# FIN Week Lecture Notes Depreciation

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```					FIN 325 Week 3 Supplemental Lecture Notes

Capital Budgeting and Risk Assessment

One of the key questions to ask in the capital budgeting process is “what rate do I use to
discount my cash flows.” Many students ask this very question when confronted with the
lack of certainty inherent in solving TVM (time value of money) problems. The accepted
rate to be used for a project varies by firm. Many companies use their cost of funds (cost
of capital) as the starting point for project evaluations, adjusting this number up and
down based on their assessment of the risks involved in various project types.

Consider a small cap company like Thomas Industries, where I currently work. Our cost
of capital is 12%, mostly because our management is conservative and our debt load is
low. Equity costs more than debt, because investors demand higher returns for the higher
inherent risks involved. Firms with more equity than debt, all things being equal, will
have higher costs of capital.

This 12% rate can be adjusted up and down depending on the nature of the project at
hand. For example, we may consider investing in a new machine, which will save us
money by eliminating certain steps in the manufacturing process. Since our knowledge
of the process is certain and our estimates likely to be good, we can assign a lower
discount rate to this project then the average cost of funds.

For higher risk projects, we might add a few percentage points to make sure we have
some safety factor in the analysis. For example, if Thomas Industries decided to invest in
an Internet sales channel, the risk of failure would be high. This would require higher
returns to ensure that our investors are kept happy.

Risk is like this in finance. Risk is considered “variation in returns” not “risk of loss.” A
high-risk project may be one that gives a variation in returns between –30% and +90%,
vs. a lower risk project with a variation in returns of –20% to +20%. Both may loose
money, but since the first one has a wide variation in returns, it’s considered the more
risky proposition. Investors don’t like risk and really don’t like uncertainty. Therefore,
they are going to demand more money (returns) of higher risk projects.

Lets consider a typical project for a moment. Say we want to buy a Lathe, which is a
machine to cut steel into parts. Say the Lathe costs \$25,000.00 and the installation costs
are \$3,000.00. Further, say the Lathe will save us some \$7,500.00 per year and that the
corporate group considers this project low risk, so a 10% cost of capital can be used.

How do we decide if we should or should not buy the lathe?

There is a little information missing. Namely, how long is the lathe good for and what is
the salvage value at the end of its life? Lets say the lathe is good for 5 years and is worth
15,000 at the end of its life. We’ll use 5 year MARCS deprecation and a tax rate of 35%
for our analysis.
The first step in any capital budgeting process is to consider what the cash flows thrown
off by the project are likely to be. Before the project starts we have to outlay money
because the Lathe costs money to buy and install.

Year zero cash flows, then are: 25,000 + 3,000 or \$28,000.00 cash outflow.

First years cash flow is the \$7,500.00 in savings, plus the tax savings of year one
depreciation. To compute this, take the one-year MARCS factor from Table 12-9 on
page 353 of the book. This factor is 0.200, making the depreciation for year one 25,000 x
.2 or \$5,000.00. (Installation costs are excluded from the depreciable base in our
company; check with your company to see what you include and don’t include before
doing your analysis.) The tax shield then is 0.35 (the tax rate) x \$5000 (the depreciation
for that year) or \$1,750.00.

This means the total cash flow for year 1 of the project is \$7500 + \$1750 or \$9,250.00
cash inflow.

Years 2 through five are similarly computed, the results summarized in the table below.

Year              Savings            MARCS              Tax Savings       Total Savings
Depreciation
2                 \$7,500             0.32 x             0.35 x \$8,000 =   \$10,300
25000=\$8,000       \$2,800
3                 \$7,500             0.192 x            0.35 x \$4,800 =   \$9,180
25000=\$4,800       \$1,680
4                 \$7,500             0.115 x            0.35 x 2875 =     \$8,506
25000=\$2,875       \$1006
5                 \$7,500             0.115 x            0.35 x 2875=      \$8,506
25000=\$2,875       \$1006

In year five, we are going to sell the machine for \$15,000.00, so this will be a positive
cash flow. Since we are selling for \$15,000.00 and we have depreciated the machine a
total of \$23,550 (\$5,000+\$8,000+\$4,800+\$2,875+\$2,875), we will recapture \$15,000 of
this depreciation, so the tax shield will be decreased by \$15,000 x 0.35 or \$5,250 (we will
pay this in additional taxes because our depreciation was too much in the prior years). So
the net value of the salvage less tax effects is \$15,000 - \$5,250 or \$9,750.

