<<

. 9
( 21)



>>

goals. The idea of participatory budgeting is to involve as many managers,
and even employees, as possible in the budgetary process.


Self-Test 1. What time periods are used in budgeting?
Questions 2. What are the primary differences between conventional and zero-based
budgets?
3. What are the primary differences between top-down and bottom-up
budgets?


Constructing a Simple Operating Budget
Table 8.3 contains the 2004 operating budget for Carroll Clinic, a large, inner
city, primary care facility. Most operating budgets are more complex than this
illustration, which has purposely been kept simple for ease of discussion.
As with most ¬nancial forecasts, the starting point for the operating
budget, which was developed in October of 2003, is volume. A volume projec-
tion gives managers a starting point for making revenue and cost estimates. As
shown in Part I of Table 8.3, Carroll Clinic™s expected patient volume for 2004
comes from two sources: a fee-for-service (FFS) population expected to total
36,000 visits and a capitated population expected to average 30,000 mem-
bers. Historically, annual utilization by the capitated population has averaged
0.15 visits per member-month, so in 2004 this population, which is expected
to total 30,000 — 12 = 360,000 member-months, will provide 360,000 —
0.15 = 54,000 visits. In total, therefore, Carroll™s patient base is expected
to produce 36,000 + 54,000 = 90,000 visits. Armed with this Part I volume
projection, Carroll™s managers can proceed with revenue and cost projections.
Part II contains revenue data. The clinic™s net collection for each FFS
visit averages $25. Some visits will generate greater revenues, and some will
229
Chapter 8: Planning and Budgeting


TABLE 8.3
I. Volume Assumptions:
Carroll Clinic:
A. FFS 36,000 visits
B. Capitated lives 30,000 members 2004 Operating
Number of member months 360,000 Budget
Expected utilization per
member-month 0.15
Number of visits 54,000 visits
C. Total expected visits 90,000 visits

II. Revenue Assumptions:
A. FFS $ 25 per visit
— 36,000 expected visits
$ 900,000
B. Capitated lives $ 3 PMPM
— 360,000 actual member months
$ 1,080,000
C. Total expected revenues $ 1,980,000

III. Cost Assumptions:
A. Variable Costs:
Labor $ 1,200,000 (48,000 hours at $25/hour)
Supplies 150,000 (100,000 units at $1.50/unit)
Total variable costs $ 1,350,000
Variable cost per visit $ 15 ($1,350,000/90,000)
B. Fixed Costs:
Overhead, plant,
and equipment $ 500,000
C. Total expected costs $ 1,850,000

IV. Pro Forma Pro¬t and Loss (P&L) Statement:
Revenues:
FFS $ 900,000
Capitated 1,080,000
Total $ 1,980,000
Costs:
Variable:
FFS $ 540,000
Capitated 810,000
Total $ 1,350,000
Contribution margin $ 630,000
Fixed costs 500,000
Projected pro¬t $ 130,000




generate less. On average, though, expected revenue is $25 per visit. Thus,
36,000 visits would produce $25 — 36,000 = $900,000 in FFS revenues.
Additionally, the premium for the capitated population is $3 PMPM, which
would generate a revenue of $3 — 360,000 member-months = $1,080,000.
Considering both patient sources, total revenues for the clinic are forecasted
to be $900,000 + $1,080,000 = $1,980,000 in 2004.
230 Healthcare Finance



Because of the uncertainty inherent in the clinic™s volume estimates, it
is useful to recognize that total revenues will be $1,980,000 only if the volume
forecast holds. In reality, Total revenues = ($25 — Number of FFS visits) +
($3 — Number of capitated member-months). If the actual number of FFS
visits is more or less than 90,000 in 2004, or the number of capitated lives
(and hence member-months) is something other than 30,000, the resulting
revenues will be different from the $1,980,000 forecast.
Part III of Table 8.3 focuses on expenses. To support the forecasted
90,000 visits, the clinic is expected to use 48,000 hours of medical labor at
an average cost of $25 per hour, for a total labor expense of 48,000 — $25 =
$1,200,000. Thus, labor costs are expected to average $1,200,000 / 90,000
= $13.33 per visit in 2004. In reality, all labor costs are not variable, but there
are a suf¬cient number of workers that either work part-time or are paid on
the basis of productivity to closely tie labor hours to the number of visits.
Supplies expense, the bulk of which is inherently variable in nature,
historically has averaged about $1.50 per bundle (unit) of supplies, with
100,000 units expected to be used to support 90,000 visits. (A unit of supplies
is a more or less standard package that contains both administrative and clinical
supplies.) Thus, supplies expense is expected to total $150,000, or $150,000
/ 90,000 = $1.67 on a per visit basis. Taken together, Carroll™s labor and
supplies variable costs are forecasted to be $13.33 + $1.67 = $15 per visit in
2004. The same amount can be calculated by dividing total variable costs by
the number of visits: $1,350,000 / 90,000 = $15.
Finally, the clinic is expected to incur $500,000 of ¬xed costs in 2004,
primarily administrative overhead, labor costs, depreciation, and lease expense.
Therefore, to serve the anticipated 90,000 visits, costs are expected to consist
of $1,350,000 in variable costs plus $500,000 in ¬xed costs, for a total of
$1,850,000. Again, it is important to recognize that some costs (in Carroll™s
case, a majority of costs) are tied to volume. Thus, total costs can be expressed
as ($15 — Number of visits) + $500,000. If the actual number of visits in 2004
is more or less than 90,000, then total costs will differ from the $1,850,000
budget estimate.
The ¬nal section (Part IV) of Table 8.3 contains Carroll Clinic™s bud-
geted 2004 pro¬t and loss (P & L) statement, the heart of the operating
budget. The difference between the projected revenues of $1,980,000 and
the projected variable costs of $1,350,000 produces a total contribution mar-
gin of $630,000. Deducting the forecasted ¬xed costs of $500,000 results
in a budgeted pro¬t of $130,000. The true purpose of the operating budget
is to set ¬nancial goals for the clinic. In effect, the operating budget can be
thought of as a contract between the organization and its managers. Thus, the
$130,000 pro¬t forecast becomes the overall pro¬t benchmark for the clinic
in 2004, and individual managers will be held accountable for the revenues
and expenses needed to meet the budget.
231
Chapter 8: Planning and Budgeting




Self-Test
1. What are some of the key assumptions required to prepare an operating
Questions
budget?
2. Do the required assumptions depend on the type of organization and
the nature of its reimbursement contracts?
3. Why is the budgeted pro¬t and loss (P & L) statement so important?


Variance Analysis
Variance analysis, which focuses on differences (variances) between realized
values and forecasts, is an important technique for controlling ¬nancial per-
formance. This section includes a discussion of the basics of variance analysis,
including ¬‚exible budgeting, as well as an illustration of the process.

