 98.50 103.00 2 103.00 11/16/2018 1/16/2021 8.00% 98.50 102.00 2 102.00 11/16/2018 1/16/2021 8.00% 98.50 101.00 2 101.00 40.527% 11.863% 9.625% 9.196% I J K L 8.1218% H N t + t^2 (t+t^2) x PV(CF) 2 6 12 20 30 42 56 72 90 110 145.455 396.694 721.262 1092.822 1490.211 1896.632 2298.948 2687.083 3053.503 45802.543 59585.153 DMac = C= CFt  (1 + i ) t t =1 1 (1 + i)2 t VB    N  t =1 ( CFt t2 + t t (1 + i) VB  )  H Convexity = 56.143 I J K L IRR= 10.0000% If Yield Changes By Bond Price Will Change By 1.00% -54.63 Modified Duration Predicts Convexity Adjustment Total Predicted Change -57.03 2.25 -54.78 Actual New Price Predicted New Price Difference 2.000 76.19 6.000 217.69 12.000 414.64 20.000 658.16 30.000 940.23 42.000 1,253.64 56.000 1,591.93 72.000 1,949.30 90.000 2,320.59 110.000 2,701.22 132.000 3,087.11 156.000 3,474.67 182.000 3,860.74 210.000 4,242.57 240.000 4,617.76 272.000 4,984.25 306.000 5,340.27 342.000 5,684.32 380.000 6,015.16 420.000 164,625.33 218,055.76 H I N -6.24% $820.74 $820.60 ($0.14) Convexity Factor years Calc CONVEXITY M N DMac = C= CFt  (1 + i ) t t t =1 VB N 1  CFt 2  2 t t +t (1 + i)  t=1 (1 + i)  ( VB 51.47 J K L M N    ) YIELD TO MATURITY every 6 mnts pmts Settlement Date= Maturity Date= Coupon Rate= Bond Pricing= Redemption Value= Coupon pmts per yr= Yield to Maturity= 1/1/2000 1/1/2010 8.000% 110 100 2 6.617% Long-Form Period 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 IRR = Coupon Payment Principal Payment Total Payment $ (1,100.00) $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 1,000.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 40.00 $ 1,040.00 3.3085% 6.617% H I J K L M N DURATIO DURATION AND CONVEXITY FORMULAS 4. ADVANCED OPTION STRATEGIES- Bear Call Spreads CALLS FB PUTS Exercise Price (X) MARCH APRIL MAY MARCH APRIL MAY 150 20.00 21.50 23.00 3.00 3.50 4.45 155 15.50 16.25 17.75 4.10 4.90 5.90 160 12.50 12.85 13.50 5.30 6.00 6.80 165 8.10 9.00 10.65 7.00 8.00 9.20 170 5.20 6.30 8.50 9.40 10.75 12.45 175 3.25 4.25 5.75 13.00 14.30 14.20 180 2.50 3.40 4.45 15.00 16.10 17.75 Bear Call Strategy: Buy the high Exercise Call Price and sell the low Exercise Call Price at the same expiration date ( Action Example: Buy the April 175 Calls -pay $4.25 premium Sell the April 165 Calls - receive $9.00 premium INPUT High X p1 Low X p2 STRATEGY Buy Exercise Call (X1) Premium Paid Per Share (p1) Sell Exercise Call (X2) Premium Received Per Share (p2) BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call BuyHigh and Sell Low Call $ 175.00 $ 175.00 $ 175.00 $ 175.00 $ 175.00 $ 175.00 $ 175.00 $ 175.00 $ $ $ $ $ $ $ $ (4.25) (4.25) (4.25) (4.25) (4.25) (4.25) (4.25) (4.25) $ $ $ $ $ $ $ $ 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 $ $ $ $ $ $ $ $ 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 p Net Premium Received Per Share $ $ $ $ $ $ $ $ 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 Current Price FaceBook (FB) So = $163.00 (Feb) Bear Call Spreads FB April 165/175 $6.00 Profit BE $169.75 $4.00 $2.00 Payoff $$(2.00) $(4.00) $ 130.00 $ 140.00 $ 150.00 $ 160.00 $ 169.75 $ 170.00 $ 180.00 $ 