Solution Set to 2003 Fall Final

©Dr. B. C. Paul 2003

Problem Set #1

• Question A– Answer The two cash flows have unequal lives.

There is no common denominator to where multiple pole barns can be used. There is not enough information to establish a 20 year salvage value for a 50 year life court house. The interest rate is low enough that truncating the problem at 20 years is unrealistic – You have to use total life cycle cost

– Points available 6– Objective – see if people recognize the unequal lives

problem in picking a true least cost alternative

Question B

• Answer – Yes, $250,000 demo cost is there regardless of what is built. $200,000 to lease office space for the next year is there regardless of decision (Billy bricks will have this cost for the second year of construction since he takes longer to complete his building). The $200,000 per year union contract for cleaning is there regardless of what is built.

• Points 6• Objective – See if people recognize what a sunk cost is

how to identify them (or other irrelevant cost data) using the question “Will anything about my current decision effect whether or not this cost will occur”?

Question C

• Answer – Year one for the Pole Barn Court house, Year two for the Brick Courthouse because the money pot is placed at the beginning of the useful life of the asset.

• Points 6• Objective – See if people recognize that in doing

a total life cycle cost the money is collected to the beginning of the useful life of the object and not to time zero like in an NPV.

Question D

• Answer about 3.5% calculated as

035.1024.1

06.1Or 3.5%

Points 6Objective – See if people recognize that real cashFlows require a real rate of return and that inflationMust be removed from the interest rate. See ifPeople remember that interest rate components areRemoved using division. See if people know howTo represent interest rates in their decimal form toPerform the division operation.

Question E

• Answer - Build the brick courthouse because the cost per year of useful life is less

Interest Rate 0.035Total Cost Per Year Total Cost Per Year

Simple Build Total 2297668 161666.4 Solid Building Total 3287617 140163.30 1600000 1.035 1656000 1600000 1.071225 17139601 start 1 0 1500000 1.035 15525002 0.966184 0 start 13 0.933511 0 0.9661844 0.901943 0 0.9335115 0.871442 0 0.9019436 0.841973 0 0.8714427 0.813501 0 0.8419738 0.785991 0 0.8135019 0.759412 0 0.785991

10 0.733731 0 0.75941211 350000 0.708919 248121.6 0.73373112 50000 0.684946 34247.29 0.70891913 50000 0.661783 33089.16 0.68494614 50000 0.639404 31970.21 0.66178315 50000 0.617782 30889.09 0.63940416 80000 0.596891 47751.25 0.61778217 80000 0.576706 46136.47 0.59689118 80000 0.557204 44576.3 0.57670619 80000 0.538361 43068.89 0.55720420 80000 0.520156 41612.46 0.53836121 80000 0.502566 40205.27 0.52015622 0.50256623 0.48557124 0.46915125 0.45328626 0.43795727 50000 0.423147 21157.352829

More on E Answer

• The correct answer is obtained by discounting all costs associated with each option to the beginning of the life of each courthouse. This discounted cost is then converted to an annuity over the useful life of the courthouse– The shown calculation was done with a spreadsheet

and P/F and F/P values but hand solutions with annuities are equally correct

– There were minor variations in how some people added costs and some people made errors in interest rates or location of the “Money Pot” c

• Minor variations or errors penalized elsewhere were not deducted here

Question E Cont

• Points 10• Objective – See whether people could correctly

use discount factors to move all money to a common point in time and then convert it to an annuity. Also see if people understood that Total Life Cycle Costs are done by discounting money to the start of the project life and then converting to an annuity over the useful life of the project– Note on answer – any answer that demonstrated a

knowledge of these principles was accepted.

Question Set #2

• Problem A– Answer Incremental Investment (an interpretation of

cost savings will allow this problem to be interpreted as an incremental all cost alternatives – answer also accepted)

– Points 11– Objective See if people recognize that problems

involving add-ons to another project must evaluate each add on by itself – see if people recognize an incremental investment problem

Question B

• Answer - $275,000

-$5,000,000 This cash flow is obtained when the initial courthouse costIs subtracted from the cost of a courthouse with a jail

The correct answer involves whether P/A*$275,000 is greater than$5,000,000.

Variations of this problem involved getting an NPV at either time 1 or time 0With some people electing to then convert all costs to an equivalent annuity.

Johnney Jailer Incremental Cash Flow

For people who chose the correct interest rate of 3.5% on question set 1 c theAnswer is positive. At 6% and higher interest rates it is not.

Answers demonstrating removal of initial courthouse cost and then checkingThe value of the $275,000 annuity against the $5,000,000 were accepted

More on B answer

• Johnny Jailers answer– P/A for 50 years at 3.5% interest is 23.46– 23.46*$275,000 = $6,450,000 which is greater than

the $5,000,000 investment cost– Thus Johnny Jailer comes out positive

• If a 6% or higher interest rate is used $275,000 * P/A for 50 years will not be greater than $5,000,000 and the incremental investment will fail– (Some people got the wrong interest rate on set 1 c,

however, these individuals were not penalized if the problem was worked correctly and their chosen answer was consistent with their findings)

More on B

• For Barney Fife’s increment$125,000

-$3,000,000

Barney Fife’s incremental cash flow

The correct answer involves subtracting initial courthouse and Johnney JailersAddition from Barney Fife’s cost to get the proper incremental cash flow.The value of the $125,000 annuity is then compared to the incremental costOf $3,000,000. As with Johnney Jailers increment people could do NPVsAt time 0 or yearly equivalent cost. People who found Johnney Jailer to beUneconomic could acceptably not do this calculation.

P/A for 50 years at 3.5% * $125,000 is $2,932,000 which is less than$3,000,000 – thus correct answers will find Barney’s increment uneconomic

More on B

• Points 22• Objective – The objective was to see if people

remembered to subtract all previous costs from the total costs for each project expansion. This meant subtracting the initial courthouse cost from the cost with Johnny’s Jail and then subtracting Johnny’s cost with a jail from Barney’s expanded jail. People also needed to show they could compare the value of future benefits from the initial cost for each increment of investment and draw correct conclusions

Question Set #3

• Problem A– Answer Comparative Investment or

Competing Investment– Points 11– Objective See if people recognize that this

problem involves picking the best investment from a collection of investments that make the minimum required return.

Question B

• Answer – Target Answer was NFV (other answers may have got a few points if the rationale was persuasive and they understood what other measures did).

• Points 11• Objective – See if people recognized that in the case of

mutually exclusive investments of different size that it is often the choice of which project leads to the greatest over-all wealth from the investment portfolio that wins (ie. NFV)– In this case the community center makes the most bang for the

buck but the hotel makes more money to help the county with those sewer bonds – sometimes bigger really is better.

Question C

• Answer – the answer depends on what was chosen in B, but what ever you choose you must do (ok for PVR that just means copy the answer).– The problem had a twist because Edward

Kennedy’s shopping mall cost more money than the county had available and therefore could not be built no matter how good it looked

More on C

• If one picked NFV it was not actually necessary to do the NFV because all three problems say they pay for their initial cost. We therefore end up with an annuity for 15 years of $250,000 for the Community Center and $300,000 for the Hotel (the mall was too expensive to build). One need not do math to see that a $300,000 annuity will net more money than a $250,000 annuity.

More on C

• Points 11

• Objective– See if people recognized that Kennedy’s

project cost more than was available– See if people could perform their chosen

financial measurement calculation (or recognize what was going to happen) and then properly interpret the result.