1. Engineering Economics
1/12/2019
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).
Copyright (c) , D.H. Jensen & K.D. Douglas

2. Reviewing…
For a capital purchase (P) with a salvage value (S), the EAC can be calculated two ways:
P(A I P, i, n) – S (A I F, i, n)
(P – S) (A I P, i, n) + S*i
Annual equivalent Opportunity
for loss of value cost

3. BOND TERMINOLOGY Face Value, Par Value, Maturity Value
– How much the borrower will pay the holder when it matures.
Coupon Rate, Nominal Annual Interest Rate
– Nominal yearly interest rate paid on face value.
Bond Dividend
– Interest paid periodically until maturity
Maturity Date
– Date at which you receive the face value
Market Value, Current Price
– What someone is willing to pay for the remaining cash flows.
Yield to Maturity
– Actual interest rate earned over holding period

4. CFD with Bond Terms… Coupon Rate Dividend Periods / Yr ib =
Dividend = (Face Value) (ib) – or – Face Value
Face Value
Yield Rate = ia = (1+ ib) m – 1
Dividend 1 2 3
n periods
(to Maturity Date)
Bond Price
Yield to Maturity = i* such that NPW = 0

5. Problem 1
A bond with a face value of $ 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?

6. Problem 1 Given: Find Max. Price: 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 qtr /yr
Face Value = $25 000 1 2 3
Dividend = (Face Value) (ib) = ($25 000) (.01) = $250/pd
n = (6 yr)(4 qtr) = 24 qtrs yr
Bond Price (maximum)

7. Problem 1, cont. Given: Find Max. Price:
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 m
i =
so inserting values and solving for i:
i = = 0.5%/qtr.
2% / yr
4 qtrs / yr

8. Problem 1, Cont. Given: Find Max. Price:
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: 1 2 3
$25 000
i = 0.5% / qtr.
$250/pd
n = 24 qtrs
Bond Price = $250(P/A, 0.5%, 24) + $25 000(P/F, 0.5%, 24)
=$250 ( ) + $ (.8872) = $

9. 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 $ that pays a coupon rate of 10% in quarterly payments, and will mature in 20 years?

10. Problem 2, Cont. Given: Find Max. Price:
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
Face Value = $10 000 1 2 3
Dividend = (Face Value) (ib) =($10 000) 2.5% = $250/pd
n = (20 yr)(4 qtr) = 80 qtrs yr
Bond Price (maximum)

11. Problem 2, cont. Given: Find Max. Price:
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:
imo = (1.12) 12 – 1 = 0.949%/mo.
b.) Find effective quarterly rate (to match dividend period):
iqtr = (1+ imo) m – 1 = ( )3 – 1 = 2.874% / qtr
Note: 3 mo. per qtr!
(Check: ia = (1+ iqtr) m – 1 = ( )4 – 1 = 12% / yr !)

12. Problem 2, Cont. Given: Find Max. Price:
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
Face Value = $10 000 1 2 3
Quarterly Yield Rate = 2.874% / qtr
Dividend = (Face Value) (ib) =($10 000) 2.5% = $250/pd
n = (20 yr)(4 qtr) = 80 qtrs yr
Bond Price = $250(P/A, 2.874%, 80) + $10 000(P/F, 2.874%, 80) =$250 ( ) + $ (.10367) = $8 834

13. 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?

14. Problem 3, Cont. Given: Find Annual Yield to Maturity:
Bond Price = $ 870
Face Value = $1 000
Coupon Rate of 6%, cpd & paid semi-annually
Maturity in 10 years
Find Annual Yield to Maturity:
i =
$1 000
ib = Coupon Rate = 6% = 3% / Dividend pd.
Dividends/yr
Dividend = (Face Value)(ib) = ($1 000) (3%) = $30/pd 1 2 3
n = (10 yr)(2 divs) = 20 pds yr
$870
Find semi-annual Yield to Maturity = i* such that NPW = 0

15. Problem 3, cont. Given: Find Annual Yield to Maturity:
Bond Price = $ 870
Face Value = $1 000
Coupon Rate of 6%, cpd & paid semi-annually
Maturity in 10 years
Find Annual Yield to Maturity:
i =
Want NPW = 0  $30 (P/A, i*, 20) + $1 000 (P/F, i*, 20) = $870
$1 000
Try 4%  $30 (P/A,4%, 20) + $1 000 (P/F, 4%, 20) = $ Low!
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 … 1 2 3
n = 20 pds
$870
Yield to Maturity = i* such that NPW = 0

16. Problem 3, cont. Given: Find Annual Yield to Maturity:
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
 x = = 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 = ( ) 2 – 1
Annual Yield to Maturity = 8.08% / yr !