Seg2510 – Management Principles for Engineering Managers

Tutorial 5

Single payments (Use of F/P or P/F Factors) Ex.1

You have just purchased 100 shares of General Electric stock at $30 per share. You will sell the stock when its market price doubles. If you expect the stock price to increase 12% per year, how long do you expect to wait before selling the stock?

Uneven-payment series-Ex. 2 Bo Smith, the former record-breaking running back from

football university, signed a $30 million package with the Nebraska Lions. The terms of the contract were $3 million immediately, $2.4 million per year for the first 5 years (with the first payment after 1 year), and $3 million per year for the next 5 years (with the first payment at the end of year six). If the interest rate is 8% compounded annually, what is Bo’s contract worth at the time of contract signing?

Linear Gradient Series-Ex.3 The maintenance expense on a machine is expected to be

$800 during the first year and to increase $150 each year for the following 8 years. What present sum of money should be set aside now to pay for the required maintenance expenses?( Assume 9% compound interest per year.)

Norminal versus Effective Interest Rates-Ex.4

A financial institution is willing to lend you $1000. However, you must repay $1125 at the end of one week. What is the norminal interest rate? What is the effective annual interest rate?

Ex. 5

You are purchasing a $9000 used automobile, which is to be paid for in 36 monthly installments of $288.72. What nominal interest rate are you paying on this financing arrangement?

APR- Ex.6

Charges are required for a loan E.g. with a 2-point loan, borrower can have only $98 for

each $100 borrowed. Yet, he/she would have to make payment just as if he or she had received $100.

Suppose that you receive a loan of $130000 payable at the end each month for 30 years with an interest rate of 9% compounded monthly, but you have been charged three points (i.e. 3%). What is the effective interest rate on this home-mortgage loan?

Comparing different financing options-Ex.7 You want to purchase a house for $85000, and you have $17000 cash

available for a down payment. You are considering the following 2 financing options: Option 1: get a new standard mortgage with 10%(APR) interest

compounded monthly and a 30-year term. Option 2: assume the seller’s old mortgage that has an interest rate of

8.5%(APR) compounded monthly, with a 25-year repayment period, a remaining balance of $35,394, and payments of $285 per month. You can obtain a second mortgage for the remaining balance, $32,606, from your credit union at 12% (APR) compounded monthly, with a 10-year repayment period.

(a) What is the effective interest rate for option 2?(b) Compute the monthly payments for each option over the life of the mortgage.(c) Compute the total interest payment for each option.(d) What homeowner’s interest rate (homeowner’s time value of the money)

makes the two financing options equivalent?

Payback period-Ex.8 It is expected that a new automated system will save $40000

per year in labor. The new system will cost about $30000 to build and test prior to operation. It is expected that operatingcosts, including income taxes, will be about $15000 per year. The system will have a five-year useful life. The expected net salvage value of the system is estimated to be $3000.

a) How long does it take to recover the investment?b) If the firms interest rate is 15% after taxes, what would be the

discounted-pay-back period for this project?

PW versus IRR criterion-Ex.9 Consider the following two investment alternatives:

The firm’s MARR is known to be 15%.a) Compute the IRR of Project B.b) Compute the PW of Project A.

$6,300?PW(15%)?30%IRR

$40,000$5,5003$0$5,5002$0$5,5001

-$20,000-$10,0000Project BProject An

Net Cash flow

IRR criterion-Ex.10 Easy Snack has estimated the cash flows in millions of

dollars over the product’s six-year useful life, including the initial investment, as shown in the table:

a) If the firm’s MARR is 18%, is this product worth marketing, based on the IRR criterion?

b) If the required investment remains unchanged, but the future cash flows are expected to be 10% higher than the original estimates, how much increase in IRR do you expect?

c) If the required investment has increased from $20 million to $22 million, but the expected future cash flows are projected to be 10% smaller than the original estimates, how much decrease in IRR do you expect?

$36$105$184$193$172$81

-$200Cash flown

MIRR, Profitability Index (PI)

Simple example of PI

5

4

3

2

1

0

Year

143

130

105

58

17

-200

Incremental CF ($ in M)

62.5

67

63.9

41.7

14.4

-200

PV(18%)

PI=(14.4+41.7+63.9+67+62.5)/200=249.5/200=1.25

Solution of Ex. 1

Rule of 72:

72/12= 6 years

yearsN

N

NPF

iPF

N

N

N

612.612.1log2log

12.1log2log

12.12

)%,12,/(3000$

)12.01(3000$6000$)1(

Solution of Ex. 2

Solution of Ex. 3

Solution of Ex. 4

Solution of Ex. 5

Solution of Ex. 6

Solution of Ex. 7

Solution of Ex. 8

Solution of Ex. 9

Solution of Ex. 10

Reference Chan S. Park, Fundamentals of Engineering Economics.

Prentice Hall Smart, Scott B., Corporate finance. Thomson South-

Western