So, to summarize our cash flows:

Year 0: (\$28,000)
Year 1: \$9,250
Year 2: \$10,300
Year 3: \$9,180
Year 4: \$8,506
Year 5: \$8,506+\$9,750 or \$18,256
Now, to determine whether the project is a “go” or “no go,” we need to discount these
cash flows and add them up to find the Net Present Value (NPV) of the project cash
flows. This is summarized in the next table:

Year              Cash Flow         PVIF(n,10%)        Discounted
Cash Flow
0                 (\$28,000)         1                  (\$28,000)
1                 \$9,250            0.9091             \$8,409
2                 \$10,300           0.8264             \$6,511
3                 \$9,180            0.7513             \$6,897
4                 \$8,506            0.6830             \$5,810
5                 \$18,256           0.6209             \$11,335
Total                                                  \$10,962

Since \$10,962 is greater than \$0, we would accept this project at 10% based on the

A few observations:

1. Project evaluation is sensitive to cash flow estimates; the more risky the cash flow
estimate, the more uncertainty (risk) in the analysis.

2. Often, the discount rate is arbitrary or unknown. Use logic and make
assumptions.

3. We have neglected the increase and decrease in net working capital that may be
the result of this project. Generally there is a year 0 cash flow to account for the
additional working capital (in process inventory, for example) that is required to
operate the project, and this same amount is released in the final year as “return of
net working capital.”

4. When valuing a new business using the above technique, it is often necessary to
include the increase in AR (Accounts Receivable) as an increase in net working
capital. You can get an estimate for this number by taking the firms Days Sales
Outstanding times the projected increase in sales that would result from the
project.

5. Another trick to use is to start with Net Income and add back Depreciation to get
the cash flow of a firm you are using this technique to value. This is not an exact
way to get a cash flow, but it is better than using net income as a substitute for
cash flows. As a first cut, adding depreciation to net income will do nicely.

DQ’s and Granny (yes, she’s back)
1. If inflation is actually 3% per year instead of the Government reported 2% per
year, what is the effect on the cost of a Latte from Starbucks in 50 years, given the
current cost of \$3.50 per cup?

2. A certain bond has a par value of \$1,000 and a coupon payment of 10% per year.
If the interest rate in the economy falls from 10% to 5%, what is the most an
investor should pay for the bond if its maturity is 10 years?

3. For the project described in the lecture, assume that the increase in net working
capital is \$10,000.00 and that this full amount is returned at the end of year five.
What is the NPV of the project factoring in the NWC requirements?

Granny Question

Sal is at it again, this time on behalf of his cousin Joe. Joe runs a small business, Joes
Bar and Grill. Joe gets almost all of his receipts (sales) from drinks, but wants to expand
into food services. Granny has the dough, but Sal needs to convince her that this project
is a go. After the will fiasco, Granny is suspicious of Sal’s motives, and wants to know
the NPV of the project given a 15% discount rate.

Joe figures that the investment required will be limited to the following:

Kitchen Remodel: \$100,000.00
Furniture: \$30,000.00

He further assumes that he can generate sales of \$600 per day in meals plus another \$150

Cost of sales for meals is 60% of sales, while cost of sales for drinks is 15% of sales.

Additional labor will be required at \$200 per day.

Given a tax rate of 15% and a project life of 5 years, prepare calculations for Sal to use to
convince Granny.

Show all work.

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 views: 6 posted: 12/31/2010 language: English pages: 4