5-1 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E Chapter 5 CAPITAL BUDGETING , QUESTIONS FOR DISCUSSION 5-1. No. Operating budgets charge the entire cost of acquisitions into the current year. Because benefits of an acquisition may extend well beyond the current year, we may incorrectly believe that an acquisition is not worthwhile if the capital budget is made part of the operating budget. A capital budget is needed because it considers costs and benefits of an acquisition over its entire useful lifetime. 5-2. Yes. Approved items from the capital budget are depreciated over their useful lifetimes. The annual depreciation expense becomes a cost included in the operating budget. 5-3. False. In theory, a capital asset is any resource that will provide benefits to the organization in more than one fiscal year. To simplify bookkeeping, however, most organizations only consider items that are expensive and have a lifetime of more than one year to be capital assets. 5-4. Some reasons that capital assets warrant special attention are that (1) the initial cost is large, (2) the items are generally kept a long time, (3) we can only understand the financial impact if we evaluate the entire lifetime of the assets, and (4) because we often pay for the asset early and receive payments as we use it later, the time value of money (or interest cost) related to the acquisition must be considered. Mistakes can be particularly costly because of the long-term commitment. Further, interest costs may not be obvious and may need to be explicitly considered.
Transcript
5-1 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
Chapter 5CAPITAL BUDGETING
,QUESTIONS FOR DISCUSSION
5-1. No. Operating budgets charge the entire cost of acquisitions into the current year. Because benefits of an acquisition may extend well beyond the current year, we may incorrectly believe that an acquisition is not worthwhile if the capital budget is made part of the operating budget. A capital budget is needed because it considers costs and benefits of an acquisition over its entire useful lifetime.
5-2. Yes. Approved items from the capital budget are depreciated over their useful lifetimes. The annual depreciation expense becomes a cost included in the operating budget.
5-3. False. In theory, a capital asset is any resource that will provide benefits to the organization in more than one fiscal year. To simplify bookkeeping, however, most organizations only consider items that are expensive and have a lifetime of more than one year to be capital assets.
5-4. Some reasons that capital assets warrant special attention are that (1) the initial cost is large, (2) the items are generally kept a long time, (3) we can only understand the financial impact if we evaluate the entire lifetime of the assets, and (4) because we often pay for the asset early and receive payments as we use it later, the time value of money (or interest cost) related to the acquisition must be considered. Mistakes can be particularly costly because of the long-term commitment. Further, interest costs may not be obvious and may need to be explicitly considered.
5-5. A dollar today is not worth the same amount as a dollar at some future time. If you have the money today, you can invest it and earn a positive return during the time period you would otherwise be waiting to receive the money. Money has an opportunity cost.
5-6. Compound interest simply refers to the fact that when money is invested going forward in time, at some point the interest earned on the money starts to earn interest itself. Discounting is just the reversal of this process as we go backward in time.
5-7. The quarterly interest rate for 3% annually is .75%. The table does not have a column for a .75% interest rate. You could take the average of the .5% and 1% columns to get an approximation of the correct answer. Alternatively, you could solve the exercise using a calculator or a computer that can solve for any interest rate.
Chapter 5: Capital Budgeting 5-2
5-8. The net present cost method is very helpful for comparing projects that have identical lifetimes. If projects have differing lifetimes, you are not comparing equal benefits unless you equalize the lifetimes. We could use the lowest common denominator of the lifetimes, extending both alternatives until their lifetimes are equal. However, the uncertainties in replacement and operating costs going forward in time may be substantial. The annualized cost method overcomes these problems. In that approach, one first finds the Net Present Cost for each alternative. Then, that cost is translated into a periodic payment for the number of years of that individual project’s lifetime. The project with the lower annualized cost is less expensive, on an annual basis, in today’s dollars.
5-9. Aside from the complexity of calculations, when cash flows are uneven from year to year, there are two important limitations. IRR assumes that cash inflows during the project are reinvested at the same rate that the project earns. Second, sometimes use of the IRR method will cause you to chose incorrectly from two mutually exclusive projects by picking a smaller project with a higher IRR rather than a larger project with a somewhat smaller IRR.
5-10. The objection to the method is that it ignores everything that happens after the payback period. It also does not consider the time value of money.
