Name : Bayu Anggara SilvatikaSubject : Financial MangementLecturer : Prof. Dr. Ahmad Rodoni

Referensi : "Fundamentals of Corporate Finance" 9th Ed. By Ross/Westerfield/JordanChapter : Ch. 7 Page 226-230

Ch. 8 Page 255-258Questions : Nomor Ganjil

CHAPTER 7 INTEREST RATES AND BOND VALUATION

Page No. Answers

226 1 Yield to maturity (YTM) is The rate required in the market on a bond.(Basic) Yes, YTM is the same thing as the required return in the rate.

Coupon rate is The annual coupon divided by the face value of a bond.

Coupon rate = 10%; and YTM = 8%.3 Staind, Inc., coupon bonds=7.5%; maturity 10 years; Annual payments. If YTM=8.75%, so current bond price?

5 Kiss the Sky Enterprises, annual payment; maturity 13 years; selling for $1,045; yield=7.5%. Coupon rate?

8.12584025535802390.5619808481481.045 = ((1.000 x CR%) x 8.1258) + 390.56= ((1045-390.56)/8.1258)/1000Coupon Rate = 8.05%

227 7 Ngata Corp., maturity 10 years (12-2); coupon rate=8.4%; semiannual payment; current bond price =105% of par value, so YTM? Assuming FV = 1.000

=((42+((1000-1050)/10))/((1000+1050)/2))*100%YTM = 3.61%

9 The nominal rate is approximately equal to the sum of the real rate and the inflation rate. Real rate interest + 3.8% = 7%The approximately real rate interest is 3.2%.1 + R = (1 + r) x (1 + h)1+7% = (1+r) x (1+3.8%)=(1.07/1.038) -1The exact real rate is 3.08%.

11 Nominal return = 14%; Real return = 9%; Inflation rate?The approximately inflation rate is 5%;=(1.14/1.09)-1The exact inflation rate is 4.59%.

13

(Intermediate)15 Bond X: coupon rate 8%; YTM 6%; maturity 13 years; annual payments. Bond Y: coupon rate 6%; maturity 13 years; annual payments. Assuming FV is $ 1.000.

Bond Price 1 year 3 years 8 years 12 years 13 yearsX $ 1,018.87 $ 1,053.46 $ 1,124.20 $ 1,167.68 $ 1,177.05 Y $ 981.48 $ 948.46 $ 885.07 $ 849.28 $ 841.92

Graphing bond prices versus time to maturity

17 Bond J = coupon rate 4%; maturity 9 years; semiannual payments; YTM 8%Bond K = coupon rate 12%; maturity 9 years; semiannual payments; YTM 8%.

Bond Price Awal Jika IR naik 2% Maka BP turun

J $ 851.29 $ 786.77 -8% $ 922.14 8%K $ 1,148.71 $ 1,071.08 -7% $ 1,233.58 7%

If interest rates rise by 2%, so the price of bond J will fall by 8% and bond K also fall by 7%.If interest rates fall by 2%, so the price of bond J will rise by 8% and bond K also rise by 7%.Higher interest rates, lower the price bonds. And lower interest rates, higher the interest rates.

There are difference between YTM and Coupon rate. Coupon rate use to determine the value of bond at a particular in time, but YTM use to estimate bond's current market value.

Current bond price = { (FV x 7.5%) x ([ 1 - (1 /(1 + 8.75%)10 )] / 8.75%) } + { FV / (1 + 8.75%)10}

Assuming FV = $1,000; so 1,045 = { (1,000 x CR%) x ([ 1 - (1 /(1 + 7.5%)13 )] / 7.5%) } + { 1.000 / (1 + 7.5%)13}

Current bond price = { (FV x CR%) x ([ 1 - (1 /(1 + YTM)t )] /YTM) } + { FV / (1 + YTM)t}

1050 = { (42) x ([ 1 - (1 /(1 + YTM)10 )] /YTM) } + { 1000 / (1 + YTM)10}

Figure 7.4; maturing in November 2027. This is a bond prices or treasury note. Coupon rate is 8%; Its bidprice is 136:29, actually translates into 136 29/32, or 136.90625 % of face value. The asked price from the previous day is 5/32 of 1%, or 0.15625 %.