Variance Analysis Basics
In accounting, a variance is the difference between an actual (realized) value
and the budgeted value, often called a standard. Note that the accounting
de¬nition of variance is different from the statistical de¬nition, although both
meanings connote a difference from some base value. In effect, variance analy-
sis is an examination and interpretation of differences between what has ac-
tually happened and what was planned. If the budget is based on realistic
expectations, variance analysis can provide managers with very useful infor-
mation. Variance analysis does not provide all the answers, but it does help
managers ask the right questions.
Variance analysis is essential to the managerial control process. Actions
taken in response to variance analysis often have the potential to dramatically
improve the operations and ¬nancial performance of the organization. For
example, many variances are controllable, so managers can take actions to
avoid unfavorable variances in the future. The primary focus of variance anal-
ysis should not be to assign blame for unfavorable results. Rather, the goal of
variance analysis is to uncover the cause of operational problems so that these
problems can be avoided, or at least minimized, in the future. Unfortunately,
not all variances are controllable by management. Nevertheless, knowledge
of such variances is essential to the overall management and well-being of
the organization. It may be necessary to revise plans, for example, to tighten
controllable costs in an attempt to offset unfavorable cost variances in areas
that are beyond managerial control.

Static Versus Flexible Budgets
To be of maximum use to managers, variance analysis must be approached
systematically. The starting point for such analyses is the static budget, which
is the original approved budget unadjusted for differences between planned
and actual (realized) volumes. However, at the end of a budget period, it is
unlikely that realized volume will equal budgeted volume, and it would be
232 Healthcare Finance



very useful to know which variances are due to volume forecast errors and
which variances are caused by other factors.
To illustrate this concept, consider Carroll Clinic™s 2004 operating
budget contained in Table 8.3. The pro¬t projection, $130,000, is predi-
cated on speci¬c volume assumptions: 36,000 visits for the FFS population
and 360,000 member-months, resulting in 54,000 visits, for the capitated
population. At the end of the year, the clinic™s managers will compare ac-
tual pro¬ts with budgeted pro¬ts. The problem, of course, is that it is highly
unlikely that actual pro¬ts will be based on 36,000 fee-for-service visits and
360,000 member months (with 54,000 visits) for the capitated population.
Thus, if Carroll™s managers were to merely compare the realized pro¬t with
the $130,000 pro¬t in the static budget, they would not know whether any
pro¬t difference is caused by volume differences or underlying operational
differences.
To provide an explanation of what is driving the pro¬t variance, man-
agers must create a ¬‚exible budget. A ¬‚exible budget is one in which the static
budget has been adjusted to re¬‚ect the actual volume achieved in the budget
period. Essentially, ¬‚exible budgets are an after-the-fact device to tell man-
agers what the results would have been under the volume level actually at-
tained, assuming all other budgeting assumptions are held constant. The
¬‚exible budget permits a more detailed analysis than is possible with a static
budget. However, a ¬‚exible budget requires the identi¬cation of variable and
¬xed costs and hence places a larger burden on the organization™s managerial
accounting system.

Variance Analysis Illustration
To illustrate variance analysis, consider Carroll™s static budget for 2004 (Table
8.3), which projects a pro¬t of $130,000. Data used for variance analysis is
tracked in various parts of Carroll™s managerial accounting information system
throughout the year, and variance analyses are performed monthly. This allows
managers to take necessary actions during the year to positively in¬‚uence an-
nual results. For purposes of this illustration, however, the monthly feedback
is not shown. Rather, the focus is on the year-end results, which are contained
in Table 8.4.

Creating the Table 8.5 contains three budgets for 2004. The static budget, taken from Ta-
Flexible Budget ble 8.3, is the forecast made at the beginning of 2004, while the actual budget,
taken from Table 8.4, re¬‚ects after-the-fact results. The ¬‚exible budget in the
center column of Table 8.5 re¬‚ects projected revenues and costs at the real-
ized (actual) volume, as opposed to the projected volume, but incorporates all
other assumptions that went into the static budget. By analyzing differences
in these three budgets, Carroll™s managers can gain insights into why the clinic
ended the year with a loss.
233
Chapter 8: Planning and Budgeting


TABLE 8.4
I. Volume:
Carroll Clinic:
A. FFS 40,000 visits
B. Capitated lives 30,000 members 2004 Results
Number of member months 360,000
Actual utilization per
member-month 0.20
Number of visits 72,000 visits
C. Total actual visits 112,000 visits

II. Revenues:
A. FFS $ 24 per visit
— 40,000 actual visits
$ 960,000
B. Capitated lives $ 3 PMPM
— 360,000 actual member months
$ 1,080,000
C. Total actual revenues $ 2,040,000

III. Costs:
A. Variable Costs:
Labor $ 1,557,400 (59,900 hours at $26/hour)
Supplies 234,600 (124,800 units at $1.88/unit)
Total variable costs $ 1,792,000
Variable cost per visit $ 16 ($1,792,000/112,000)
B. Fixed Costs:
Overhead, plant,
and equipment $ 500,000
C. Total actual costs $ 2,292,000

IV. Pro¬t and Loss Statement:
Revenues:
FFS $ 960,000
Capitated 1,080,000
Total $ 2,040,000
Costs:
Variable:
FFS $ 640,000
Capitated 1,152,000
Total $ 1,792,000
Contribution margin $ 248,000
Fixed costs 500,000
Actual pro¬t ($ 252,000)




Note that the ¬‚exible budget maintains the original budget assump-
tions of Revenues = ($25 — Number of FFS visits) + ($3 — Number of
capitated member-months) and Expenses = ($15 — Number of FFS visits) +
($15 — Number of capitated visits) + $500,000. However, the ¬‚exible budget
¬‚exes (adjusts) revenues and costs to re¬‚ect actual volume levels. Thus, in the
234 Healthcare Finance


TABLE 8.5
Static Flexible Actual
Carroll Clinic:
Budget Budget Budget
Static, Flexible,
and Actual Assumptions:
Budgets for FFS visits 36,000 40,000 40,000
Capitated visits 54,000 72,000 72,000
2004
Total 90,000 112,000 112,000

Revenues:
FFS $ 900,000 $1,000,000 $ 960,000
Capitated 1,080,000 1,080,000 1,080,000
Total $1,980,000 $2,080,000 $2,040,000
Costs:
Variable:
FFS $ 540,000 $ 600,000 $ 640,000
Capitated 810,000 1,080,000 1,152,000
Total $1,350,000 $1,680,000 $1,792,000
Contribution margin $ 630,000 $ 400,000 $ 248,000
Fixed costs 500,000 500,000 500,000
Pro¬t $ 130,000 ($ 100,000) ($ 252,000)



¬‚exible budget column, Revenues = ($25 — 40,000) + ($3 — 360,000) =
$1,000,000 + $1,080,000 = $2,080,000, and Expenses = ($15 — 40,000)
+ ($15 — 72,000) + $500,000 = $600,000 + $1,080,000 + $500,000 =
$1,680,000 + $500,000 = $2,180,000.
The ¬‚exible budget can be described as follows. The $2,080,000 in
total revenues is what the clinic would have expected at the start of the year if
the volume estimates had been 40,000 FFS visits and a capitated membership
of 30,000. In addition, the total variable costs of $1,680,000 in the ¬‚exible
budget are the costs that Carroll would have expected for 40,000 FFS visits
and 72,000 capitated visits (based on a membership of 30,000). By de¬nition,
the ¬xed costs should be the same, within a reasonable range, no matter
what the volume level. On net, the $100,000 loss shown on the ¬‚exible
budget represents the pro¬t expected given the initial assumed revenue, cost,
and volume relationships, coupled with a forecasted volume that equals the
realized volume.