EXERCISES
Important Notes Re: A. RoundingB. Excel SolutionsC. Clearing data from calculator memoryD. Solutions using Time Value of Money Tables
A. It is common to have some rounding errors in time value of money calculations. In the following exercises and problems, answers are rounded either to the penny or to the dollar. Exercise care when rounding off before the final calculation. For example, if dividing 8% by 12 to get a monthly rate, the rate should be carried out to at least 4 decimal places. It will not be unusal for answers to differ slightly when using different solution approaches (calculator, formula, Excel) because of different rounding conventions used.
B. When solving using Excel or a similar spreadsheet, your actual TVM spreadsheet formula will refer to cell references, such as D12 or E32, rather than numbers or values. However, since each student’s solution may place the raw data in different cells, the cell references in the formulas shown in different solutions to the problem will be different. If the students are asked to indicate values rather than cell references in their spreadsheet formulas, it will make grading or comparison across students easier. This can also facilitate testing students’ ability to use Excel for time value of money problems during a test, without computers.
C. A common error is failure to clear the calculator memory between calculations. It is important to press the All Clear button on your calculator when starting a new calculation.
D. Starting with Exercise 14 and going through Exercise 18, and for selected problems, solutions are shown using the Time Value of Money tables. The tables appear at the end of Chapter 5 in Appendix 5-A and the use of such tables is discussed in that appendix. Students who have not been assigned Appendix 5–A should ignore the part of the solutions referring to those tables.
5-3 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
B. Spreadsheet Formula Solution=rate(nper,pmt,pv,fv,type,guess)=rate(60, , -20000, 30000) = .68%
5-13. You will have $1,250 with simple interest ($1,000 * .05 * 5 years plus the original $1,000 investment) and $1,251.79 with compound interest (PV = $1,000, N = 60 months, i= 4.5%/12 months, FV = ?). You are better off with 4.5% compounded than with 5% simple interest.
C. Spreadsheet Formula SolutionAnnual Compounding=FV(rate,nper,pmt,pv,type)=FV(3%,5, ,-20000) Note that the PV must be shown as a negative number=$23,185.48 to result in a positive value for the FV.Quarterly Compounding=FV(rate,nper,pmt,pv,type)=FV(.75%,20, ,-20000)=$23,223.68
D. Time Value of Money Tables (See Appendix 5-A)Annual CompoundingFV= PV ´ (FVF from FV of $1 Table 5-A-1, i, N)FV= PV ´ (FVF from FV of $1 Table 5-A-1, 3%, 5)FV= $20,000 ´ 1.1593FV= $23,186.00
Quarterly CompoundingFV= PV ´ (FVF from FV of $1 Table 5-A-1, i, N)FV= PV ´ (FVF from FV of $1 Table 5-A-1, .75%, 20)Table does not have a column for .75%.
One could interpolate, taking the average result using .5% and 1% as follows:at .5% FV=$20,000 ´ 1.1049 = $22,098at 1.0% FV=$20,000 ´ 1.2202 = $24,404at .75% FV= [($22,098 + $24,404) 2] = $46,502/2 = $23,251
5-15. (Present Value) A. Math Formula Solution
PV = FV/(1+i)N
PV = $5,000/(1 + 5%)8
PV= $5,000/1.4775 = $3,384.09
B. Financial Calculator SolutionN = 8 i = 5% FV = $5,000 PV = ?
Raw Data: 20 .75 -20000 N I/Y PV PMT FV
Result: = 23,223.68
Raw Data: 8 5 -5000 N I/Y PV PMT FV
Result: = 3,384.20
5-5 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
C. Spreadsheet Formula Solution =PV(rate,nper,pmt,fv,type)=PV(5%,8, ,-5000)=$3,384.20
D. Time Value of Money Tables (See Appendix 5-A)PV = FV ´ (PVF from PV of $1 Table 5-A-2, i, N)PV = FV ´ (PVF from PV of $1 Table 5-A-2, 5%, 8)PV = $5,000 ´ .6768PV = $3,384.00
5-16. (Number of Compounding Periods) A. Math Formula Solution
PV = FV/(1+i)N
$7,500 = $9,500/(1 + 3%)N = 7.997 or rounding, 8 years
B. Financial Calculator Solutioni = 3% PV = $7,500 FV = $9,500 N = ?
C. Spreadsheet Formula Solution=NPER(rate,pmt,pv,fv,type)=NPER(3%, ,-7500,9500)=7.997238Note that either the present value or the future value must be input as a negative number.