190.00 -10 -8 -6 -4 -2 0 2 4 $(6.00) $(8.00) $(10.00) $(12.00) rice at the same expiration date (Vertical Spread) OUTPUT S S - X1 + X2 Market Price Stock Price (S) Net Payoff $ 130.00 $ 140.00 $ 150.00 $ 160.00 $ 169.75 $ 170.00 $ 180.00 $ 190.00 $ $ $ $ $ (4.75) $ (5.00) $ (10.00) $ (10.00) Net Profit $ $ $ $ $ $ $ $ Maximum Loss 4.75 4.75 4.75 4.75 (0.25) $ (5.25) $ (5.25) $ Maximum Profit $ $ $ $ 4.75 4.75 4.75 4.75 Breakeven (5.25) (5.25) (5.25) Figure 13.10 -10 -8 -6 -4 -2 0 2 4 $ 130.00 $ 140.00 $ 150.00 $ 160.00 $ 169.75 $ 170.00 $ 180.00 $ 190.00 Payoff $ $ $ $ $ (4.75) $ (5.00) $ (10.00) $ (10.00) Profit $ 4.75 $ 4.75 $ 4.75 $ 4.75 $ $ (0.25) $ (5.25) $ (5.25) 5. ADVANCED OPTION STRATEGIES - Long Butterfly Call Spreads CALLS FB PUTS Exercise Price (X) MARCH APRIL MAY MARCH APRIL MAY 150 20.00 21.50 23.00 3.00 3.50 4.45 155 15.50 16.25 17.75 4.10 4.90 5.90 160 12.50 12.85 13.50 5.30 6.00 6.80 165 8.10 9.00 10.65 7.00 8.00 9.20 170 5.20 6.30 8.50 9.40 10.75 12.45 175 3.25 4.25 5.75 13.00 14.30 14.20 180 2.50 3.40 4.45 15.00 16.10 17.75 Long Butterfly Call Strategy: Buy the Low Exercise Call Price, Buy the High Exercise Price and sell the average Call Exerci Action Example: Buy the May Call 150 -pay $23 premium Buy the May 180 Calls - pay $4.45 premium Sell the May 165 Calls - receive $10.65 premium Sell the May 165 Calls - receive $10.65 premium INPUT STRATEGY Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High Buy Low, High and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call and Sell Avg Call Low X1 p1 High X2 p2 2 x Avg X3 2 x p3 Buy Exercise Call (X1) Premium Paid Per Share (p1) Buy Exercise Call (X2) Premium Paid Per Share (p2) Sell Exercise Call (X2) Premium Received Per Share (p3) $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ 150.00 $ $ $ $ $ $ $ $ $ $ $ $ $ (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) (23.00) $ $ $ $ $ $ $ $ $ $ $ $ $ 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 180.00 $ $ $ $ $ $ $ $ $ $ $ $ $ (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) (4.45) $ $ $ $ $ $ $ $ $ $ $ $ $ 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 165.00 $ $ $ $ $ $ $ $ $ $ $ $ $ 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 21.30 Current Price FaceBook (FB) So = $163.00 (Feb) Long Butterfly Call Spread FB May 150/180 $20.00 BE $156.15 BE $173.85 $15.00 $10.00 $5.00 Payoff Profit $$(5.00) $ $ $ $ $ $ $ $ $ $ $ 145.00 150.00 155.00 156.15 160.00 165.00 170.00 173.85 175.00 180.00 185.00 -10 -8 -6 -4 -2 0 2 4 6 8 10 $(10.00) d sell the average Call Exercise Price twice at the same expiration date (Vertical Spread) OUTPUT p S Net Premium Paid Per Share Market Price Stock Price (S) $ 140.00 $ 145.00 $ 150.00 $ 155.00 $ 156.15 $ 160.00 $ 165.00 $ 170.00 $ 173.85 $ 175.00 $ 180.00 $ 185.00 $ 190.00 $ $ $ $ $ $ $ $ $ $ $ $ $ (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) (6.15) S - X1 + X2 Net Profit Net Payoff BE BE $ $ $ $ $ $ $ $ $ $ $ $ $ 0.00 5.00 6.15 10.00 15.00 10.00 6.15 5.00 - $ $ $ $ $ $ $ $ $ $ $ $ $ Maximum Maximum Profit Loss (6.15) (6.15) (6.15) (1.15) 0.00 3.85 8.85 $ 3.85 