Conducting the To begin the variance analysis, consider Carroll™s total, or pro¬t, variance.
Variance Pro¬t variance is merely the difference between the realized pro¬t (Table 8.4)
Analysis and the static pro¬t (Table 8.3). Thus, Pro¬t variance = Actual pro¬t ’ Static
pro¬t, or (’$252,000) ’ $130,000 = ’$382,000. In words, Carroll™s 2004
pro¬tability was $382,000 below standard, or $382,000 less than expected.
Although this large negative variance should generate considerable concern
235
Chapter 8: Planning and Budgeting


TABLE 8.6
Profit Pro¬t Variance
Variance and Revenue and
“$382,000
Cost
Components

Revenue Cost
Variance Variance
$60,000 “$442,000


= Actual pro¬t ’ Static pro¬t.
Pro¬t variance
= Actual revenues ’ Static revenues.
Revenue variance
= Static costs ’ Actual costs.
Cost variance



among Carroll™s managers, a more detailed analysis is required to determine
the underlying causes.
Perhaps the ¬rst question that Carroll™s management would want an-
swered is this: Is the large negative loss (as compared to expectations) due to
a revenue shortfall, cost overruns, or both? Table 8.6 shows the ’$382,000
pro¬t variance at the top, and then breaks it down into its revenue and cost
components. In calculating all variances, we are using de¬nitions (given in the
bottom of each variance table) that show “bad” results as a negative number.4
The revenue variance of $60,000 tells Carroll™s managers that realized
revenues were actually higher than expected. However, the ’$442,000 cost
variance indicates that realized costs were much greater than expected. The
net effect of the revenue and cost variances is the $60,000 + (’$442,000) =
’$382,000 pro¬t variance. By breaking down the pro¬t variance into revenue
and cost components, it is readily apparent that the major cause of Carroll™s
poor ¬nancial performance in 2004 was that costs were too high. However,
the analysis thus far does not discriminate between cost overruns caused by
volume forecast errors and those caused by managerial actions.
Regarding the revenue variance, it would be nice to know if the greater-
than-expected revenues were due to greater-than-expected volume or greater-
than-expected prices (reimbursement). Table 8.7 examines the revenue
variance in more detail. Here, the $60,000 positive revenue variance is de-
composed into a $100,000 volume variance and a ’$40,000 price variance.
These variances tell Carroll™s managers that a higher-than-expected volume
should have resulted in revenues being $100,000 greater than expected in
2004. However, this potential revenue increase was partially offset by the fact
that realized prices (reimbursement) were less than expected. The end result
of higher volume at lower prices is realized revenue that was $60,000 higher
than forecasted. Note that to keep this illustration manageable, the number of
covered lives (enrollment) was the same in both the static and actual budgets.
236 Healthcare Finance


TABLE 8.7
Revenue
Variance and
Volume and
Cost
Components




Revenue variance = Actual revenues ’ Static revenues.
Volume variance = Flexible revenues ’ Static revenues.
= Actual revenues ’ Flexible revenues.
Price variance

Note: In our example, there are no enrollment differences. However, if some patients are capitated, and there are
enrollment differences between expected and realized budgets, the situation becomes more complex. Then, it is
necessary to create two ¬‚exible budgets: (1) one ¬‚exed for both enrollment and utilization and (2) one ¬‚exed only
for enrollment. With two ¬‚exible budgets, volume variances can be calculated for both changes in the number of
covered lives and changes in utilization.

= Flexible (enrollment and utilization) revenues ’ Static revenues.
Volume variance
Enrollment variance = Flexible (enrollment) revenues ’ Static revenues.
Utilization variance = Flexible (enrollment and utilization) revenues ’ Flexible (enrollment) revenues.




If this had not been the case, the volume variance would have two compo-
nents. (Refer to the note at the bottom of Table 8.7.)
Now let™s change our focus to the cost side of the analysis. Table 8.8
breaks the ’$442,000 cost variance into volume and management compo-
nents. The volume variance of ’$330,000 indicates that a large portion of the
$442,000 cost overrun was caused by the incorrect volume forecast: Higher-
than-expected volume resulted in higher-than-expected costs. This higher-
than-expected volume would not be a ¬nancial problem if it were due to fee-
for-service patients, in which higher costs due to higher volume would likely
be more than offset by higher revenues. However, the fact that a majority
of the higher volume (18,000 of 22,000 visits) came from capitated patients
means that there is no matching revenue increase.
In addition to the problem of higher-than-expected volume, $112,000
of the $442,000 cost overrun was due to other factors. This amount is the so-
called management variance, which gets its name from the assumption that
any cost variances not caused by volume forecast inaccuracies are a result
of either good or bad management performance. The theory here is that
most managers have very limited (if any) control over the volume of services
supplied, but they do have control over factors such as the amount of labor
used, wage rates, supplies costs, and so forth. Thus, the $112,000 cost overrun
classi¬ed as a management variance can be in¬‚uenced by managerial actions.
If all standards in the static budget except the volume estimate were met, the
cost overrun would have been only $330,000, and not the $442,000 realized.
237
Chapter 8: Planning and Budgeting


TABLE 8.8
Cost Cost Variance
Variance and Volume and
“$442,000
Management
Components

Volume Management
Variance Variance
“$330,000 “$112,000


= Static costs ’ Actual costs.
Cost variance
= Static costs ’ Flexible costs.
Volume variance
Management variance = Flexible costs ’ Actual costs.



To attempt to eliminate the managerial variance in future years, Car-
roll™s managers must determine precisely where the cost overruns lie. The pri-
mary resources involved in operating costs are labor and supplies, so it would
be valuable to learn which of the two areas contributed most to the manage-
ment variance. Perhaps a more probing investigation can be made within labor
and supplies: Is too much of each resource being used or is too much money
being paid for what is being used?
Table 8.9 examines the components of the management variance. We
see that $64,075 of the management variance of $112,000 is a result of labor
costs, so with no ¬xed cost variance, the remainder is the result of supplies
costs. Furthermore, the $64,075 labor variance can be decomposed into
that portion caused by productivity (the ef¬ciency variance) problems and
that portion caused by wage rate (the rate variance) overages. The numbers
indicate that only a very small portion of the labor cost overrun was caused by
productivity problems; the vast majority of the overrun was caused by higher-
than-expected wage rates. This suggests that Carroll™s managers have to take
a close look to ensure that they are not paying more than the local market for
labor dictates. Of course, Carroll wants to have quality employees, but, at the
same time, management needs to be concerned about labor costs.
How did Carroll do in 2004 regarding supplies costs? If $64,075 of
the management variance of $112,000 is caused by labor costs, the remain-
der, $47,925, must be caused by supplies costs. Within the $47,925 supplies
variance, the amount caused by excess utilization (the usage variance) and the
amount caused by price differentials (the price variance) can be determined.
$525 of the supplies variance of $47,925 is caused by usage differences; the
remainder ($47,400) is caused by price differences. Thus, the supplies cost
overrun was a result, almost totally, of price increases; supplies usage was al-
most on target when volume differences are accounted for. Thus, it would be
prudent for management to investigate the clinic™s purchasing policy to see
238 Healthcare Finance


TABLE 8.9
Management
Management Variance
Variance and “$112,000
Components


Labor Fixed Cost Supplies
Variance Variance Variance
“$64,075 $0 “$47,925




Rate Efficiency Price Usage
Variance Variance Variance Variance
“$59,900 “$4,175 “$47,400 “$525


= Flexible costs ’ Actual costs.
Management variance
= Flexible ¬xed costs ’ Actual ¬xed costs.
Fixed cost variance
= Flexible labor costs ’ Actual labor costs.
Labor variance
= (Static rate ’ Actual rate) — Actual labor hours.
Rate variance
= (Flexible hours ’ Actual hours) — Static rate.
Ef¬ciency variance
= Flexible supplies costs ’ Actual supplies costs.
Supplies variance
= (Static price ’ Actual price) — Actual units.
Price variance
= (Flexible units ’ Actual units) — Static price.
Usage variance

Note: The calculations of the component variances are not complex but lengthy. They are omitted for ease of
illustration.




if prices can be lowered through such actions as changing vendors, making
larger purchases at a single time, joining a purchasing alliance, or just negoti-
ating better.

