FIN 300 PRACTICE SETS 5, 6 and 7
MOST OF US NEED HELP WITH THESE PROBLEMS AS I CAN SEE FROM ALL THE EMAILS I AM GETTING
SO I CREATED THIS WIKI SO WE CAN ALL POST A COUPLE OF PROBLEMS THAT WE HAVE SOLVED
THEN EVERYONE CAN CHECK TO SEE HOW THE PROBLEMS ARE DONE.
IF YOU DO NOT KNOW HOW TO USE THIS WIKI, ALL YOU HAVE TO DO IS
1. CLICK "EDIT" AT THE TOP OF THE PAGE TO ADD SOMETHING
2. CLICK "SAVE CHANGES" AT THE BOTTOM OF THE PAGE TO SAVE THE WIKI
THANKS FOR EVERYONES INPUT!!
All of practice Set 5!!!!!!!!!!!!!!
A bond has a yield to maturity of 7.77% and the coupon rate is the same as Amkor Technology. If the bond matures in 2022, what is the value of this bond? YTM= .0777 r= .0777 A= $35.625(Coupon Rate: 7.125%) n=13 m=2 ANSWER= VB= 947.80
VB= A [ 1- (1/ (1+ r/m)mn / r/m] + 1000/ (1+ r/m)mn
VB= 35.625 [ 1- (1/ (1+ .0777/2) 26 / (.0777 / 2)] + 1000 / (1+ .0777/2) 26
Two years ago you purchased 316 corporate bonds. The bonds mature in 2029, have a coupon rate of 8 5/8% and a yield to maturity of 6.46%. What was the cost of the entire purchase? n=22 m=2 r= .0646 A= $43.125 (CR: .08625 *1000 / 2)
VB= 43.125 [ 1- (1/ (1+ .0646/2) 44 / (.0646 / 2)] + 1000 / (1+ .0646/2) 44 VB= $1252.39 1252.39*316=395,755.24
Seven years ago you inherited 117 Six Flags bonds. At that time the YTM was 10.21%. By how much has the total value of your bonds increased or decreased? YTM=10.21 m=2 n= 12 r=.1021 A= $48.125 (coupon rate= 9.625%)
VB= 48.125 [ 1- (1/ (1+ .1021/2) 24 / (.1021 / 2)] + 1000 / (1+ .1021/2) 24 VB= $960.05 Last Price= 23.250% of 1000 $232.50
960.05 – 232.50 = (727.55) (727.55) * 117 bonds = ($85,123.35) LOSS!!!
You purchased 21 February 2027 bonds 8 years ago when the bonds were purchased for 3:31 points less than their current purchase price. If you sell these bonds 12 years after you purchase them, what will be your profit or loss from this transaction, assuming the YTM when you sell them will be 4.97%? Buy=140:11 less 3:31 so, 140 11/32% – 3 31/32% $1403.4375- $39.6875 = $1363.75
Coupon rate= 6.625% so A= $33.125 m=2 n= 14 yrs to maturity r= .0497 (the given YTM)
VB= 33.125 [ 1- (1/ (1+ .0497/2) 28 / (.0497 / 2)] + 1000 / (1+ .0497/2) 28 VB= $1165.52selling price
1165.52 – 1363.75 (purchase price) = (198.23) * 21 bonds = $4,162.83 LOSS!!!
From problem 4: suppose you had sold the bonds 5 years ago when the YTM was 5.44% and invested the money is a mutual fund that yields an average of 8.61%, what would that investment be worth 17 years from today? (Assume monthly compounding.)
r= YTM 5.44% (.0544) n=23 (2027-2004) m= 2 A= 33.125 VB= 33.125 [ 1- (1/ (1+ .0544/2) 46 / (.0544 / 2)] + 1000 / (1+ .0544/2) 46
VB= $1154.45*21 bonds= $24,243.45 Use:FVS= PVS (1 + r/m )mn r= .0861 m=12 n= 17 FVS=24,243 (1+.0861/12)204 FVS= $104,232
You sold 650 lots of Caterpillar and bought a bond that matures 10 years after JP Morgan, and the coupon rate is 500 basis points more than JP Morgan’s coupon rate. Assuming a YTM of 7.36%, how many bonds can you buy?
