CTC 475 Review Methods for determining whether an alternative is feasible or not Methods for determining whether an alternative is feasible or not Establishing

CTC 475 Review CTC 475 Review

Methods for determining whether an Methods for determining whether an alternative is feasible or notalternative is feasible or not

Establishing MARREstablishing MARR Net cash flowsNet cash flows

FeasibilityFeasibility

Initial investment $84,000Initial investment $84,000 Net Annual Revenue is $18,000Net Annual Revenue is $18,000 Salvage value=$0Salvage value=$0 Study period=6 yearsStudy period=6 years MARR=18%MARR=18%

Using PW, is this project feasible?Using PW, is this project feasible?

AnswerAnswer

PW = PW = -$84K-$84K+$18K(P/A+$18K(P/A18,618,6)) PW = PW = -$84K-$84K+$18K(3.4976)+$18K(3.4976) PW = PW = -$84K-$84K +$62,957 +$62,957 PW = PW = -$21,043-$21,043

PW is negative; not feasiblePW is negative; not feasible

FeasibilityFeasibility

Initial investment $10,000Initial investment $10,000 Annual Receipts = $8,000Annual Receipts = $8,000 Annual Expenses = $4,000Annual Expenses = $4,000 Salvage value=-$1000 (negative value Salvage value=-$1000 (negative value

means you must pay to dispose asset)means you must pay to dispose asset) Study period=5 yearsStudy period=5 years MARR=15%MARR=15%

Using FW, is this project feasible?Using FW, is this project feasible?

AnswerAnswer

FW = FW = -$10K(F/P-$10K(F/P15,515,5 ) )+$4K(F/A+$4K(F/A15,515,5) ) -$1K-$1K FW = FW = -$10K(2.0114)-$10K(2.0114)+$4K(6.7424)+$4K(6.7424) - -

$1K$1K FW = FW = -$20,114-$20,114 +$26,967 +$26,967 -$1K -$1K FW = +$5,853FW = +$5,853

FW is positive; project is feasibleFW is positive; project is feasible

FeasibilityFeasibility Initial investment $50,000Initial investment $50,000 Annual Receipts = $20,000Annual Receipts = $20,000 Annual Expenses = $5,000Annual Expenses = $5,000 Salvage value= $0Salvage value= $0 Study period=5 yearsStudy period=5 years MARR=20%MARR=20%

Using AW, is this project feasible?Using AW, is this project feasible?

AnswerAnswer

AW = AW = -$50K(A/P-$50K(A/P20,520,5 ) )+$15K+$15K AW = AW = -$50K(.3344)-$50K(.3344)+$15K+$15K AW = AW = -$16,720-$16,720 +$15K +$15K AW = AW = -$1,720-$1,720

AW is negative; project is not feasibleAW is negative; project is not feasible

CTC 475 CTC 475

BondsBonds

ObjectivesObjectives

Know why bonds are issuedKnow why bonds are issued Know how bonds workKnow how bonds work Solve bond problemsSolve bond problems

Bonds – Why are they issued?Bonds – Why are they issued?

Government agencies/private firms Government agencies/private firms issue bonds as a way to raise capital issue bonds as a way to raise capital ($)($)

Roads, bridges, water & ww plants Roads, bridges, water & ww plants are very expensiveare very expensive

Govt. Agencies often use bonds to Govt. Agencies often use bonds to pay for infrastructurepay for infrastructure

Bonds – How they WorkBonds – How they Work

XYZ company issues $5 million worth XYZ company issues $5 million worth of bondsof bonds

Brokerage firms split into smaller Brokerage firms split into smaller units ($1000, $5000) and sell to units ($1000, $5000) and sell to individual investorsindividual investors

Bond-Face ValueBond-Face Value

The stated value on the individual The stated value on the individual bond is the face, or par value (Ex bond is the face, or par value (Ex $1000)$1000)

The face value is paid back after a The face value is paid back after a specified length of time (5, 10 years)specified length of time (5, 10 years)

BondsBonds

Issuing unit is obligated to Issuing unit is obligated to redeemredeem the bond at the bond at par valuepar value at at maturitymaturity. . Issuing unit must specify a Issuing unit must specify a bond ratebond rate on the on the par valuepar value between the between the date of date of issuanceissuance and and date of maturitydate of maturity