Final It is important to recognize that the Carroll Clinic example presented here
Comments on was meant to illustrate variance analysis techniques as opposed to illustrate a
Variance complete analysis. A complete analysis would encompass many more variances.
Analysis Furthermore, at most organizations, variance analysis would be conducted at
the department level, as well as other sub-levels such as service or contract
lines, in addition to the organization as a whole. Nevertheless, the Carroll
Clinic example is suf¬cient to give readers a good feel for how variance analysis
is conducted as well as its bene¬ts to the organization.
Variance analysis helps managers identify the factors that cause realized
pro¬ts to be different from those expected. If pro¬ts are higher than expected,
managers can see why and then try to exploit even further those factors
in the future. If pro¬ts are lower than expected, managers can identify the
causes and then embark on a plan to correct the de¬ciencies. Larger health
services organizations have made signi¬cant improvements in their use of
variance analysis. The bene¬t from expanding the level of information detail
is that it is easier for managers to isolate and presumably rectify problem
239
Chapter 8: Planning and Budgeting



areas. Fortunately, the marginal cost of obtaining such detailed information is
lower now than ever before because large amounts of managerial accounting
information are being generated at many health services organizations both
to support cost-control efforts and to aid in pricing and service decisions.


Self-Test
1. What is variance analysis, and what is its value to healthcare providers?
Questions
2. What is the difference between a static budget and a ¬‚exible budget?
3. What are the components of pro¬t variance? Of revenue variance? Of
cost variance?


The Cash Budget
Thus far, our discussion of budgeting has focused on the operating budget. As
shown in the Carroll Clinic illustration, the operating budget, along with the
budgetary control process, provides managers with numerous insights into the
ef¬ciency of an organization™s operations. However, the operating budget is
based on accrual accounting principles and hence does not provide managers
with much information about a business™s cash position. This situation is
corrected by the cash budget.
To create a cash budget, managers begin by forecasting volume, rev-
enue, and collections data. Then, they forecast both ¬xed asset acquisition and
inventory requirements, along with the times when such payments must be
made. Finally, this information is combined with cash outlay projections for
operating and ¬nancial expenses such as wages and bene¬ts, interest payments,
tax payments, and so on. All this collection and payment information is then
combined to show the organization™s projected cash in¬‚ows and out¬‚ows
over some speci¬ed period. Generally, “the cash budget” consists of individual
monthly cash budgets forecasted for one year, plus a more detailed daily or
weekly cash budget for the coming month. The monthly cash budget is used
for liquidity planning purposes, and the daily or weekly budget is used for
actual cash control.
Creating a cash budget does not require the application of a complex set
of accounting rules. Rather, all the entries in a cash budget represent the actual
movement of cash into or out of the organization. To illustrate, Table 8.10
contains a monthly cash budget that covers six months of 2005 for Madison
Homecare, a small, for-pro¬t home health care company. Madison™s cash
budget, which is broken down into three sections, is typical, although there is
a great deal of variation in formats used by different organizations. Also, for
ease of illustration, the cash budget has been constrained to relatively few lines.
The ¬rst section of Madison™s cash budget contains the collections work-
sheet, which translates the billing for services provided into cash revenues. Be-
cause of its location in a summer resort area, Madison™s patient volume, and
hence billings, peak in July. However, like most health services organizations,
240 Healthcare Finance


TABLE 8.10 Mar Apr May June July Aug Sept Oct
Madison
Collections Worksheet:
Homecare:
1. Billed charges $50,000 $50,000 $ 100,000 $ 150,000 $200,000 $ 100,000 $ 100,000 $ 50,000
May Through 2. Collections:
a. Within 30 days 19,600 29,400 39,200 19,600 19,600 9,800
October Cash
b. 30“60 days 35,000 70,000 105,000 140,000 70,000 70,000
Budget c. 60“90 days 5,000 5,000 10,000 15,000 20,000 10,000
3. Total collections $ 59,600 $ 104,400 $ 154,200 $ 174,600 $ 109,600 $ 89,800

Supplies Worksheet:
4. Amount of supplies ordered $ 10,000 $ 15,000 $ 20,000 $ 10,000 $ 10,000 $ 5,000
5. Payments made for supplies $ 10,000 $ 15,000 $ 20,000 $ 10,000 $ 10,000 $ 5,000

Net Cash Gain (Loss):
6. Total collections (from Line 3) $ 59,600 $ 104,400 $ 154,200 $ 174,600 $ 109,600 $ 89,800
7. Total purchases (from Line 5) $ 10,000 $ 15,000 $ 20,000 $ 10,000 $ 10,000 $ 5,000
8. Wages and salaries 60,000 70,000 80,000 60,000 60,000 60,000
9. Rent 2,500 2,500 2,500 2,500 2,500 2,500
10. Other expenses 1,000 1,500 2,000 1,000 1,000 500
11. Taxes 20,000 20,000
12. Payment for capital assets 50,000
13. Total payments $ 73,500 $ 109,000 $ 104,500 $ 123,500 $ 93,500 $ 68,000
14. Net cash gain (loss) ($ 13,900) ($ 4,600) $ 49,700 $ 51,100 $ 16,100 $ 21,800

Surplus/De¬cit Summary:
15. Cash at beginning with no borrowing $ 15,000 $ 1,100 ($ 3,500) $ 46,200 $ 97,300 $ 113,400
16. Cash at end with no borrowing $ 1,100 ($ 3,500) $ 46,200 $ 97,300 $ 113,400 $ 135,200
17. Target cash balance 10,000 10,000 10,000 10,000 10,000 10,000
18. Cumulative surplus (de¬cit) ($ 8,900) ($ 13,500) $ 36,200 $ 87,300 $ 103,400 $ 125,200




Madison rarely collects when services are provided. What is relevant from a
cash budget perspective is not when services are provided or when billings
occur but when cash is collected. Based on previous experience, Madison™s
managers know that most collections occur 30 to 60 days after billing. In
fact, Madison™s managers have created a collections table that allows them to
forecast, with some precision, the timing of collections. This table was used
to convert the billings shown on Line 1 of Table 8.10 into the collection
amounts shown on Lines 2 and 3.
The next section of Madison™s cash budget is the supplies worksheet,
which accounts for both the amount of supplies purchased and timing dif-
ferences between when supplies are ordered and when the resulting bills are
paid. Madison™s patient volume forecasts, which are used to predict the billing
amounts shown on Line 1, are also used to forecast the supplies (primarily
medical) needed to support patient services. These supplies are ordered and
received one month prior to expected usage, as shown on Line 4. However,
Madison™s suppliers do not demand immediate payment. Rather, Madison
has, on average, 30 days to pay for supplies after they are received. Thus, the
actual payment occurs one month after purchase, as shown on Line 5.
241
Chapter 8: Planning and Budgeting