Jika IR turun 2%

Maka BP naik

$1.177,05

$1.167,68

$1.124,20

$1.053,46

$1.018,87

$ 981,48

$ 948,46

$ 885,07

$ 849,28

$ 841,92

Bond

Val

ue ($

)

Interest Rate (%)

5 6 7 8

1 year

3 years

13 years

12 years

8 years

228 19 Seether Co., maturity 20years; coupon bonds 8%; bond price $930; semiannual payments. Bond yield?

=((40+((1000-930)/40))/((1000+930)/2))*100%Bond Yield = 4.33%

21 Bond; coupon rate 6.8%; clean price $1.073; semiannual payment; due to in two months. The invoice price?

23 Company (Ticker) Coupon Maturity Last Price Last Yield EST (000s)

IOU (IOU) 7.2 15-Apr-23 108.96 ? 1,827

Current Yield = Annual Interest / Current PriceCurrent date is April 15, 2009 and FV is $ 1.000.

=((72+((1000-1827)/23))/((1000+1827)/2))*100%YTM is 2.55 %Last Yield is YTM = 2.55%Current Yield = (2.55% x 1.000)/1.827=(2.55%*1000)/1827Current Yield is 1.40%

25 Tesla Corporation; ZCB maturity 25 years; required return 9%;a) These bonds sell at a price that is much lower than its stated value.

The Initial Price is $ 115.97 Assuming FV is $1.000

c) Repeat part b) using the straight-line method for the interest deduction.

Year Beginning Value Ending Value Year Ending Value

1 $ 115.96 $ 126.40 $ 10.44 $ 35.36 14 $ 355.53 $ 387.53 $ 32.00 $ 35.36 2 $ 126.40 $ 137.78 $ 11.38 $ 35.36 15 $ 387.53 $ 422.41 $ 34.88 $ 35.36 3 $ 137.78 $ 150.18 $ 12.40 $ 35.36 16 $ 422.41 $ 460.43 $ 38.02 $ 35.36 4 $ 150.18 $ 163.70 $ 13.52 $ 35.36 17 $ 460.43 $ 501.87 $ 41.44 $ 35.36 5 $ 163.70 $ 178.43 $ 14.73 $ 35.36 18 $ 501.87 $ 547.03 $ 45.17 $ 35.36 6 $ 178.43 $ 194.49 $ 16.06 $ 35.36 19 $ 547.03 $ 596.27 $ 49.23 $ 35.36 7 $ 194.49 $ 211.99 $ 17.50 $ 35.36 20 $ 596.27 $ 649.93 $ 53.66 $ 35.36 8 $ 211.99 $ 231.07 $ 19.08 $ 35.36 21 $ 649.93 $ 708.43 $ 58.49 $ 35.36 9 $ 231.07 $ 251.87 $ 20.80 $ 35.36 22 $ 708.43 $ 772.18 $ 63.76 $ 35.36

10 $ 251.87 $ 274.54 $ 22.67 $ 35.36 23 $ 772.18 $ 841.68 $ 69.50 $ 35.36 11 $ 274.54 $ 299.25 $ 24.71 $ 35.36 24 $ 841.68 $ 917.43 $ 75.75 $ 35.36 12 $ 299.25 $ 326.18 $ 26.93 $ 35.36 25 $ 917.43 $ 1,000 $ 82.57 $ 35.36

13 $ 326.18 $ 355.53 $ 29.36 $ 35.36 TOTAL $ 884.0 $ 884.0

229 27 Coupon bond 10%; maturity?Maturity is the specified date on which the principal amount of a bond is paid.

Assuming future value is same as present value.t = 0 year.

(Challenge) 29 Descript. Bond P Bond DKind Premium Bond DiscountCoupon 12% Coupon 6% CouponPayment Annual PaymentYTM 9%Maturity 5 yearsAnnual Interest $ 120.00 $ 60.00 Current Price $ 1,116.69 $ 883.31 Current Yield 10.75% 6.79%

9.06% 10.49%

The relationship between current yield and expected capital gain yield is lower current yield, so higher expected capital gain yield.31 The Mc Keegan Corporation

Descript. Bond M Bond N Periode Bond MFace Value $ 20,000 Maturity 20 years 40First six years No Payment No Payment 1

$ 1,100 No Payment 11

over 6 years $ 1,400 No Payment 28

7%

Current Price $ 6,339.21 $ 5,051.45 33

Maturity Coupon Bid Asked Change Asked yield9-May-09 9125 100:03 100:04 … -2.15

YTM negative?