0.00 (1.15) (6.15) (6.15) (6.15) $ $ $ (6.15) (6.15) (6.15) $ $ $ (6.15) (6.15) (6.15) 8.85 Figure 13.12 -10 -8 -6 -4 -2 0 2 4 6 8 10 $ 145.00 $ 150.00 $ 155.00 $ 156.15 $ 160.00 $ 165.00 $ 170.00 $ 173.85 $ 175.00 $ 180.00 $ 185.00 Payoff $ $ $ 5.00 $ 6.15 $ 10.00 $ 15.00 $ 10.00 $ 6.15 $ 5.00 $ $ - Profit $ (6.15) $ (6.15) $ (1.15) $ 0.00 $ 3.85 $ 8.85 $ 3.85 $ 0.00 $ (1.15) $ (6.15) $ (6.15) ENTER FIRST NAME ENTER LAST NAME First Name: Last Name: PLEASE DO NOT INSERT LINES OR COLUMNS AND DO NOT COPY AND PASTE FORMULAS FROM OTHER SPREADSH SECTION I – STOCKS (20 POINTS) QUESTION 1 (10 points): You obtain $10,000 margin loan with 5% interest to buy 120 shares of IBM $240. A year later you sold all the shares at $26 received a total dividend of $500. What is your $ profit and return of your investment $ Profit = HPR% = QUESTION 2 (10 points): Usingthe information below calculat the Current stock price and stock price value using the DDM valuation methd. INPUT Trading EBITDA Multiple Book Value of Equity Shares Outstanding Total Debt Total Liabilities Total Assets Cash EBITDA Dividends per share Risk Free Rate Market Return Beta Expected Dividend Growth 10.000X 1,500 130 1,300 1,500 3,000 250 550 $ 2.50 1.25% 10.00% 1.650X 8.00% million million million million million million million per share Trading Stock Price = Stock Value Price based on Dividend Discount Model (assume next year's Dividend in your calculation) = SECTION II– BONDS (30 POINTS) Question 3 (8 points) Calculate the Invoice Price of the Elm Corp.'s Corporate Bond given the following information INPUT Face Value Trading Price Trading Date Coupon Rate Coupon Payment Days Frequency = 1,000 99.000 Wednesday, January 16 7.25% Mar 31, Sep 30 2 Price = Invoice Price = Current Yield = Question 4 (14 points) Given the following data, calculate the YTM, all 4 years of YTC, YTW and Current Yield: INPUT Issuance Date= Settlement Date= Maturity Date= Current Market Price= Coupon Rate= Redemption value at Maturity %= Coupon Pmts per year= 10/15/2017 11/1/2018 10/15/2027 98 8.000% 100 2 YTM = Call Price Provision Year INPUT (I.E. ENTER 9/15/2018) Call Price One year from Issuance Date= 104 Two years from Issuance Date= 103 Three years from Issuance Date= 102 Dates Four years from Issuance Date= 101 YTW = Current Yield = Question 5 (10 points) Given the following data, calculate the Price, Duration and Convexity of the Bond: INPUT Face Value Coupon Rate Yield Remaining Years to Maturity Redemption Price Frequency CALCULATIONS Time until Maturity Payments 1 2 3 4 5 6 7 8 9 10 1,000 8.000% 9.250% 3 100 2 Payment 40.00 40.00 40.00 40.00 40.00 1,040.00 PV Pmt 38.23 36.54 34.93 33.38 31.91 792.90 % Weight 0.0395 0.0378 0.0361 0.0345 0.033 0.8192 Duration (Years) Factor Years Convexity Calc Total= Price= Duration= Convexity= SECTION III– OPTIONS (50 POINTS) Question 6 (10 points) Calculate the Payoff, Profit/Loss, BE of the stock and HPR% given the information below (1 point per option answe Exercise Action Option Premium Stock Price Payoff Profit /Loss Price Buy Call 100.00 8.60 125.00 Buy Call 105.00 15.45 105.00 Buy