1lot=100 shares so 650 * 100 = 65,000 shares * closing price of Caterpillar 37.23= $2,419,950 JP Morgan’s Coupon Rate= 3.125% + 5% (500 basis points) new CR= 8.125% * 1000 = 81.25 / 2 = A = 40.625 r= .0736 m=2 n= 12 (2021-2009=12)
VB= 40.625 [ 1- (1/ (1+ .0736/2) 24 / (.0736 / 2)] + 1000 / (1+ .0736/2) 24 VB= $1,060.28 2,419,950 / 1,060.28 = 2,282 BONDS
You purchased $21,000,000 face value of July 16, 2009 treasury bills (see date on quote sheet). If you hold these bills until maturity, how many Proctor and Gamble bonds can you buy with the interest from the bills, assuming the coupon rate on the bonds is 6.2% and the YTM by the time you purchase them will be 7.46%? The bonds mature in 2030.
DTM=(31-16)+28+31+30+31+30+16 =181 PriceT-Bill= 1000[ 1- ( DTM/ 360 * DR] = 1000 [ 1- (181/360 * .00250 ] DR is Ask=.250
PriceT-Bill= $998.74 now 1,000 – 998.74 = $1,26 per bill So, $21,000,000 Face Value / 998.74 = 21,026 Bills * 1.26= $26,492.76
VB= 31 [ 1- (1/ (1+ .0746/2) 42 / (.0746 / 2)] + 1000 / (1+ .0746/2) 42 where r=.0746 m=2 n= 21 (30-9) A=31 VB= $867.38
$26,492.76 / 867.38 = 31 P&G Bonds
In three years when you are 25, you will gain control of a trust fund that consists of 2525 General Electric Capital Bonds. You plan to sell these bonds and buy an annuity that you hope will yield an average of 9.73%. In three years, the YTM on the bonds is forecast at 8.18%. Assuming you will live for another 60 years, how much will you receive each month from this annuity?
r= .0818 m=2 n= 27 bc Gen. Elc. Matures in 2039 (2039-2012) A=34.375 bc CR is 6.875% for Gen. Elc.
VB= 34.375 [ 1- (1/ (1+ .0818/2) 54 / (.0818 / 2)] + 1000 / (1+ .0818/2) 54 VB= $858.78 * 2525 bonds = $2,168,419.50
PVAO= A[ 1- (1/ (1+ r/m)mn / r/m ] where r=.0973 m=12 n= 60 2,168,419 = A [ 1- (1/ (1+ .0973/12)720 / .0973/12 ] A= $17,634
The Altria bonds are callable and are being called today at 109.66. If you purchased them 3 years ago when the YTM was 10.01%, what is your yield to call? r= .1001 A=48.5 bc CR=9.7% m=2 n=12 (2018-2006)
VB = 48.5 [ 1- (1/ (1+ .1001/2) 24 / (.1001 / 2)] + 1000 / (1+ .1001/2) 24 VB= $978.62
YTC= {[(CP-P) / t ] + I } / [ (CP+P) / 2 ] = {[(1096.6 - 978.62 ) / 3 ] + 97 } / [ (1096.6+978.62) / 2 ] = 13.14%
You inherited 52,431 shares of a stock that has a dividend yield of 2.7% and the same price as Pentair Inc. You have saved 2 dividend checks and plan to use the money to buy bonds that have a current yield of 4.29% and a coupon rate of 5.47%. What will be the amount of one interest check from the bonds? Div.Yield= Annual Div /Closing Price .027= X /23 so AD=0.621
r= .0429 m=2 A=27.35 .0429= 54.7 / p p=1275.06 54.7 / 2 = 27.35 per bond 52,431 * .3105 (.621/4quaters = .15525 *2 checks) =$16,279.83 16,279.83 / 1275.06 = 12.77 so 13 BONDS so 13 * 27.35 = $355.55
PS 5 # 1
r=YTM= 7.77%
m= 2 (semiannual interest)
n= 13 (# of years to maturity = 2002-2009)
A= annuity = .07125*1000 = 71.25/2 = 35.625
Value of Bond = PV (semiannual interest) + PV (lump sum face value)
= 35.625 ((1-1/1+(.0777/2))26)) + (1000/(1+(.0777/2))26))
576.41 + 371.22
= 947.63
PS 5 #2
r=YTM=6.46%
m=2 (semiannual interest)
n=# of years to maturity = 22
A= .08625*1000 = 86.25/2 =43.125 (divide by 2 because semiannual interest)
43.125 ((1-(1/(1+(.0646/2))44)) + (1000/(1+(.0646/2))44))
1005.48 + 246.91
= 1252.39
1252.39 x 316 bonds = $395,755.24
If anyone could do the whole practice set 5, that would be great. If anyone needs practice set 7, problems 1-3, ill post them here later on.