Current bond price = { (FV x CR%) x ([ 1 - (1 /(1 + YTM)t )] /YTM) } + { FV / (1 + YTM)t}

930 = { (40) x ([ 1 - (1 /(1 + BY)40 )] /BY) } + { 1000 / (1 + BY)40}

The Invoice Price = Dirty price = 1.073 + (0.5 x 6.8% x 1.000 x 2/4) = 1.073+17 = $ 1.090.

Current bond Price = { (FV x CR%) x ([ 1 - (1 /(1 + YTM)t )] /YTM) } + { FV / (1 + YTM)t}

1.827 = { (72) x ([ 1 - (1 /(1 + YTM)23 )] /YTM) } + { 1000 / (1 + YTM)23}

b) Using IRS amortization role, interest deduction is $ ((1.000-115.97)/25) = $ 35.36

Implicit Interest Expense

Stright-line Interest Expense

Beginning Value

Implicit Interest Expense

Straight-line Interest Expense

d) According part b) and c), Tesla Corporation prefer Straight-line method because the deductions for interest expense were stabil but if use the implicit interest method were larger in the early years.

1000 = 1000/(1.1)t

Expected Capital Gains Yield

semiannual until 6 years

Semiannual compound

Treasury Bond in The Wall Street Journal

Anyone would buy this Treasury bond with negative YTM use other analysis, because the bond yields (YTM) only represent the combined effect of no fewer than six things. The first is the real rate of interest. On top of the real rate are five premiums representing compensation for (1) expected future inflation; (2) IRR; (3) default risk; (4) taxibility; and (5) lack of liquidity.

35

Descript. The Stock The Bondeach month 900 450expected return 11% 7%periode (25-30) y 60 60PV $ 103.04 $ 465.95 Withdrawal @mont $ 103.04 $ 465.95 combine $ 568.99 effective return 9%inflation 4%PV $ 1,827.67

- by -

Planning for retirement, over 30 years, invest $900 a month in a stock and $450 a month in a bond. The stock have annual expected return 11% and bond 7%; When retairement, I will combine in an account with a 9% effective return. Inflation this periode 4%. How much can i withdraw each month from account in real terms assuming a 25-year with drawal period?the nominal dollar amount of my last withdral?

Name : Bayu Anggara SilvatikaSubject : Financial MangementLecturer : Prof. Dr. Ahmad Rodoni

Referensi : "Fundamentals of Corporate Finance" 9th Ed. By Ross/Westerfield/JordanChapter : Ch. 7 Page 226-230

Ch. 8 Page 255-258Questions : Nomor Ganjil

CHAPTER 8 STOCK VALUATION

Page No. Answers

255 1 The Jackson-Timberlake Wardrobe Co. devidend $1.95 per share, rate constant 6%. If investor require 11% return, Current Price? The price in 3 years? 15 years?

(Basic) Po = EPS / r In 3 years and 15 years, the price is constant ($ 32.5)Po = 1.95/0.06 Because the rate is constant.Po = 32.5If r = 11%r = {EPS/Po} + {(P1-Po)/Po}11% = 6% + {(P1-32.5)/32.5}P1 = 34.125So, the current price is $ 34.125.

3

5 R = (D1/Po) + gDividend yield 6.3%(D1/Po) = Divident yieldRequired return ( R) = 6.3% + 5.2% = 11.5%

7 Apocalyptica Corp.; dividend $ 9.75; for 11 years; required return 10%. The current share price?

The current price = $ 27.82256 9

Red Inc. Yellow Corp. Blue CompanyDividend $ 2.35 $ 2.35 $ 2.35 Growth rate 5% 5% 5%Required return 8% 11% 14%Stock price $ 78.33 $ 39.17 $ 26.11

(Intermediate) 11 Metallica Bearings.Periode Dividend

0-9 No10 $ 10

next increase 5%If the required return 14%, the current share price?D1-9 0D10 $ 2.70 P10 D10 x (1+5%)/(14%-5%)

$ 31.47

P0 = $ 9.22

So, the current price is $ 9.22.13 Far Side Corporation; dividend 4 years with expected to pay $11; $8; $5; dan $2.

growth rate: 5%; required return 12%. The current price?Periode Devidend P(t)

1 $ 11 $ 9.82 2 $ 8 $ 6.38 3 $ 5 $ 3.56 4 $ 2 $ 1.27

P4 $ 19.07 $ 12.12 The current price is $ 33.15

15 Eva Corp.Year Total Dividend P(t)

1 =76*1.25 $ 96 $ 88.67 2 =96*1.25 $ 120 $ 102.88 3 =120*1.25 $ 151 $ 120.03

P3 $ 960.56 $ 762.53 The current price is $ 1,074.10

The devidend coming year is $ 53.705, or $(1.074,10/20), if there were 20 million share.

