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 that is  0. Service projects are “have to do” situations, select largest EAW (lowest EAC).

2 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

3 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

4 CFD with Bond Terms… n periods (to Maturity Date) Bond Price Dividend Face Value Yield Rate = i a = (1+ i b ) m – 1 Coupon Rate Dividend Periods / Yr i b = Coupon Rate Dividend Periods / Yr Dividend = (Face Value) (i b ) – or – Face Value 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: MARR = 2% per year, cpd quarterly Face Value = $ Coupon Rate of 4%, paid quarterly Maturity in 6 years Find Max. Price: n = (6 yr)(4 qtr) = 24 qtrs yr Dividend = (Face Value) (i b ) = ($25 000) (.01) = $250/pd Face Value = $ i b = Coupon Rate = 4% / yr = 1% /qtr. Dividends/yr 4 qtr /yr Bond Price (maximum)

7 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: MARR = 2% per year, cpd quarterly Face Value = $ Coupon Rate of 4%, paid quarterly Maturity in 6 years Find Max. Price: 2% / yr 4 qtrs / yr r m

8 Problem 1, Cont. Given: MARR = 2% per year, cpd quarterly Face Value = $ Coupon Rate of 4%, paid quarterly Maturity in 6 years Find Max. Price: n = 24 qtrs $250/pd $ i = 0.5% / qtr. Bond Price = $250(P/A, 0.5%, 24) + $25 000(P/F, 0.5%, 24) =$250 ( ) + $ (.8872) = $ Finding NPW of remaining cash flows at effective MARR:

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: MARR = 12% per year, cpd monthly Face Value = $ Coupon Rate of 10%, paid quarterly Maturity in 20 years Find Max. Price: n = (20 yr)(4 qtr) = 80 qtrs yr Dividend = (Face Value) (i b ) =($10 000) 2.5% = $250/pd Face Value = $ i b = Coupon Rate = 10% = 2.5%/pd. Dividends/yr 4 Bond Price (maximum)

11 Problem 2, cont. Given: MARR = 12% per year, cpd monthly Face Value = $ Coupon Rate of 10%, paid quarterly Maturity in 20 years Find Max. Price: Yield Rate = effective 12%/yr, so find a quarterly equivalent rate! Annual Bond Yield needs to equal MARR: (Check: i a = (1+ i qtr ) m – 1 = ( ) 4 – 1 = 12% / yr !) Note: 3 mo. per qtr! a.) Find effective monthly rate (to match compounding), so set: 12% =.12 = (1 + i mo ) 12 – 1 and solving for i: 1 i mo = (1.12) 12 – 1 = 0.949%/mo. b.) Find effective quarterly rate (to match dividend period): i qtr = (1+ i mo ) m – 1 = ( ) 3 – 1 = 2.874% / qtr

12 Problem 2, Cont. Given: MARR = 12% per year, cpd monthly Face Value = $ Coupon Rate of 10%, paid quarterly Maturity in 20 years Find Max. Price: 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 Face Value = $ Quarterly Yield Rate = 2.874% / qtr i b = Coupon Rate = 10% = 2.5%/pd. Dividends/yr 4 Dividend = (Face Value) (i b ) =($10 000) 2.5% = $250/pd

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

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: $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!

16 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 Annual Yield to Maturity = 8.08% / yr ! Need to convert semi-annual (6 mo.) yield rate to Annual Yield Rate: Yield Rate = i a = (1+ i 6 mo ) m – 1  i a = ( ) 2 – 1  x = = 3.96% / 6 mo. 136