D. Time Value of Money Tables (See Appendix 5-A)PV = FV ´ (PVF from PV of $1 Table 5-A-2, i, N)$7,500 = $9,500 ´ (PVF from PV of $1 Table 5-A-2, 3%, N)$7,500/$9,500 = (PVF from PV of $1 Table 5-A-2, 3%, N)(PVF from PV of $1 Table 5-A-2, 3%, N) = .7895Looking at Table 5-A-2, the 3% column, we see that .7895 is closest to the factor for N=8
5-17. (Annuity Payment – Annuity in Arrears) A. Math Formula Solution
B. Financial Calculator SolutionN=8 i = 4% FV = $100,000 PMT = ?
C. Spreadsheet Formula Solution=PMT(rate,nper,pv,fv,type)=PMT(4%,8, ,-100000)= $10,852.78
D. Time Value of Money Tables (See Appendix 5-A)FVA = PMT ´ (FVAF from FVA of $1 Table 5-A-3, i, N)$100,000 = PMT ´ (FVAF from FVA of $1 Table 5-A-3, 4%, 8)$100,000 = PMT ´ 9.2142PMT = $100,000/9.2142PMT = $10,852.81
5-18. (Annuity in Arrears - Future Value) A. Math Formula Solution
B. Financial Calculator SolutionN=7 i = 6% PMT = $10,000 FV = ?
C. Spreadsheet Formula Solution=FV(rate,nper,pmt,pv,type)=FV(6%,7,-10000)=$83,938.38
D. Time Value of Money Tables (See Appendix 5-A)FVA = PMT ´ (FVAF from FVA of $1 Table 5-A-3, i, N)FVA = $10,000 ´ (FVAF from FVA of $1 Table 5-A-3, 6%, 7)FVA = $10,000 ´ 8.3938FVA = $83,938.00
Raw Data: 8 4 100000 N I/Y PV PMT FV
Result: = -10,852.78
Raw Data: 7 6 -10000 N I/Y PV PMT FV
Result: = 83,938.38
5-7 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
5-19. (TVM)
a. Note for quarterly compounding, 6% / 4 quarters per year = 1.5% per quarter and 3 years x 4 quarters per year = 12 periods
A. Financial Calculator Solution
FV = $50,000 N=12 i=1.5% PV = ?
B. Spreadsheet Formula Solution=PV(rate,nper,pmt,fv,type)=PV(1.5%,12, ,-50000)=$41,819.37
b.A. Financial Calculator Solution
PV = $35,000 N=12 i=3% FV = ?
B. Spreadsheet Formula Solution=PV(rate,nper,pmt,fv,type)=PV(3%,12, ,-35000)=$49,901.63
No, she will not have $50,000. She is about $98 short of that amount.
c.A. Financial Calculator Solution
PV = $37,000 N=12 FV=50,000 i = ?
Raw Data: 12 1.5 -50000 N I/Y PV PMT FV
Result: = 41,819.37
Raw Data: 12 3 -35000 N I/Y PV PMT FV
Result: = 49,901.63
Raw Data: 12 -37000 50000 N I/Y PV PMT FV
Result: = 2.54
Chapter 5: Capital Budgeting 5-8
B. Spreadsheet Formula Solution=rate(nper,pmt,pv,fv,type,guess) (remember to show PV as a negative number;=rate(12, ,-37000,50000) there is no annuity payment, so pmt can be left
blank with a comma before and after; type and guess may also be left blank, assuming the 50000 FV comes at the END of the 3rd year. Type would be 1 if the FV came at the start of the 3rd year.)
= .0254
Note that this is 2.54% per quarter, or 10.16% per year.
d.A. Financial Calculator Solution
FV = $50,000 N=36 i=8%/12 PV = ?
B. Spreadsheet Formula Solution=PV(rate,nper,pmt,FV,type)=PV(8%/12,36, ,50000)=($39,362.73)
You must pay $39,362.73 now to get $50,000 in 3 years.
e.A. Financial Calculator Solution
FV = $50,000 N=12 i=2% PMT = ?
B. Spreadsheet Formula Solution=PMT(rate,nper,pv,fv,type)=PMT(2%,12, ,50000)=($3,727.98)
You must pay $3,727.98 each quarter to get $50,000 in 3 years.