The next section combines data from the collections and supplies work-
sheets with other projected cash out¬‚ows to show the net cash gain (loss) for
each month. Cash from collections is shown on Line 6. Lines 7 through 12
list cash payments that are expected to be made during each month, including
payments for supplies. Then, all payments are summed, with the total shown
on Line 13. The difference between expected cash receipts and cash payments,
Line 6 minus Line 13, is the net cash gain or loss during the month, which is
shown on Line 14. For May, there is a forecasted net cash out¬‚ow of $13,900,
where the parentheses indicate a negative cash ¬‚ow.
Although Line 14 contains the “meat” of the cash budget, Lines 15
through 18 (the surplus/de¬cit summary) extend the basic budget data to
show Madison™s monthly forecasted cumulative cash position. Line 15 shows
the forecasted cash on hand at the beginning of each month assuming that
no borrowing takes place. Madison is expected to enter the budget period,
the beginning of May, with $15,000 of cash on hand. For each succeeding
month, Line 15 is merely the value shown on Line 16 for the previous month.
The values on Line 16, which are obtained by adding Lines 14 and 15, show
the cash on hand at the end of each month assuming no borrowing takes
place. For May, Madison expects a cash loss of $13,900 on top of a starting
balance of $15,000, for an ending cash balance of $1,100, in the absence
of any borrowing. This amount is the cash at beginning with no borrowing
amount for June shown on Line 15.
To continue, Madison™s target cash balance (i.e., the amount that it
wants on hand at the beginning of each month), which is shown on Line
17, is $10,000. The target cash balance is subtracted from the forecasted
ending cash with no borrowing amount to determine the ¬rm™s monthly
de¬cit (shown in parentheses) or surplus (shown without parentheses). Be-
cause Madison expects to have ending cash, as shown on Line 16, of only
$1,100 in May, it will have to obtain $1,100 ’ $10,000 = ’$8,900 to bring
the cash account up to the target balance of $10,000. If this amount is bor-
rowed, as opposed to obtained from other sources such as liquidating mar-
ketable securities, the total loan outstanding will be $8,900 at the end of
May. (The assumption here is that Madison will not have any loans outstand-
ing on May 1 because the beginning cash balance exceeds the ¬rm™s target
balance.)
The cumulative cash surplus or de¬cit is shown on Line 18; a positive
value indicates a cash surplus, while a negative value indicates a de¬cit. The
surplus cash or de¬cit shown on Line 18 is a cumulative amount. Thus,
Madison is projected to require $8,900 in May; it has a cash shortfall during
June of $4,600, as reported on Line 14, so its total de¬cit projected for the
end of June is $8,900 + $4,600 = $13,500, as shown on Line 18.
The same procedures are followed in subsequent months. Patient vol-
ume and billings are projected to peak in July, accompanied by increased pay-
ments for supplies, wages, and other items. However, collections are projected
242 Healthcare Finance



to increase by a greater amount than costs, and Madison expects a $49,700
net cash in¬‚ow during July. This amount is suf¬cient to pay off the cumulative
loan (if one is used) of $13,500 and have a $36,200 cash surplus on hand at
the end of the month.
Patient volume, and the resulting operating costs, is expected to fall
sharply in August, but collections will be the highest of any month because
they will re¬‚ect the high June and July billings. As a result, Madison would
normally be forecasting a healthy $101,100 net cash gain during the month.
However, the company expects to make a cash payment of $50,000 to pur-
chase a new computer system during August, so the forecasted net cash gain is
reduced to $51,100. This net gain adds to the surplus, so August is projected
to end with $87,300 in surplus cash. If all goes according to the forecast, later
cash surpluses will enable Madison to end this budget period with a surplus
of $125,200.
The cash budget is used by Madison™s managers for liquidity planning
purposes. For example, the Table 8.10 cash budget indicates that Madison will
need to obtain $13,500 in total to get through May and June. Thus, if the
¬rm does not have any marketable securities to convert to cash, it will have to
arrange a loan, typically a line of credit, to cover this period. Furthermore, the
budget indicates a $125,200 cash surplus at the end of October. Madison™s
managers will have to consider how these funds can best be utilized. Perhaps
the money should be returned to owners as dividends or bonuses, or be used
for ¬xed asset acquisitions or be temporarily invested in marketable securities
for later use within the business. This decision will be made on the basis of
Madison™s overall ¬nancial plan.
This brief illustration shows the mechanics and managerial value of the
cash budget. However, before concluding the discussion, several additional
points need to be made. First, if cash in¬‚ows and out¬‚ows are not uniform
during the month, a monthly cash budget could seriously understate a busi-
ness™s peak ¬nancing requirements. The data in Table 8.10 show the situation
expected on the last day of each month, but on any given day during the
month it could be quite different. For example, if all payments had to be
made on the ¬fth of each month, but collections came in uniformly through-
out the month, Madison would need to borrow cash to cover within-month
shortages. Looking at August, the $123,500 of cash payments would occur
before the full amount of the $174,600 in collections have been made. In this
situation, some amount of cash would be needed to cover shortfalls in August,
even though the end of month cash ¬‚ow after all collections had been made is
positive. Because Madison™s cash ¬‚ows do occur unevenly during each month,
it also prepares weekly cash budgets to forecast within-month shortages.
Also, because the cash budget represents a forecast, all the values in the
table are expected values. If actual patient volume, collection times, supplies
purchases, wage rates, and so on differ from forecasted levels, the projected
cash de¬cits and surpluses will be incorrect. Thus, there is a reasonable chance
243
Chapter 8: Planning and Budgeting



that Madison may end up needing to obtain a larger amount of funds than
is indicated on Line 18. Because of the uncertainty of the forecasts, spread-
sheets are particularly well suited for constructing and analyzing cash budgets.
For example, Madison™s managers could change any assumption”say, pro-
jected monthly volume or the time third-party payers take to pay”and the
cash budget would automatically and instantly be recalculated. This would
show Madison™s managers exactly how the ¬rm™s cash position changes under
alternative operating assumptions. Typically, such an analysis is used to deter-
mine the size of the credit line needed to cover temporary cash shortages.5 In
Madison™s case, such an analysis indicated that a $20,000 line is suf¬cient.


Self-Test
1. Considering all the information in the operating budget, why do
Questions
organizations need a cash budget?
2. Does the cash budget require an extensive knowledge of accounting
principles?
3. In your view, what is the most important line of the cash budget?