Bond RateBond Rate

Examples of Bond Rates:Examples of Bond Rates: 10%/yr payable quarterly10%/yr payable quarterly 9-½%/yr payable semiannually9-½%/yr payable semiannually 6%/yr payable annually6%/yr payable annually

The bond rate applies to the par The bond rate applies to the par valuevalue

ExampleExample

7-year treasury note 7-year treasury note Face value =$1000Face value =$1000 Interest rate 9 3/8% payable Interest rate 9 3/8% payable

semiannuallysemiannually Earned interest of $46.90 every 6 Earned interest of $46.90 every 6

monthsmonths After 7 years, received $1000 After 7 years, received $1000

Bond ComplicationsBond Complications

Bonds are not complicated if the bond is Bonds are not complicated if the bond is bought at the bought at the date of issuancedate of issuance and held and held to the to the date of maturitydate of maturity

Bonds do get complicated when they Bonds do get complicated when they are sold between the are sold between the date of issuancedate of issuance and the and the date of maturitydate of maturity

Because interest rates fluctuate bonds Because interest rates fluctuate bonds are not usually sold at par valueare not usually sold at par value

BondsBonds

If you bought a $1000 bond paying If you bought a $1000 bond paying 9% and a new $1000 bond is paying 9% and a new $1000 bond is paying 4% you wouldn’t sell the bond unless 4% you wouldn’t sell the bond unless you got more than $1000.you got more than $1000.

Likewise, if you sell a $1000 bond Likewise, if you sell a $1000 bond paying 2% and a new $1000 bond is paying 2% and a new $1000 bond is paying 4% no one will buy your bond paying 4% no one will buy your bond unless you sell it for less than $1000unless you sell it for less than $1000

Bond ComplicationsBond Complications

Interest rates fluctuateInterest rates fluctuate

Selling bonds between the date of Selling bonds between the date of issuance and date of maturity for issuance and date of maturity for something other than the par value something other than the par value changes the actual yield ratechanges the actual yield rate

Bond EquationBond EquationP=Vr(P/AP=Vr(P/Ai,ni,n)+F(P/F)+F(P/Fi,ni,n))

P=purchase price of bondP=purchase price of bond F=sales price of a bondF=sales price of a bond V=par or face value of a bondV=par or face value of a bond R=bond rate per interest periodR=bond rate per interest period i=yield rate per interest periodi=yield rate per interest period A=V*r=interest payment receivedA=V*r=interest payment received

HintsHints

P (purchase price) may or may not P (purchase price) may or may not equal the par value. If the bond was equal the par value. If the bond was bought at the date of issuance then bought at the date of issuance then the purchase price = par valuethe purchase price = par value

F (sales price) may or may not equal F (sales price) may or may not equal the par value. If the bond is held to the par value. If the bond is held to maturity then the sales price = par maturity then the sales price = par valuevalue

Bond Problem TypesBond Problem Types

Find sales price (F)Find sales price (F) Find purchase price (P)Find purchase price (P) Find yield rate (i)Find yield rate (i)

Find sales price (F)Find sales price (F)

Find the selling price of a bond (F) if Find the selling price of a bond (F) if you want to sell it before it matures you want to sell it before it matures and you want a desired yield iand you want a desired yield i

Find purchase price (P)Find purchase price (P)

Determine the purchase price of a Determine the purchase price of a bond (P) so that you can make a bond (P) so that you can make a desired yield i for the future desired yield i for the future

Find effective yield (i)Find effective yield (i)

Determine the effective yield (i) for a Determine the effective yield (i) for a bond if it wasn’t bought and/or bond if it wasn’t bought and/or redeemed at par value redeemed at par value

Find F exampleFind F example

An individual purchased a $1000, 8% An individual purchased a $1000, 8% semi-annual bond for $1050 3 years semi-annual bond for $1050 3 years ago and is considering selling it. ago and is considering selling it. How much should be asked for the How much should be asked for the bond in order to earn a yield rate of bond in order to earn a yield rate of 6% compounded semiannually (3% 6% compounded semiannually (3% per semi comp. semi)?per semi comp. semi)?