17 Teder Corporation; currently stock $64 per share. Required return 10%; growth rate constant 4.5%. The most recent dividend per share?

Po = D1 / (R-g)D1 = P0 x (R-g)D1 = 64 x (10% - 4.5%)D1 = 3.52D1 = D0 x (1 + g)D0 = D1 / (1+g)D0 = 3.52 / (1+4.5%)D0 = 3.37So, the most recent dividend is $ 3.37 per share.

From the previous problem, the dividend yield is 5%; the expected capital gain yield is 14.29% or (48-(2.10/5%))/(2.10/5%)).

The current price = Po x (1 + g)11

The current price = 9.75 x (1 + 10%)11

Red Inc., Yellow Corp., and Blue Company; devidend $2.35 next year. The growth rate 5%; The required return 8%, 11%, 14%. The stock price?the relationship between the required return and stock price?

The relationship between the required return and stock price is Higher required return, lower the stock price.

(D1/(1+14%)1) + (D2/(1+14%)2) + … + P10/(1+14%)10)

257 19 RJW Enterprise, Inc.52-week

HI LO STOCK (DIV) YLD (%) PE VOL (100S) CLOSE NET CHG72.18 53.17 RJW 1.48 2.1 19 17652 ?? -.23

21

P11 =(1.74*((1+25%)^11))*((1+6%))/(12%-6%) $ 357.86

Stock price 11 years is $ 357.86.

Po = (((1.74*1.25)/(12%-25%)) * (1-((1.25/1.12)^11)))+ (E89/((1.12)^11)) $ 142.14

(Chalange)23 a) Currently pays a $3.20 annual dividend, raising this dividend by 6% per year indefinitely. If the required return 12%, the current share price?

Periode Devidend P(t)1 $ 3.20 $ 2.86

P1 $ 50.48 $ 45.07 The current price is $ 47.93

b) Quarterly installments, just paid a $ .80 dividend per share, as it has for the previos three quarters. The current share price?Periode Devidend P(t)

3/4 $ 0.80 $ 0.73 P1 $ 12.98 $ 11.92 The current price is $ 12.66

258 25 Storico Co. has the current share price $ 63.82, according the previous problem. Rate of return?Dividend $ 2.45, increase dividend by 20%; reduce growth rate by 5% and reach average 5% dividend constant growth.

P1 =(2.45*((1+20%)^1))*((1+5%))/(R-5%)= 2.94 * (1.05/(R-5%)

Po = (((2.45*1.20)/(R-20%)) * (1-((1.20/((1+R))^1)))+ ( (2.94 * (1.05/(R-5%))/((1+R)^1))Trial and error

R P0 Po (Current)0% -58.8

10% 58.863.82

9% 73.5So, the rate of return is between 9% to 10%.Rate of return is 9.66%

27 The Formula of The Price of a Share of Stock Today

Po =Do x (1+g1) x D0 x (1+g2)

(R-g1) (R-g2)

- by -

The closing price for this stock is $ (53.17 - 0.23), or $ 52.94 per share.If company has 25 million shares, net income for the most recent four quarter is $ (52.94 x 25 million), or $ 1.323,50 million.Chartreuse Country Choppers Inc.; dividend growth at 25% per year for the next 11 years before leveling off at 6% into perpetuity. The required return 12%. If dividend per share just paid was $ 1.74, the stock price?

P11 = { D12 / (R-g2) } = { [D0 x [ (1+g1)5 ] x (1+g2) ] / (R-g2) }

Po = D1 / (R-g1) x [ 1 - {((1+g1)/(1+R))t} + [Pt /((1+R)t)]

So, the stock price today is $ 142.14.

P1 = { D2 / (R-g2) } = { [D0 x [ (1+g1)1 ] x (1+g2) ] / (R-g2) }

Po = D1 / (R-g1) x [ 1 - {((1+g1)/(1+R))t} + [Pt /((1+R)t)]

x [ 1 - ((1+g1)/(1+R))t] + ((1+g1)/(1+R))t

Present Value of amount stock and Total dividend, with first rate of return (g1)

Present Value of amount stock and Total dividend, with second rate of return (g2) and adjusted from g1 to g2.