Key Concepts
Planning and budgeting are important managerial activities. In particular,
budgets allow health services managers to plan for and set expectations for
the future, assess ¬nancial performance on a timely basis, and ensure that
operations are carried out in a manner consistent with expectations. The key
concepts of this chapter are:
• Planning encompasses the overall process of preparing for the future,
while budgeting is the accounting process that ties together planning and
control functions.
• The strategic plan, which provides broad guidance for the future, is the
foundation of any organization™s planning process. More detailed
managerial guidance is contained in the operating plan, often called the
¬ve-year plan.
• The ¬nancial plan, which is the ¬nancial portion of the operating plan,
contains a long-term plan, working capital management plan, and
managerial accounting plan.
• Budgeting provides a means for communication and coordination of
organizational expectations as well as allocation of ¬nancial resources. In
addition, budgeting establishes benchmarks for control.
• There are several types of budgets, including the statistics budget, revenue
budget, expense budget, operating budget, and cash budget.
• The conventional approach to budgeting uses the previous budget as the
basis for constructing the new budget. Zero-based budgeting begins each
budget as a clean slate, and hence all entries have to be justi¬ed each
budget period.
244 Healthcare Finance



• Bottom-up budgeting, which begins at the unit level, encourages maximum
involvement by junior managers. Conversely, top-down budgeting, which is
less participatory in nature, is a more ef¬cient way to communicate senior
management™s views.
• The operating budget is the basic budget of an organization in that it sets
the pro¬t target for the budget period.
• A variance is the difference between a budgeted (planned) value, or
standard, and the actual (realized) value. Variance analysis examines
differences between budgeted and realized amounts with the goal of
¬nding out why things went either badly or well.
• A budget that fully re¬‚ects realized results is called the actual budget.
When the original, or static budget, is recast to re¬‚ect the actual volume of
patients treated, leaving all other assumptions unchanged, the result is
called a ¬‚exible budget. To be most useful, variance analysis examines
differences between the actual, ¬‚exible, and static budgets.
• A cash budget, which is the primary cash management tool, forecasts the
cash in¬‚ows and out¬‚ows of an organization with the goal of identifying
expected surpluses and shortfalls.
• In general, monthly cash budgets are used for planning purposes while
weekly or daily budgets are used for cash management purposes.

This chapter concludes the discussion of managerial accounting. Chapter 9
begins the examination of basic ¬nancial management concepts.


Questions
8.1 Why is planning and budgeting so important to an organization™s
success?
8.2 Brie¬‚y describe the planning process. Be sure to include summaries of
the strategic, operating, and ¬nancial plans.
8.3 Describe the components of a ¬nancial plan.
8.4 How are the statistics, revenue, expense, and operating budgets related?
8.5 a. What are the advantages and disadvantages of conventional budgeting
versus zero-based budgeting?
b. What organizational characteristics create likely candidates for
zero-based budgeting?
8.6 If you were the CEO of Bayside Memorial Hospital, would you
advocate a top-down or bottom-up approach to budgeting? Explain
your rationale.
8.7 What is variance analysis?
8.8 a. Explain the relationships among the static budget, ¬‚exible budget,
and actual budget.
b. Assume that a group practice has both capitated and fee-for-service
(FFS) patients. Furthermore, the number of capitated enrollees
245
Chapter 8: Planning and Budgeting



has changed over the budget period. In order to calculate the
volume variance and break it down into enrollment and utilization
components, how many ¬‚exible budgets must be constructed?
8.9 a. What is a cash budget and how is it used?
b. Should depreciation expense appear on a cash budget? Explain your
answer.



Problems
8.1 Consider the following 2004 data for Newark General Hospital (in
millions of dollars):
Static Flexible Actual
Year Budget Budget Budget
Revenues $4.7 $4.8 $4.5
Costs 4.1 4.1 4.2
Pro¬ts 0.6 0.7 0.3

a. Calculate and interpret the pro¬t variance.
b. Calculate and interpret the revenue variance.
c. Calculate and interpret the cost variance.
d. Calculate and interpret the volume and price variances on the revenue
side.
e. Calculate and interpret the volume and management variances on the
cost side.
f. How are the variances calculated above related?
8.2 Here are the 2004 revenues for the Wendover Group Practice
Association for four different budgets, in thousands of dollars:
Flexible Flexible
Static (Enrollment/Utilization) (Enrollment) Actual
Budget Budget Budget Budget
$425 $200 $180 $300

a. What does the budget data tell you about the nature of Wendover™s
patients: Are they capitated or fee-for-service? (Hint: See the note to
Table 8.7.)
b. Calculate and interpret the following variances:
• Revenue variance
• Volume variance
• Price variance
• Enrollment variance
• Utilization variance
8.3 Here are the budgets of Brandon Surgery Center for the most recent
historical quarter, in thousands of dollars:
246 Healthcare Finance



Static Flexible Actual
Number of surgeries 1,200 1,300 1,300
Patient revenue $2,400 $2,600 $2,535
Salary expense 1,200 1,300 1,365
Non-salary expense 600 650 585
Pro¬t $ 600 $ 650 $ 585

The center assumes that all revenues and costs are variable and hence
tied directly to patient volume.
a. Explain how each amount in the ¬‚exible budget was calculated.
(Hint: Examine the static budget to determine the relationship of
each budget line to volume.)
b. Determine the variances for each line of the pro¬t and loss statement,
both in dollar terms and in percentage terms. (Hint: Each line has a
total variance, a volume variance, and a management variance.)
c. What do the Part b results tell Brandon™s managers about the surgery
center™s operations for the quarter?
8.4 Refer to Carroll Clinic™s 2004 operating budget contained in Table 8.3.
Instead of the actual results reported in Table 8.4, assume the results
reported below:

Carroll Clinic: New 2004 Results

I. Volume:
A. FFS 34,000 visits
B. Capitated lives 30,000 members
Number of member months 360,000
Actual utilization per
member-month 0.12
Number of visits 43,200 visits
C. Total actual visits 77,200 visits
II. Revenues:
A. FFS $ 28 per visit
— 34,000 actual visits
$ 952,000
B. Capitated lives $ 2.75 PMPM
— 360,000 actual member months
$ 990,000

C. Total actual revenues $1,942,000

III. Costs:
A. Variable Costs:
Labor $1,242,000 (46,000 hours at $27/hour)
Supplies 126,000 (90,000 units at $1.40/unit)
Total variable costs $1,368,000
Variable cost per visit $ 17.72 ($1,368,000/77,200)
247
Chapter 8: Planning and Budgeting


B. Fixed Costs:
Overhead, plant,
and equipment $ 525,000

C. Total actual costs $1,893,000
IV. Pro¬t and Loss Statement:
Revenues:
FFS $ 952,000
Capitated 990,000
Total $1,942,000
Costs:
Variable:
FFS $ 602,487
Capitated 765,513
Total $1,368,000
Contribution margin $ 574,000
Fixed costs 525,000
Actual pro¬t $ 49,000

a. Construct Carroll™s ¬‚exible budget for 2004.
b. What are the pro¬t variance, revenue variance, and cost variance?
c. Consider the revenue variance. What is the component volume
variance? The price variance?
d. Break down the cost variance into volume and management
components.
e. Break down the management variance into labor, supplies, and ¬xed
costs variances.
f. Break down the labor variance into rate and ef¬ciency components.
g. Break down the supplies variance into price and usage components.
h. Interpret your results. In particular, focus on the differences between
the variance analysis here and the Carroll Clinic illustration presented
in the chapter.
8.5 Refer to Problem 8.4. Assume the results reported in that problem hold,
except that a difference existed among budgeted, static enrollment and
realized enrollment. The corrected results are:

Carroll Clinic: Corrected 2004 Results

I. Volume:
A. FFS 34,000 visits
B. Capitated lives 31,000 members
Number of member months 372,000
Actual utilization per
member-month 0.11613
Number of visits 43,200 visits
C. Total actual visits 77,200 visits
II. Revenues:
A. FFS $ 28 per visit
— 34,000 actual visits
$ 952,000
248 Healthcare Finance


