ENGR 3360U Winter 2014Unit 5.6-7

Life Cycle Costs and Bonds

Dr. J. Michael Bennett, P. Eng., PMP, UOIT,

Version 2014-I-01

Unit 5 Present Worth Analysis

Change Record

• 2014-I-01 Initial Creation• Text Chapter 5

2014-I-015-2 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-3

5.6 Life Cycle Costs Another extension of present worth methodApplied to systems over their total estimated system life span Critical to estimate the system life span in yearsDifficulties – estimation of costs far removed from time t = 0 The life cycle may be defined by two main time phases

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-4

Life Cycle Concept

Two main phases are: Acquisition Phase

Operations Phase

Many cash flow estimates are needed, thus making the analysis less reliable as the life gets longer

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-5

5.7 Present Worth of Bonds Bond problems – typical present worth applicationCommon analysis problem in the world of finance Bond is basically an “iou” Bond – represent “debt” financing Corporations sell bonds to raise capital Bonds pay a stated rate of interest (bond dividend) to the bond holder for a specified period of time

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-6

Bonds Parameters and Examples

1. Face value, V = $10002. Life of the bond, n = 30 years3. Coupon rate, b = 8% per year, paid quarterly4. Number of dividend payments per year, c = 4

Bond dividend = I = Vb/cI = 1000(.08)/4 = $20 per quarter

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-7

Types of BondsType Issued By Characteristics Examples

Treasury securities Ottawa Backed by

Canada

Bills Marketable bondPremium bondsSavings bonds

Provincial Provinces May be guaranteed Bonds

Municipal Local governments

Issued against taxes received Bonds

Mortgage Corporation Backed by house1st mortgage2nd mortgageReverse mortgage

Debenture Corporation Backed by reputation Convertible

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-8

Cash Flow Profile for Bond Purchase Typical cash flow to bond buyer:

Bond Purchase, V at t = 0

Repayment of the face

value

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-9

Example 5.6Loblaw Ltd. Has issued $5,000,000 worth of $5,000 ten-year

debenture bonds. Each bond pays interest quarterly at 6%. (a) Determine the amount a purchaser will receive each 3 months

and after 10 years.(b) Suppose a bond is purchased at a time when it is discounted

by 2% to $4900. What are the quarterly interest amounts and the final payment at maturity date?

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-10

Solution(a) The quarterly interest is (5000)(0.06)/4 = $75 and $5000 is

repaid after 10 years(b) The discount dos not change either the interest or the final

repayment amounts.

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-11

Discounting a Bond Bonds are seldom purchased for their face value Most of the time a bond is “discounted” in the bond market by a few percentage points But the face value and the periodic dividend payments remain unchanged

For example, V = $10,000 bond purchased for 98% of V now, but repays full face value, V, in 10 years

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-12

Bond Purchase: Example 5.7 $5,000 10-year bond that pays 4.5% semi-annually is under consideration As the potential buyer you require a rate of return of 8% per year, compounded quarterly on your purchase What should you be willing to pay for this bond now in order to receive at least the required rate of return?

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-13

Bond Purchase: Example Draw the cash flow diagram using “6 month periods” as the unit of time Bond dividend = $5000(0.045)/2 = $112.50 every 6 months

/ / /0 1 2 3 4 18 19 20

A = $112.50

$5,000

PW = ? (willing to pay)“n” is 20 since bond dividend

payments are semi-annual

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-14

Bond Purchase: Example Investor requires 8% per year, compounded quarterly i/qtr = 0.8/4 = 2% per quarterEffective semiannual rate is (1.02)2 – 1 = 4.04% per 6 months

/ / /0 1 2 3 4 18 19 20

$5,000

A = $112.50

Find the PW at 4.04% of this cash flow series

PW = max amount to pay for the bond

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-15

Bond Purchase: Example

P = 112.50(P/A,4.04%,20) + 5000(P/F,4.04%,20) = $3788

If the bond can be purchased for $3788, or less, the investor will make the required rate of return If the bond cost more than $3788, the investment is not worth it financially

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-16

Sct 5.

Spreadsheet Applications – PW Analysis and Payback Period

Review the Excel financial functions NPV and PV functions are useful analysis tools built into Excel

Unit 5 Present Worth Analysis

2014-I-01 Dr. J.M. Bennett, P.Eng., PMP ENGR 3360U Eng Eco5-17

Chapter Summary

PW method requires comparison over same number of years – equal service comparison Alternative comparison using PW – select the alternative with the numerically larger PW value, that is, higher new positive cash flow value, or lower net cost in PW termsExtension of PW method are: capitalized cost, life-cycle costs, payback period, bondsNever use payback period as the primary selection method; only as supplemental with other methods such as PW, FW, AW or ROR (as covered in later chapters)