1 Reviewing…Reviewing… EAW and Types of Projects: Revenue projects are expected to make money at a rate at least as high as the MARR, select largest EAW

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Reviewing…Reviewing…Reviewing…Reviewing…

EAW and Types of Projects:•Revenue projects are expected to make money at a rate at least as high as the MARR, select largest EAW that is 0.•Service projects are “have to do” situations, select largest EAW (lowest EAC).

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Reviewing…Reviewing…Reviewing…Reviewing…

For a capital purchase (P) with a salvage value (S), the EAC can be calculated two ways:

1.P(A I P, i, n) – S (A I F, i, n)

2.(P – S) (A I P, i, n) + S*i

Annual equivalentOpportunity

for loss of value cost

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BOND TERMINOLOGYBOND TERMINOLOGYBOND TERMINOLOGYBOND TERMINOLOGY

1. Face Value, Par Value, Maturity Value – How much the borrower will pay the holder when it matures.

2. Coupon Rate, Nominal Annual Interest Rate – Nominal yearly interest rate paid on face value.

2. Bond Dividend– Interest paid periodically until maturity

4. Maturity Date – Date at which you receive the face value

5. Market Value, Current Price– What someone is willing to pay for the remaining cash flows.

6. Yield to Maturity – Actual interest rate earned over holding period

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CFD with Bond Terms…CFD with Bond Terms…CFD with Bond Terms…CFD with Bond Terms…

01 2 3 n periods

(to Maturity Date)

Bond Price

Dividend

Face Value

Yield Rate = ia = (1+ ib) m – 1

Coupon Rate

Dividend Periods / Yrib =

Coupon Rate

Dividend Periods / YrDividend = (Face Value) (ib) – or – Face Value

Yield to Maturity = i* such that NPW = 0

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Problem 1Problem 1Problem 1Problem 1

A bond with a face value of $25 A bond with a face value of $25 000 pays a coupon rate of 4% in 000 pays a coupon rate of 4% in quarterly payments, and will quarterly payments, and will mature in 6 years.mature in 6 years.

If the current MARR is 2% per If the current MARR is 2% per year, compounded quarterly, year, compounded quarterly, how much should the maximum how much should the maximum bond price be?bond price be?

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Problem 1Problem 1Problem 1Problem 1Given:Given:

MARR = 2% per year, cpd MARR = 2% per year, cpd quarterlyquarterlyFace Value = $25 000 Face Value = $25 000 Coupon Rate of 4%, paid quarterly Coupon Rate of 4%, paid quarterly Maturity in 6 yearsMaturity in 6 years

Find Max. Price:Find Max. Price:

n = (6 yr)(4 qtr) = 24 qtrs

yr

01 2 3

Dividend = (Face Value) (ib) = ($25 000) (.01) = $250/pd

Face Value = $25 000ib = Coupon Rate = 4% / yr = 1% /qtr. Dividends/yr 4 qtr /yr

Bond Price (maximum)

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Problem 1, cont.Problem 1, cont.Problem 1, cont.Problem 1, cont.

MARR = 2%/yr, cpd quarterly, so find a quarterly equivalent rate!Finding effective MARR to match dividend period:

i =

a.) Find effective quarterly rate (to match compounding), since pp = cp:

so inserting values and solving for i:

i = = 0.5%/qtr.

Given:Given:MARR = 2% per year, cpd MARR = 2% per year, cpd quarterlyquarterlyFace Value = $25 000 Face Value = $25 000 Coupon Rate of 4%, paid quarterly Coupon Rate of 4%, paid quarterly Maturity in 6 yearsMaturity in 6 years


2% / yr

4 qtrs / yr

r

m

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Problem 1, Cont.Problem 1, Cont.Problem 1, Cont.Problem 1, Cont.Given:Given:

MARR = 2% per year, cpd MARR = 2% per year, cpd quarterlyquarterlyFace Value = $25 000 Face Value = $25 000 Coupon Rate of 4%, paid quarterly Coupon Rate of 4%, paid quarterly Maturity in 6 yearsMaturity in 6 years


n = 24 qtrs0

1 2 3

$250/pd

$25 000i = 0.5% / qtr.

Bond Price = $250(P/A, 0.5%, 24) + $25 000(P/F, 0.5%, 24)

=$250 (22.5629) + $25 000 (.8872) = $27 822.30

Finding NPW of remaining cash flows at effective MARR:

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Problem 2Problem 2Problem 2Problem 2

You desire to make an You desire to make an investment in bonds provided investment in bonds provided you can earn a yield rate of 12% you can earn a yield rate of 12% per year on your investment, per year on your investment, compounding monthly. compounding monthly.