Raw Data: 36 8/12 50000 N I/Y PV PMT FV
Result: = -39,362.73
Raw Data: 12 2 50000 N I/Y PV PMT FV
Result: = -3,727.98
5-9 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
f.A. Financial Calculator Solution
PV = $100,000 FV=$1,000,000 i=7%/12 N = ?
B. Spreadsheet Formula Solution=nper(rate,pmt,pv,fv,type)=PMT(7%/12, ,-100000,1000000)= 395.88
Morduch has a way to go. She will need to work another 396 months or 33 years!
PROBLEMS
5-20. (TVM)A. Financial Calculator Solution
B. Spreadsheet Formula Solution=PV(rate,nper,pmt,fv,type)=PV(.75%,36,-430,0,0) or=PV(.75%,36,-430)=$13,522.13
5-21. (NPC)A. Financial Calculator Solution
High Security
Net Present Cost = 90,322.52 + 40,000 = 130,322.52
Raw Data: 7/12 -100000 1000000 N I/Y PV PMT FV
Result: = 395.88
Raw Data: 36 1 -3000 N I/Y PV PMT FV
Result: = 90,322.52
Raw Data: 36 .75 -430 N I/Y PV PMT FV
Result: = 13,522.13
Chapter 5: Capital Budgeting 5-10
Tight Security
Net Present Cost = 36,129.00 + 85,000 = 121,129.00Choose Tight Security. It is less expensive.
B. Spreadsheet Formula Solution
High SecurityNPC= $40,000 + PV(rate,nper,pmt,fv,type)
B. Spreadsheet Formula Solution= NPV(rate,value1,value2,…)-1200000= NPV(8%,500000,450000,350000,320000)-1200000= $161,816.27
Raw Data: 1 8 -500000 N I/Y PV PMT FV
Result: =462,963
Raw Data: 2 8 -450000 N I/Y PV PMT FV
Result: =385,802
Raw Data: 3 8 -350000
N I/Y PV PMT FV Result: =277,841
Raw Data: 4 8 320000 N I/Y PV PMT FV
Result: =235,210
Chapter 5: Capital Budgeting 5-16
5-27. (TVM)A. Financial Calculator Solution
PV = ?
B. Spreadsheet Formula Solution=PV(rate,nper,pmt,FV,type)=PV(6%,10,25000)=($184,002.18)
No. The pension should have been funded over the years that the clerk worked. The taxpayers of those years received the benefits, and money for the pension should have been put aside during those years, rather than upon retirement or in the future.
You can draw $7,352 per month for living expenses during retirement.
5-29. (Buy or Lease)
The problem could also have been solved by calculating the value of the two
annuities rather than the individual cash flows as follows:
Buy the van. It costs less on an annualized-cost basis.
Annuity Approach Lease OwnNumber of periods for the Annuity 4 5Payment ($7,700) ($2,250)
Purchase or Make Ready ($2,500.00) ($31,000.00)PV Of Annuity ($25,503.38) ($8,983.60)PV of net resale proceeds $4,883.81Net Present Cost ($28,003.38) ($35,099.78)
B. Spreadsheet Formula Solution= NPV(6%,9000,9000,9000,9000,9000)-60000= ($22,088.73)
The O’Regan Ambulance Paramedics will need donations of $22,088.73 to cover the shortfall.
Raw Data: 1 6 -9000 N I/Y PV PMT FV
Result: = 8,491
Raw Data: 2 6 -9000 N I/Y PV PMT FV
Result: = 8,010
Raw Data: 3 6 -9000 N I/Y PV PMT FV
Result: = 7,557
Raw Data: 4 6 -9000 N I/Y PV PMT FV
Result: = 7,129
Raw Data: 5 6 -9000 N I/Y PV PMT FV
Result: = 6,725
5-19 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
5-31. (IRR) Set PV inflows = PV outflows
PV of $800/yr. for 7 years = $5,000
A. Financial Calculator SolutionN = 7 PMT = 800 PV = 5000 i = ?
B. Spreadsheet Formula Solution= Rate(nper,pmt,pv,fv,type,guess)= Rate(7,800,-5000)= 2.92%
5-32. (IRR) A. Financial Calculator Solution
IRR, on monthly basis, must multiply by 12 to find IRR per annum
%
Annual IRR is more than 18%, so accept the contract.