If somebody missed class today problem #2 set 7.
Problem 2 set7.doc
Practice set 7 #1
Cost(Mkt Value)=8,675,000
mod=1,271,000
ebdit=3,475,000
sv=8,275,000
wc=749,000
cost of capital=17.3%
tax rate=25%
8,675,000+1,271,000+749,000=10,695,000- investment value
depreciation yr1 5yr macrs depr base depreciation
1 20% 9,946,000 1,989,200
2 32% 9,946,000 3,182,720
3 19% 9,946,000 1,889,740
4 12% 9,946,000 1,193,520
5 11% 9,946,000 1,094,060
t1
ebdit-depr1=1,485,800(EBT)
ebt*0.75=1,485,800*0.75=1,114,350
so, NI=1,114,350
ACF1=3,103,550
t2, same as t1, except use the depreciation for year 2
t3
ebt yr3=ebdit-depreciation yr 3
ebt yr3=1,585,260
NI yr3=ebt3*0.75=1,188,945
AFC=3,028,685
Sale=8,275,000
Tax=(Mkt value-Book Value)*0.25=1,347,667
Book value=Mkt value+mod-depr yr1-depr yr2-depr yr3=2,844,040
t3=acf+sv-tax+wc=10,755,020
t0=mkt value+mod+wc=10,695,000
1.73=1+cost of capital
NVP=t0+(t1/1.1731)+
(t2/1.1732) +
(t3/1.1733) =
1,087,009.94
7 #3
Adding new product line. Device retail for $250. Sell 5000 yr 1, 5000 yr 2, 2600 yr 3. Gross margin=55% fixed expenses not changed. Machinery to make product will cost $1,000,000 and be worthless at the end of its 3 yr life. 3 yr MACRS. 38% income and capital gains. Cost of cap: 16.2% NVP and PP?
Additional/less working cap: W/o new product line W/ new product line Working cap=CA-CL
Current Assets 433,000 Current Assets 346,000
Current Liabilities 334,000 Current Liabilities 220,000
Long term debt 875,000 Long Term Debt 875,000
Equity 822,000 Equity 822,000
Step 1: Depreciation Schedule
Useful Life Dep. Base * 3yr MACRS
1,000,000 * .33 =
1,000,000 * .45 =
1,000,000 * .15 = Annual Dep.