How much can you afford to pay How much can you afford to pay for a bond with a face value of for a bond with a face value of $10 000 that pays a coupon rate $10 000 that pays a coupon rate of 10% in quarterly payments, of 10% in quarterly payments, and will mature in 20 years?and will mature in 20 years?

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MARR = 12% per year, cpd monthlyMARR = 12% per year, cpd monthlyFace Value = $10 000 Face Value = $10 000 Coupon Rate of 10%, paid quarterly Coupon Rate of 10%, paid quarterly Maturity in 20 yearsMaturity in 20 years


n = (20 yr)(4 qtr) = 80 qtrs

yr

01 2 3

Dividend = (Face Value) (ib) =($10 000) 2.5% = $250/pd

Face Value = $10 000ib = Coupon Rate = 10% = 2.5%/pd. Dividends/yr 4

Bond Price (maximum)

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Problem 2, cont.Problem 2, cont.Problem 2, cont.Problem 2, cont.Given:Given:



Yield Rate = effective 12%/yr, so find a quarterly equivalent rate!Annual Bond Yield needs to equal MARR:

(Check: ia = (1+ iqtr) m – 1 = (1+.02874)4 – 1 = 12% / yr !)

Note: 3 mo. per qtr!

a.) Find effective monthly rate (to match compounding), so set:12% = .12 = (1 + imo )12 – 1

and solving for i: 1 imo = (1.12) 12 – 1 = 0.949%/mo.

b.) Find effective quarterly rate (to match dividend period): iqtr = (1+ imo) m – 1 = (1+.00949)3 – 1 = 2.874% / qtr

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n = (20 yr)(4 qtr) = 80 qtrs

yr

01 2 3

Bond Price = $250(P/A, 2.874%, 80) + $10 000(P/F, 2.874%, 80) =$250 (31.19054) + $10 000 (.10367) = $8 834

Face Value = $10 000

Quarterly Yield Rate = 2.874% / qtr

ib = Coupon Rate = 10% = 2.5%/pd. Dividends/yr 4

Dividend = (Face Value) (ib) =($10 000) 2.5% = $250/pd

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Problem 3Problem 3Problem 3Problem 3A $1 000 face value bond will A $1 000 face value bond will mature in 10 years. The annual mature in 10 years. The annual rate of interest is 6%, payable rate of interest is 6%, payable semi-annually. semi-annually.

If compounding is semi-annual If compounding is semi-annual and the bond can be purchased and the bond can be purchased for $870, what is the yield to for $870, what is the yield to maturity in terms of the maturity in terms of the effective annual rate earned?effective annual rate earned?

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Bond Price = $ 870Bond Price = $ 870Face Value = $1 000 Face Value = $1 000 Coupon Rate of 6%, cpd & paid semi-annually Coupon Rate of 6%, cpd & paid semi-annually Maturity in 10 yearsMaturity in 10 years

Find Annual Yield to Maturity:Find Annual Yield to Maturity:

01 2 3

$870

$1 000

i =

Find semi-annual Yield to Maturity = i* such that NPW = 0

ib = Coupon Rate = 6% = 3% / Dividend pd. Dividends/yr 2

Dividend = (Face Value)(ib) = ($1 000) (3%) = $30/pd

n = (10 yr)(2 divs) = 20 pds

yr

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Find Annual Yield to Maturity:Find Annual Yield to Maturity:

01 2 3

$870

$1 000

Still need to come up with a closer value …

i =

Yield to Maturity = i* such that NPW = 0

Want NPW = 0 $30 (P/A, i*, 20) + $1 000 (P/F, i*, 20) = $870

Dividend = $30/pd

n = 20 pds

Try 3% $30 (P/A,3%, 20) + $1 000 (P/F, 3%, 20) = $1 000 High!

Try 4% $30 (P/A,4%, 20) + $1 000 (P/F, 4%, 20) = $ 864 Low!

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Find Annual Yield to Maturity:Find Annual Yield to Maturity:Need to interpolate: 4% $ 864 (Low), 3% $1000 (High), Find x% = $870:

x% – 3% = 4% – 3%

870 – 1000 864 – 1000

Annual Yield to Maturity = 8.08% / yr !

Need to convert semi-annual (6 mo.) yield rate to Annual Yield Rate:

Yield Rate = ia = (1+ i6 mo) m – 1 ia = (1+ .0396) 2 – 1

x = 3 + 130 = 3.96% / 6 mo.

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Documents

1 Reviewing…Reviewing… EAW and Types of Projects: Revenue projects are expected to make money at a rate at least as high as the MARR, select largest EAW