Put 110.00 13.25 102.00 Buy Put 105.00 15.25 105.00 Sell Put 115.00 16.05 115.00 Sell Put 120.00 12.50 120.00 Sell Call 120.00 4.10 115.00 Sell Call 110.00 11.20 135.00 Sell Straddle 125.00 18.70 145.00 Buy Straddle 105.00 19.20 135.00 Question 7 (10 points) Calculate the Payoff and Profit/Loss given the information below (2 points each): CALL Exercise Price Nov 2020 100 8.40 11.25 105 5.90 110 PUT Dec 2020 Jan 2021 Nov 2020 Dec 2020 Jan 2021 17.60 2.30 6.15 11.00 9.90 15.25 3.70 8.90 15.05 3.95 7.55 11.00 6.52 13.05 17.95 115 3.00 5.65 8.90 8.70 15.85 22.90 120 2.55 3.90 7.05 12.30 19.95 28.55 125 2.25 3.45 5.25 16.05 24.85 32.45 Stock Price Total Payoff Premiums Action Option Buy Bull Call Nov Spread Buy Bull Put Dec Spread Buy Bear Put Jan Spread Long Butterfly Call Jan Spread Short Butterfly Call Nov Spread Exercise (Calc the Prices net amount) 100 110 115 125 120 125 100 120 105 115 120 90 90 112 130 Question 8 (10 points) Consider a stock worth $65 that can go up or down by 25% per period. The risk free rate is 5%. And exercise price Pricing Methods (both methods - Method 1 (6 steps) and Method 2 (the probability concept) to calculate the call pre METHOD 1 (enter the answer of each step) Step 1 = Step 2 = Step 3 = Step 4 = Step 5 = Premium = METHOD 2 Premium Question 9 (10 points) Consider the following binomial option pricing problem. This option has two periods to go before expiring. Its stock is $75. The risk-free rate is 4%, the value of u is 1.15 and the value of the d is 0.7. The stock pays dividend at the e 2%. Construct the 2-period Binomial Option Tree model and find the value of both the call and put premiums Call Premium = Put Premium = Question 10 (10 points) ELEM Corporation's stock price is currently trading at $85. The investor is considering of buying the 6 month stradd risk-free rate is 3.5%, the Standard Deviation is 0.25. The stock pays dividend at the end of the first period at the ra the Put and the Straddle options premiums using the Black-Scholes Option Pricing Model. d1 = d2 = N(d1) = N(d2) = Call Premium = Put Premium = Straddle Prem. = LAST NAME ENTER 8-DIGIT STUDENT ID Student ID Student# OM OTHER SPREADSHEETS 20 POINTS) old all the shares at $265. During the hold period you ANSWERS aluation methd. Matching Algorithm # 15778 ANSWERS ock Price = 30 POINTS) ANSWERS ANSWERS YTC (50 POINTS) point per option answer - no partial credit BE Stock High Low High Low Total Profit 5%. And exercise price is $62. Use one Binomial Option o calculate the call premium fore expiring. Its stock price is $80 and its exercise price k pays dividend at the end of the first period at the rate of d put premiums ANSWERS ing the 6 month straddle with exercise price of $85. The he first period at the rate of 3%. Calculate both the Call, ANSWERS Points Score 100 100 4 4 4 4 4 4 2 2 2 2 2 2 2 2 4 4 4 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 2 2 4 4 1 1 1 1 2 2 1 78 157- Question 1 120 240 265 500 65 Question 8 25.00 62 Question 9 80 75 4 1.15 0.7 2 Question 10 0.25 0.75 3.5 85 85 3 Question 13 100 230 500 23 Purchase answer to see full attachment