1 330,000
2 450,000
3 150,000
Step 2: Investment DB (1,000,000)
WC (27,000)
Investment (1,027,000)
WC old=433000-334000=99,000
WC new=346000-220000=126,000
ΔWC=126000-99000=$27,000
Step 3: Life of asset GM EBDIT
Rev: t=1: 250*5000=$1,250,000*.55=$687,500
Rev-COGS=Gross profit t=2 250*5000=$1,250,000*.55=$687,500
GM=gross profit/sales t=3 250*2600=$650,000 *.55=$357,500
T=1 EBDIT: 687,500 t=2 EBDIT: 687,500
-Dep1 330,000 -Dep 2: 450,000
EBIT=EBT: 357,500*(1-.38) EBIT=EBT: 237,500*.62
NI: 221,650 NI: 147,250
+dep1: 330,000 +dep2: 450,000
ACF1: $551,650 ACF2: 597,250
T=3 EBDIT: 357,500
-Dep3: 150,000 ACF’ 278,650 MV=0
EBIT=EBT: 207,500*.62 +WC 27,000 BV=1000000-330000-450000-150000=70,000
NI: 128,650 +tax credit 26,600 loss tax credit70,000*.38=26,600
+dep3: 150,000 ACF3 $332,250
ACF’: $278,650
NPV r=.162 m=1 t=1,2,3 NPV=(1,027,000)+551650/1.162+597250/(1.162)2+332250/(1.162)3=$101,830Accept
PP 551650+597250=1,148,900 PP=2 (b/w yr 1 and 2) accept
7 # 4
Capital Budgeting:
Equity = CS + RE
Working Cap = Cur Assets – Cur Liability
Replacing jet. Old plane purchased 10 yrs ago for $672,000. Econ and actg life of 14 yrs. Depreciated to salvage value $0, SLD. Could be sold today:$118,400
New Plane cost $3.7 million, used for 4 yrs, and then sold to another airline for $400,000. Tax rt. 41% and the cost of capital 18.2% Capital gains rt. 20% Revenue under new plane increase from $875,000 to $1,734,000/yr. Expenses not affected. 3 yr MACRS Buy new plane?
Step 1: Depreciation Schedule
Old: DB=$672,000 SLD=(672,000-0)/14=$48,000/yr
New: BV=$3,700,000
MACRS DEP: Yr1 Yr2 Yr3 Yr4 Yr5 Yr6
3 Year 33% 45% 15% 7%
5 Year 20% 32% 19% 12% 11% 6%
Useful Life Dep. Base * 3yr MACR = Dep. NEW - Dep. OLD = ∆Dep.
1 3.7 mil. .33 1,221,000 48,000 1,173,000
2 3.7 mil. .45 1,665,000 48,000 1,617,000
3 3.7 mil. .15 555,000 48,000 507,000
4 3.7 mil. .07 259,000 48,000 211,000
Step 2: New (3,700,000)
+Sale old 118,400
+tax credit 14,720
Investment (3,566,880)
MV old=118,400
BV=672,000-(10*48000)=192,000
loss tax credit= 3,600*.2=14,720
Step 3: Revenue new-old=1734000-875000=$859,000=ΔEBDIT
T=1 ΔEBDIT: 859,000 t=2 ΔEBDIT: 859,000
-ΔDep1 1,173,000 -ΔDep 2: 1,617,000
ΔEBIT=EBT: (314,000)*(1-.41) ΔEBIT=EBT: (758,000)*.59
ΔNI: (185,260) ΔNI: (447,220)
+Δdep1: 1,173,000 +Δdep2: 1,617,000
ΔACF1: $987,740 ΔACF2: $1,169,780
T=3 ΔEBDIT: 859,000 t=4 ΔEBDIT: 859,000
-ΔDep3 507,000 -ΔDep 4: 211,000 ACF’ 593,320 MV new=400,000
ΔEBIT=EBT: 352,000*.59 ΔEBIT=EBT: 648,000*.59 Sale new 400,000 BV=3.7 mill-1.665mil-555,000-259,000=0
ΔNI: 207,680 ΔNI: 382,320 -tax liab. (80,000) gain tax liab=400000*.2=80,000
+Δdep1: 507,000 +Δdep4: 211,000 -salvage 0
ΔACF3: $714,680 ΔACF’: $593,320 ACF4 $913,320
NPV r=.182 m=1 t=1,2,3 NPV= (356,6880) +987740/1.182+1169780/(1.182)2+712680/(1.182)3+913320/(1.182)4= $(993,279) Reject