P=$1050 P=$1050 (bond wasn’t bought at date of issuance)(bond wasn’t bought at date of issuance)

F=?F=? V=$1000V=$1000 r=4% per semi comp. semir=4% per semi comp. semi i=3% per semi comp. semii=3% per semi comp. semi n=6 semi’s n=6 semi’s (r,i & n periods must match)(r,i & n periods must match)

A=V*r=$40A=V*r=$40


F = $995F = $995

If owner of bond can sell it for at If owner of bond can sell it for at least $995 then the owner effectively least $995 then the owner effectively earns 6% per year compounded earns 6% per year compounded semiannuallysemiannually

Find P exampleFind P example

If a $1000, 12% semiannual bond is If a $1000, 12% semiannual bond is purchased, held for 3 years and purchased, held for 3 years and redeemed at par value, what must redeemed at par value, what must the purchase price have been in the purchase price have been in order for the bond to be preferred order for the bond to be preferred over investing at 14% compounded over investing at 14% compounded semiannually? semiannually?


P=? P=? (bond wasn’t bought at date of issuance)(bond wasn’t bought at date of issuance)

F=$1000 F=$1000 (bond held to maturity)(bond held to maturity)

V=$1000V=$1000 r=6% per semi comp. semir=6% per semi comp. semi i=7% per semi comp. semii=7% per semi comp. semi n=6 semi’s n=6 semi’s (r,i & n periods must match)(r,i & n periods must match)

A=V*r=$60A=V*r=$60


P = $952.29P = $952.29

If an investor can buy the bond for If an investor can buy the bond for $952 and hold it to maturity then the $952 and hold it to maturity then the owner effectively receives 14% per owner effectively receives 14% per year compounded semiannually. year compounded semiannually.

Find i exampleFind i example

If a $1000, 12% quarterly bond is If a $1000, 12% quarterly bond is purchased for $1020 and sold 3 purchased for $1020 and sold 3 years later for $950:years later for $950:

a) What was the quarterly yield?a) What was the quarterly yield?

b) What was the effective annual b) What was the effective annual return?return?


P=$1020 P=$1020 (bond wasn’t bought at date of issuance)(bond wasn’t bought at date of issuance)

F=$950 F=$950 (bond wasn’t held to maturity)(bond wasn’t held to maturity)

V=$1000V=$1000 r=3% per qtr. comp. qtr.r=3% per qtr. comp. qtr. i=?% per qtr. comp. qtr.i=?% per qtr. comp. qtr. iieffeff-?% per yr. comp. yearly-?% per yr. comp. yearly N=12 qtrs. N=12 qtrs. (r,i & n periods must match)(r,i & n periods must match)

A=V*r=$30A=V*r=$30


P=Vr(P/AP=Vr(P/Ai,ni,n)+F(P/F)+F(P/Fi,ni,n))

$1020=$30(P/A$1020=$30(P/Ai,12i,12)+$950(P/F)+$950(P/Fi,12i,12)) By trial and error: By trial and error: i = 2.444% per qtr. comp. qtr.i = 2.444% per qtr. comp. qtr.

iieff eff = (1+i)= (1+i)nn-1 = (1.0244)-1 = (1.0244)44-1 =-1 = iieffeff=10.12 %=10.12 %

Bond ProblemsBond Problems

Mr. Investor wishes to purchase a Mr. Investor wishes to purchase a $10,000 bond which has a fixed $10,000 bond which has a fixed nominal interest rate of 8% per year, nominal interest rate of 8% per year, payable quarterly. What should he payable quarterly. What should he pay for the bond to earn 10% per pay for the bond to earn 10% per year compounded quarterly?year compounded quarterly?

Answer (Find P = $8,908)Answer (Find P = $8,908)


Answer (Find P = $8,908)Answer (Find P = $8,908)


A bond with a face value of $5,000 A bond with a face value of $5,000 pays interest of 8% per year. The pays interest of 8% per year. The bond will be redeemed at part value bond will be redeemed at part value at the end of its 20-year life. If the at the end of its 20-year life. If the bond is purchased now for $4,600, bond is purchased now for $4,600, what annual yield would the buyer what annual yield would the buyer receive?receive?


Answer (Find i = 8.9%)Answer (Find i = 8.9%)

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CTC 475 Review Methods for determining whether an alternative is feasible or not Methods for determining whether an alternative is feasible or not Establishing