B. Capitated lives $ 2.75 PMPM
— 372,000 actual member months
$1,023,000
C. Total actual revenues $1,975,000

III. Costs:
A. Variable Costs:
Labor $1,242,000 (46,000 hours at $27/hour)
Supplies 126,000 (90,000 units at $1.40/unit)
Total variable costs $1,368,000

Variable cost per visit $ 17.72 ($1,368,000/77,200)

B. Fixed Costs:
Overhead, plant,
and equipment $ 525,000
C. Total actual costs $1,893,000

IV. Pro¬t and Loss Statement:
Revenues:
FFS $ 952,000
Capitated 1,023,000
Total $1,975,000
Costs:
Variable:
FFS $ 602,487
Capitated 765,513
Total $1,368,000
Contribution margin $ 607,000
Fixed costs 525,000
Actual pro¬t $ 82,000



a. Construct Carroll™s ¬‚exible budgets for 2004. (Hint: Because of a
change in enrollment, creating three ¬‚exible budgets is necessary. See
the note to Table 8.7.)
b. What are the pro¬t variance, revenue variance, and cost variance?
c. Focus on the revenue side. What is the volume variance? The
price variance? Break the volume variance into enrollment and
utilization components. How does your answer here differ from your
corresponding answer to Problem 8.4.
d. Now consider the cost side. What are the volume and management
varances? Break down the management variance into labor, supplies,
and ¬xed costs variances.
e. Break down the labor variance into rate and ef¬ciency components.
f. Break down the supplies variance into price and usage components.
g. Interpret your results. In particular, focus on the differences between
the variance analysis here and the one in Problem 8.4.
249
Chapter 8: Planning and Budgeting



Notes

1. For more information on budgeting processes in general, see Robert Rachlin
(editor), Handbook of Budgeting (Wiley, 2001). For more information
on budgeting within healthcare organizations, see Alan G. Herkimer, Jr.,
Understanding Health Care Budgeting (Aspen, 1988) or William J. Ward, Jr.,
Health Care Budgeting and Financial Management for Non-Financial Managers
(Album House, 1994).
2. Financial statement forecasting is an important function of any business™s
¬nancial staff. However, this discussion will be left to other texts. For more
information, see Louis C. Gapenski, Understanding Health Care Financial
Management, 4th ed. (AUPHA Press/Health Administration Press, 2003).
3. For an extensive discussion of zero-based budgeting within hospitals, see
Matthew M. Person, III, The Zero-Base Hospital (Health Administration Press,
1997).
4. Variances can be de¬ned so the resulting value is either a positive or negative
number. For example, when cost variances are calculated, they can be de¬ned
so that a negative variance means costs less than standard, which is good, or
costs greater than standard, which is bad, depending on which budget value is
subtracted from the other. In this example, all variances have been de¬ned so
that a negative number indicates an undesirable variance and not necessarily that
the realized value is less than the standard. For example, a higher-than-standard
wage rate would be a negative variance, indicating that the variance is harmful to
the clinic, even though realized wages were higher than that expected.
5. A credit line is an agreement between a borrower and a ¬nancial institution that
obligates the institution to furnish credit over a time period, typically a year,
up to the agreed-upon amount. The borrower may use some, all, or none of
the credit line. Usually, credit lines require borrowers to pay an upfront fee for
the credit guarantee, called a commitment fee, as well as interest charges on the
amount of credit actually used.



References
Berlin, M. F., and M. R. Budzyuski. 1998. “Budget Variance Analysis Using RVUs.”
Medical Group Management Journal (November“December): 50“52.
Cardamone, M. A., M. Shaver, and R. Worthman. 2004. “Business Planning: Reasons,
De¬nitions, and Elements.” Healthcare Financial Management (April): 40“
46.
Gapenski, L. C. 2003. Understanding Health Care Financial Management. Chicago:
Health Administration Press.
Ginter, P. M., L. M. Swayne, and W. Jack Duncan. 1998. Strategic Management of
Health Care Organizations. Malden, MA: Blackwell.
Herkimer, A. G., Jr. 1988. Understanding Health Care Budgeting. Rockville, MD:
Aspen.
HFMA. 2004. “How are Hospitals Financing the Future“Core Competencies in
Capital Planning.” Healthcare Financial Management (July): 44“49.
250 Healthcare Finance



Maitland, D. 1993. “Flexible Budgeting and Variance Analysis: Why Leave Staff
Nurses in the Dark?” Hospital Cost Accounting (December): 1“8.
Person, M. M., III. 1997. The Zero-Base Hospital. Chicago: Health Administration
Press.
Zuckerman, A. M. 1998. Healthcare Strategic Planning: Approaches for the 21st Cen-
tury. Chicago: Health Administration Press.
PAR T



IV
Basic Financial Management Concepts
This page intentionally left blank
CHAP TER



9
TIME VALUE ANALYSIS

Learning Objectives
After studying this chapter, readers will be able to:

• Explain why time value analysis is so important to healthcare
¬nancial management.
• Find the present and future values for lump sums, annuities, and
uneven cash ¬‚ow streams.
• Solve for interest rate and number of periods.
• Explain and apply the opportunity cost principle.
• Measure the ¬nancial return on an investment in both dollar and
percentage terms.
• Create an amortization table.
• Describe and apply stated, periodic, and effective annual interest
rates.


Introduction
The monetary value of any asset, whether a ¬nancial asset, such as a stock
or a bond, or a real asset, such as a piece of diagnostic equipment or an
ambulatory surgery center, is based on future cash ¬‚ows. However, a dollar to
be received in the future is worth less than a current dollar because a dollar in
hand today can be invested in an interest-bearing account and hence can be
worth more than one dollar in the future.1 Because current dollars are worth
more than future dollars, valuation analyses must account for cash ¬‚ow timing
differences.
The process of assigning proper values to cash ¬‚ows that occur at
different points in time is called time value analysis. It is an important part of
healthcare ¬nancial management because most ¬nancial analyses involve the
valuation of future cash ¬‚ows. In fact, of all the ¬nancial analysis techniques
that are discussed in this book, none is more important than time value
analysis. The concepts presented here are the cornerstones of many ¬nancial
analyses, so a thorough understanding of time value concepts is essential to
good ¬nancial decision making.



253
254 Healthcare Finance



Time Lines
The creation of a time line is the ¬rst step in time value analysis, especially
when ¬rst learning time value concepts. Time lines make it easier to visualize
when the cash ¬‚ows in a particular analysis occur. To illustrate the time line
concept, consider the following ¬ve-period time line:

0 1 2 3 4 5



Time 0 is any starting point; Time 1 is one period from the starting point, or
the end of Period 1; Time 2 is two periods from the starting point, or the end
of Period 2; and so on. Thus, the numbers on top of the tick marks represent
end-of-period values. Often, the periods are years, but other time intervals
such as quarters, months, or days are also used when needed to ¬t the timing
of the cash ¬‚ows being evaluated. If the time periods are years, the interval
from 0 to 1 would be Year 1, and the tick mark labeled 1 would represent
both the end of Year 1 and the beginning of Year 2.
Cash ¬‚ows are shown on a time line directly below the tick marks that
indicate the point in time that they are expected to occur. The interest rate
that is relevant to the analysis is sometimes shown directly above the time
line in the ¬rst period. Additionally, unknown cash ¬‚ows”the ones to be
determined in the analysis”are sometimes indicated by question marks. To
illustrate, consider the following time line:

0 1 2 3
5%

’$100 ?

