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).
1
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 equivalent
Opportunity
for loss of value
cost
2
BOND 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
3
CFD with Bond Terms…
ib =
Coupon Rate
Dividend Periods / Yr
Dividend = (Face Value) (ib) – or – Face Value
Coupon Rate
Dividend Periods / Yr
Face Value
Yield Rate = ia = (1+ ib) m – 1
Dividend
0
1
2
3
n periods
(to Maturity Date)
Bond Price
Yield to Maturity = i* such that NPW = 0
4
Problem 1
A bond with a face value of $25 000
pays a coupon rate of 4% in quarterly
payments, and will mature in 6 years.
If the current MARR is 2% per year,
compounded quarterly, how much
should the maximum bond price be?
5
Problem 1
Given:
MARR = 2% per year, cpd quarterly
Face Value = $25 000
Coupon Rate of 4%, paid quarterly
Maturity in 6 years
Find Max. Price:
ib = Coupon Rate = 4% / yr = 1% /qtr.
Dividends/yr 4 qtr /yr
Face Value = $25 000
Dividend = (Face Value) (ib)
= ($25 000) (.01) = $250/pd
0
1
2
3
n = (6 yr)(4 qtr) = 24 qtrs
yr
Bond Price (maximum)
6
Problem 1, cont.
Given:
MARR = 2% per year, cpd quarterly
Face Value = $25 000
Coupon Rate of 4%, paid quarterly
Maturity in 6 years
Find Max. Price:
Finding effective MARR to match dividend period:
MARR = 2%/yr, cpd quarterly, so find a quarterly equivalent rate!
a.) Find effective quarterly rate (to match compounding), since pp = cp:
r
i=
m
so inserting values and solving for i:
2% / yr
i=
= 0.5%/qtr.
4 qtrs / yr
7
Problem 1, Cont.
Given:
MARR = 2% per year, cpd quarterly
Face Value = $25 000
Coupon Rate of 4%, paid quarterly
Maturity in 6 years
Find Max. Price:
Finding NPW of remaining cash flows at effective MARR:
$25 000
i = 0.5% / qtr.
$250/pd
0
1
2
3
n = 24 qtrs
Bond Price = $250(P/A, 0.5%, 24) + $25 000(P/F, 0.5%, 24)
=$250 (22.5629) + $25 000 (.8872) = $27 822.30
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Problem 2
You desire to make an investment in
bonds provided you can earn a yield
rate of 12% per year on your
investment, compounding monthly.
How much can you afford to pay for a
bond with a face value of $10 000 that
pays a coupon rate of 10% in quarterly
payments, and will mature in 20 years?
9
Problem 2, Cont.
Given:
MARR = 12% per year, cpd monthly
Face Value = $10 000
Coupon Rate of 10%, paid quarterly
Maturity in 20 years
Find Max. Price:
ib = Coupon Rate = 10% = 2.5%/pd.
Dividends/yr
4
Face Value = $10 000
Dividend = (Face Value) (ib)
=($10 000) 2.5% = $250/pd
0
1
2
3
n = (20 yr)(4 qtr) = 80 qtrs
yr
Bond Price (maximum)
10
Problem 2, cont.
Given:
MARR = 12% per year, cpd monthly
Face Value = $10 000
Coupon Rate of 10%, paid quarterly
Maturity in 20 years
Find Max. Price:
Annual Bond Yield needs to equal MARR:
Yield Rate = effective 12%/yr, so find a quarterly equivalent rate!
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
Note: 3 mo. per qtr!
(Check: ia = (1+ iqtr)
m
– 1 = (1+.02874)4 – 1 = 12% / yr !)
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Problem 2, Cont.
Given:
MARR = 12% per year, cpd monthly
Face Value = $10 000
Coupon Rate of 10%, paid quarterly
Maturity in 20 years
Find Max. Price:
ib = Coupon Rate = 10% = 2.5%/pd. Face Value = $10 000
Dividends/yr
4
Quarterly Yield Rate = 2.874% / qtr
Dividend = (Face Value) (ib)
=($10 000) 2.5% = $250/pd
0
1
2
3
n = (20 yr)(4 qtr) = 80 qtrs
yr
Bond Price = $250(P/A, 2.874%, 80) + $10 000(P/F, 2.874%, 80)
=$250 (31.19054) + $10 000 (.10367) = $8 834
12
Problem 3
A $1 000 face value bond will mature
in 10 years. The annual rate of
interest is 6%, payable semi-annually.
If compounding is semi-annual and
the bond can be purchased for $870,
what is the yield to maturity in terms
of the effective annual rate earned?
13
Problem 3, Cont.
Given:
Bond Price = $ 870
Face
i = Value = $1 000
Coupon Rate of 6%, cpd & paid semi-annually
Maturity in 10 years
Find Annual Yield to Maturity:
$1 000
ib = Coupon Rate = 6% = 3% / Dividend pd.
Dividends/yr
2
Dividend = (Face Value)(ib)
= ($1 000) (3%) = $30/pd
0
1
2
3
n = (10 yr)(2 divs) = 20 pds
yr
$870
Find semi-annual Yield to Maturity = i* such that NPW = 0
14
Problem 3, cont.
Given:
Bond Price = $ 870
Face
i = Value = $1 000
Coupon Rate of 6%, cpd & paid semi-annually
Maturity in 10 years
Find Annual Yield to Maturity:
Want NPW = 0  $30 (P/A, i*, 20) + $1 000 (P/F, i*, 20) = $870
Try 4%  $30 (P/A,4%, 20) + $1 000 (P/F, 4%, 20) = $ 864 Low!
$1 000
Try 3%  $30 (P/A,3%, 20) + $1 000 (P/F, 3%, 20) = $1 000 High!
Dividend = $30/pd
Still need to come up
with a closer value …
0
1
2
3
n = 20 pds
$870
Yield to Maturity = i* such that NPW = 0
15
Problem 3, cont.
Given:
Bond Price = $ 870
Face Value = $1 000
Coupon Rate of 6%, cpd & paid semi-annually
Maturity in 10 years
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
 x = 3 + 130 = 3.96% / 6 mo.
136
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
Annual Yield to Maturity = 8.08% / yr !
16