B. Spreadsheet Formula Solution= Rate(nper,pmt,pv,fv,type,guess)= Rate(36,5000,-125000)= 2.12% per month= 25.5%
Annual rate exceeds 18%, so accept the contract.
Raw Data: 7 -5000 800 N I/Y PV PMT FV
Result: = 2.92
Raw Data: 36 -125000 5000 N I/Y PV PMT FV
Result: = 2.12
Chapter 5: Capital Budgeting 5-20
5-33. (Capital Asset Schedule)
CASE STUDY: MEAD MEALS ON WHEELS CENTER—PART II1
Problem 3 is a capital budgeting problem. You were asked to decide whether MMWC should spend $625,000 for some new kitchen equipment. The equipment will allow MMWC to prepare 10,400 meals per day. This is an increase of 800 meals per day. That means that MMWC can feed 400 more people per week with the addition of the equipment.
Each person that MMWC feeds generates gross revenues of $32. Offsetting this is the marginal (variable) cost of providing them with food. We know from the director’s instructions to use the new food bid that the marginal cost of food is $23.25 per person per week. ($24.50 – $1.25). So, each additional person that MMWC feeds results in a marginal “cash flow” (the excess of marginal revenue over marginal expenses) of $32 – $23.25, or $8.75 per person per week. Because the new equipment will let you feed 400 additional people per week, purchasing the equipment generates $3,500 ($8.75 per person times 400 people) worth of cash flow each week.
To find out if this is enough to justify the purchase of the equipment, you need to do a net-present-value analysis. Buying the equipment gives MMWC $3,500 of cash flow per week for 260 weeks (5 years times 52 weeks per year). This is an annuity. The case tells you that your interest cost is 12% per annum, approximately .23% per week (12% interest per annum divided by 52 weeks in a year). (If you did not use a spreadsheet to solve the problem, you probably did the calculations on a quarterly basis. In that case, the periodic interest is 3% per quarter [12% divided by 4 quarters per year] and the number of periods is 20, i.e., 5 years ´ 4 quarters per year).
1 Mead Meals on Wheels Center and its solution were written by Robert Purtell, Robert F. Wagner Graduate School of Public Service, New York University. Used with permission.
5-21 Instructor’s Manual for Financial Management for Public, Health, and Not-for-Profit Organizations, 3E
Here is the problem setup:
OutflowsPurchase price = $625,000
Net InflowsPMT = Cash Flow = $3,500 ´ number of weeks in the period that you have chosen. (e.g., for a
quarterly model $3,500 ´ 13 weeks = $45,500 per quarter)
iInterest rate (nper) = 12% divided by the number of periods in the year (n) (e.g., for a quarterly
model 12%/4 quarters per year = 3% per quarter)
Present Value of the benefits = Present Value of an Annuity (pmt) ´ Cash Flow per periodNet Present Value = Present Value of the benefits minus purchase price
Depending on whether you did the analysis on a weekly or quarterly basis, the results are as shown below. In both cases, the net present value of the cash flow from the investment is greater than zero. In other words, the equipment more than pays for itself even after we take the cost of capital into account. So, the organization should buy the equipment.
Note that the net present values derived from the weekly and quarterly calculations are different. This is due to the timing and frequencies of cash flows in the two models. Theoretically, if MMWC gets paid weekly, the weekly model is more correct.
Capital Budget Analysis Weekly Quarterly AnnualPV of Equipment Purchase $625,000 $625,000 $625,000Periodic Revenue from New Equipment $3,500 $45,500 $182,000Periodic Interest Rate .23% 3.00% 12.00%Present Value of Benefit from Equipment $683,727 $676,925 $656,069Net Present Value $58,727 $51,925 $31,069
Problem 4 asks you to prepare an incremental budget for the coming year. Let’s review what has happened:
Weekly people fed—up to 5,200 from 4,800, an increase of 400 per weekRevenue per person-week—unchanged at $32 per person per weekFood cost per person-week—$23.25, down from $24.00Quarterly depreciation—up by $28,125 to account for the new equipmentQuarterly interest payments—up by $18,750 because of the equipment loanFirst quarter fixed costs—up by $2,000 per week because of actual experienceOther quarterly fixed costs—unchanged
All of the calculations are the same as they are in question 1. Using that methodology and the revised data, we get the following budget:
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