In this case, the interest rate for each of the three periods is 5 percent, an
investment of $100 is made at Time 0, and the Time 3 value is the unknown.
The $100 is an out¬‚ow because it is shown as a negative cash ¬‚ow. (Out¬‚ows
are sometimes designated by parentheses rather than by minus signs.) In more
complicated analyses, it is essential to use the proper signs to get the correct
answer. Furthermore, many ¬nancial calculators require that signs be attached
to cash ¬‚ows in all analyses, even simple ones, before the calculation can be
completed. Thus, to ensure that readers are familiar with the sign convention
used in time value analyses, we will use them on most illustrations.
Time lines are essential when learning time value concepts, but even
experienced analysts use time lines when dealing with complex problems. The
time line may be an actual line, as illustrated above, or it may be a series of
columns (or rows) on a spreadsheet. Time lines will be used extensively in
the remainder of this book, so get into the habit of creating time lines when
conducting analyses that involve future cash ¬‚ows.
255
Chapter 9: Time Value Analysis




Self-Test
1. Draw a three-year time line that illustrates the following situation: An
Question
investment of $10,000 at Time 0; in¬‚ows of $5,000 at the end of Years
1, 2, and 3; and an interest rate of 10 percent during the entire three
years.


Future Value of a Lump Sum (Compounding)
The process of going from today™s values, or present values, to future values is
called compounding. Although compounding is not used extensively in health-
care ¬nance, it is the best starting point for learning time value analysis. To
illustrate lump sum compounding, which deals with a single starting amount,
suppose that the manager of Meridian Clinics deposits $100 in a bank account
that pays 5 percent interest each year. How much would be in the account
at the end of one year? To begin, here are some terms that are used in the
solution:

• PV = $100 = present value, or beginning amount, of the account.
• I = 5% = interest rate the bank pays on the account per year. The interest
amount, which is paid at the end of the year, is based on the balance at the
beginning of each year. Expressed as a decimal, I = 0.05.
• INT = dollars of interest earned during each year, which equals the
beginning amount multiplied by the interest rate. Thus, INT = PV — I.
• FVN = future value, or ending amount, of the account at the end of N
years. Whereas PV is the value now, or present value, FVN is the value N
years into the future after the interest earned has been added to the
account.
• N = number of years involved in the analysis.

In this example, N = 1, so FVN can be calculated as follows:

FVN = FV1 = PV + INT
= PV + (PV — I)
= PV — (1 + I).
The future value at the end of one year, FV1 , equals the present value multi-
plied by 1.0 plus the interest rate. This future value relationship can be used
to ¬nd how much $100 will be worth at the end of one year, if it is invested
in an account that pays 5 percent interest:

FV1 = PV — (1 + I) = $100 — (1 + 0.05) = $100 — 1.05 = $105.
What would be the value of the $100 if Meridian Clinics left the money
in the account for ¬ve years? Here is a time line that shows the amount at the
end of each year:
256 Healthcare Finance



0 1 2 3 4 5
5%
Beginning
amount ’$100
Interest earned $ 5 $ 5.25 $ 5.51 $ 5.79 $ 6.08
End of year amount 105 110.25 115.76 121.55 127.63.

Note the following points:

• The account is opened with a deposit of $100. This is shown as an out¬‚ow
at Year 0.
• Meridian earns $100 — 0.05 = $5 of interest during the ¬rst year, so the
amount in the account at the end of Year 1 is $100 + $5 = $105.
• At the start of the second year, the account balance is $105. Interest of
$105 — 0.05 = $5.25 is earned on the now larger amount, so the account
balance at the end of the second year is $105 + $5.25 = $110.25. The
Year 2 interest, $5.25, is higher than the ¬rst year™s interest, $5, because
$5 — 0.05 = $0.25 in interest was earned on the ¬rst year™s interest.
• This process continues, and because the beginning balance is higher in
each succeeding year, the interest earned increases in each year.
• The total interest earned, $27.63, is re¬‚ected in the ¬nal balance,
$127.63, at the end of Year 5.

To better understand the mathematics of compounding, note that the Year 2
value, $110.25, is equal to:

FV2 = FV1 — (1 + I)
= PV — (1 + I) — (1 + I)
= PV — (1 + I)2
= $100 — (1.05)2 = $110.25.
Furthermore, the balance at the end of Year 3 is:

FV3 = FV2 — (1 + I)
= PV — (1 + I)3
= $100 — (1.05)3 = $115.76,
Continuing the calculation to the end of Year 5 gives:

FV5 = $100 — (1.05)5 = $127.63.
These calculations show that a pattern clearly exists in future value
calculations. In general, the future value of a lump sum at the end of N years
can be found by applying this equation:

FVN = PV — (1 + I)N .
257
Chapter 9: Time Value Analysis



Future values, as well as most other time value problems, can be solved three
ways: regular calculator, ¬nancial calculator, or spreadsheet.

To use a regular calculator, multiply the PV by (1 + I) for N times or use the Regular
exponential function to raise (1 + I) to the Nth power and then multiply the Calculator
result by the PV. Perhaps the easiest way to ¬nd the future value of $100 after Solution
¬ve years when compounded at 5 percent is to enter $100, then multiply this
amount by 1.05 for ¬ve times. If the calculator is set to display two decimal
places, the answer would be $127.63:

0 1 2 3 4 5

$100 — 1.05 — 1.05 — 1.05 — 1.05 — 1.05= $127.63


As denoted by the arrows, compounding involves moving to the right along
the time line.

Financial calculators have been programmed to solve many types of time value Financial
problems. In effect, the future value equation is programmed directly into the Calculator
calculator. With a ¬nancial calculator, the future value is found using three of Solution
the following ¬ve time value input keys:2




Note that these keys correspond to the ¬ve time value variables that are
commonly used:

• N = number of periods.
• I = interest rate per period.
• PV = present value.
• PMT = payment. (This key is used only if the cash ¬‚ows involve an
annuity, which is a series of equal payments. Annuities are discussed in a
later section.)
• FV = future value.

Also, note that this chapter deals with time value problems that involve only
four of the variables at any one time. Three of the variables will be known, and
the calculator will solve for the fourth, unknown variable. In Chapter 11, when
bond valuation is discussed, all ¬ve variables will be included in the analysis.
To ¬nd the future value of $100 after ¬ve years at 5 percent interest
using a ¬nancial calculator, just enter PV = 100, I = 5, and N = 5, and
then press the FV key. The answer, 127.63 (rounded to two decimal places),
will appear. As stated previously, many ¬nancial calculators require that cash
258 Healthcare Finance



¬‚ows be designated as either in¬‚ows or out¬‚ows (entered as either positive or
negative values). Applying this logic to the illustration, Meridian deposits the
initial amount, which is an out¬‚ow to the ¬rm, and takes out, or receives, the
ending amount, which is an in¬‚ow to the ¬rm. If the calculator requires this
sign convention, the PV would be entered as ’100. (If the PV was entered
as 100, a positive value, the calculator would display ’127.63 as the answer.)
The calculator solution can be shown pictorially as follows:

’100
Inputs 5 5

<<

. 9
( 21)



>>